MS Excel и VBA для моделирования различных задач. 9785913593153

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Ʉɢɥɶɞɢɲɨɜ ȼ.Ⱦ.

MS Excel ɢ VBA ɞɥɹ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɪɚɡɥɢɱɧɵɯ ɡɚɞɚɱ

Ɇɨɫɤɜɚ ɋɈɅɈɇ-ɉɪɟɫɫ 2019

ɍȾɄ 681.3.06 ȻȻɄ 32.973.26-018.2 Ʉ 39 Ʉɢɥɶɞɢɲɨɜ ȼ.Ⱦ. Ʉ39 MS Excel ɢ VBA ɞɥɹ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɪɚɡɥɢɱɧɵɯ ɡɚɞɚɱ.— Ɇ.: ɋɈɅɈɇɉɪɟɫɫ, 2019 — 256 ɫ.: ɢɥ. ISBN 978-5-91359-315-3 Ʉɧɢɝɚ ɹɜɥɹɟɬɫɹ ɩɪɚɤɬɢɱɟɫɤɢɦ ɪɭɤɨɜɨɞɫɬɜɨɦ ɩɨ ɦɨɞɟɥɢɪɨɜɚɧɢɸ ɡɚɞɚɱ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɩɪɢɥɨɠɟɧɢɹ MS Excel ɢ VBA. ɉɨɫɨɛɢɟ ɩɪɟɞɧɚɡɧɚɱɟɧɨ ɞɥɹ ɲɤɨɥɶɧɢɤɨɜ, ɫɬɭɞɟɧɬɨɜ ɢ ɩɪɟɩɨɞɚɜɚɬɟɥɟɣ, ɤɨɬɨɪɵɟ ɯɨɬɹɬ ɛɵɬɶ ɡɧɚɤɨɦɵ ɫ MS Excel ɢ VBA «ɧɚ ȼɵ» ɢ ɧɚɭɱɢɬɶɫɹ ɦɨɞɟɥɢɪɨɜɚɧɢɸ, ɪɚɡɪɚɛɨɬɤɟ ɦɨɞɟɥɟɣ, ɚɥɝɨɪɢɬɦɨɜ ɢ ɩɪɨɝɪɚɦɦ, ɚ ɬɚɤɠɟ ɩɪɢɥɨɠɟɧɢɣ ɫ ɮɨɪɦɚɦɢ. ɉɪɨɱɢɬɚɜ ɷɬɭ ɤɧɢɝɭ, ȼɵ ɧɚɭɱɢɬɟɫɶ ɢɫɩɨɥɶɡɨɜɚɬɶ ɜɨɡɦɨɠɧɨɫɬɢ MS Excel ɢ VBA, ɨ ɤɨɬɨɪɵɯ ɪɚɧɟɟ ɧɟ ɡɧɚɥɢ. ȻȻɄ 32.973.26-018.2 Ɉɬɜɟɬɫɬɜɟɧɧɵɣ ɡɚ ɜɵɩɭɫɤ: Ɇɢɬɢɧ ȼ.Ⱥ. Ʉɨɦɩɶɸɬɟɪɧɚɹ ɜɟɪɫɬɤɚ: Ʉɢɥɶɞɢɲɨɜ ȼ.Ⱦ. Ɉɛɥɨɠɤɚ: ɋɈɅɈɇ-ɉɪɟɫɫ Ɉɩɬɨɜɵɟ ɡɚɤɭɩɤɢ ɈɈɈ ɄɌɄ «Ƚɚɥɚɤɬɢɤɚ» 115487, ɝ. Ɇɨɫɤɜɚ, ɩɪɨɫɩɟɤɬ Ⱥɧɞɪɨɩɨɜɚ, ɞ. 38 Ɍɟɥɟɮɨɧɵ: (499) 782-38-89 E-mail: [email protected], http://www.alians-kniga.ru ɈɈɈ «ɋɈɅɈɇ-ɉɪɟɫɫ» 115487, ɝ. Ɇɨɫɤɜɚ, ɩɪ-ɤɬ Ⱥɧɞɪɨɩɨɜɚ, ɞɨɦ 38, ɩɨɦɟɳɟɧɢɟ ʋ 8, ɤɨɦɧɚɬɚ ʋ 2. Ɏɨɪɦɚɬ 70×100/16. Ɉɛɴɟɦ 16 ɩ. ɥ. Ɍɢɪɚɠ 50 ɷɤɡ.

ISBN 978-5-91359-315-3

© Ʉɢɥɶɞɢɲɨɜ ȼ.Ⱦ., 2019 © ɋɈɅɈɇ-ɉɪɟɫɫ,2019

ɋɨɞɟɪɠɚɧɢɟ ɉɪɟɞɢɫɥɨɜɢɟ ..................................................................................................... 5 1. Ɉ ɦɨɞɟɥɢɪɨɜɚɧɢɢ, ɪɟɲɟɧɢɢ ɡɚɞɚɱ, ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɢ ɢ MS Excel ......................................................................................................... 6 1.1. Ɉ ɪɟɲɟɧɢɢ ɡɚɞɚɱ ɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ .......................................................... 6 1.2. Ɉ ɩɪɟɢɦɭɳɟɫɬɜɚɯ MS Excel ɩɪɢ ɢɡɭɱɟɧɢɢ ɨɫɧɨɜ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ .......................................................................................... 10 1.3. Ɉɫɧɨɜɧɵɟ ɨɫɨɛɟɧɧɨɫɬɢ ɢɫɩɨɥɶɡɨɜɚɧɢɹ MS Excel ɩɪɢ ɪɟɲɟɧɢɢ ɡɚɞɚɱ ɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ ................................................................................... 14 1.4. VBA ɢ Excel .............................................................................................. 23 1.5. ɋɨɡɞɚɧɢɟ ɫɱɟɬɱɢɤɨɜ ɞɥɹ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɩɪɨɰɟɫɫɚ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ..... 38 2. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ MS Excel........................................ 52 2.1. Ɇɚɬɟɦɚɬɢɤɚ ............................................................................................. 52 2.1.1. ȼɪɚɳɟɧɢɟ ɝɪɚɮɢɤɨɜ............................................................................... 52 2.1.2. Ʉɨɦɩɥɟɤɫɧɨɟ ɧɚɯɨɠɞɟɧɢɟ ɤɨɪɧɟɣ ɭɪɚɜɧɟɧɢɣ ..................................... 55 2.1.3. Ɉɩɪɟɞɟɥɟɧɢɟ ɩɪɟɞɟɥɨɜ .......................................................................... 57 2.1.4. ȼɫɬɪɟɱɚ ɩɭɬɧɢɤɨɜ .................................................................................. 58 2.1.5. ɉɟɪɟɩɪɚɜɚ ɱɟɪɟɡ ɪɟɱɤɭ .......................................................................... 60 2.1.6. Ɍɭɪɢɫɬ..................................................................................................... 61 2.1.7. Ⱦɜɚ ɩɥɨɜɰɚ ............................................................................................. 63 2.1.8. Ʉɚɬɟɪ ɢ ɩɥɨɬ ........................................................................................... 64 2.1.9. ȼɟɥɨɫɢɩɟɞɢɫɬ ......................................................................................... 64 2.1.10. Ɇɨɞɟɥɢɪɨɜɚɧɢɹ ɤɚɫɚɬɟɥɶɧɨɣ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ ɮɭɧɤɰɢɢ ................ 65 2.1.11. ȿɞɢɧɢɱɧɚɹ ɨɤɪɭɠɧɨɫɬɶ ɢ ɫɢɧɭɫ ɭɝɥɚ ................................................ 68 2.1.12. ɉɨɫɬɪɨɟɧɢɟ ɩɪɨɫɬɟɣɲɢɯ ɨɛɴɟɦɧɵɯ ɮɢɝɭɪ........................................ 70 2.1.13. Ɋɟɲɟɧɢɟ ɝɪɚɮɨɚɧɚɥɢɬɢɱɟɫɤɢɦ ɦɟɬɨɞɨɦ ɡɚɞɚɱ ɥɢɧɟɣɧɨɝɨ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ .......................................................................................... 73 2.1.14. ȼɵɱɢɫɥɟɧɢɟ ɱɢɫɥɚ ɩɢ ɦɟɬɨɞɨɦ Ⱥɪɯɢɦɟɞɚ ........................................ 77 2.1.15. ȼɵɱɢɫɥɟɧɢɟ ɱɢɫɥɚ ɩɢ ɦɟɬɨɞɨɦ Ɇɨɧɬɟ-Ʉɚɪɥɨ .................................. 80 2.1.16. ɉɨɫɬɪɨɟɧɢɟ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɰɢɮɪ ɱɢɫɥɚ ɩɢ ....................................... 86 2.2. Ɏɢɡɢɤɚ ...................................................................................................... 91 2.2.1. Ȼɪɨɭɧɨɜɫɤɨɟ ɞɜɢɠɟɧɢɟ ɱɚɫɬɢɰ ............................................................. 91 2.2.2. Ɍɪɚɟɤɬɨɪɢɹ ɩɨɥɟɬɚ ɛɪɨɲɟɧɧɨɝɨ ɬɟɥɚ ................................................... 93 2.2.3. Ɉɰɟɧɤɚ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɛɪɨɫɚɧɢɣ ɬɟɥɚ ɩɨ ɦɢɲɟɧɢ ............................ 96 2.2.4. Ⱦɜɢɠɟɧɢɟ ɬɟɥɚ ɩɨ ɧɚɤɥɨɧɧɨɣ ɝɨɪɤɟ ..................................................... 97 2.2.5. Ɇɚɹɬɧɢɤ................................................................................................ 101 2.2.6. Ⱦɜɢɠɟɧɢɟ ɛɪɭɫɤɚ ɩɪɢ ɩɨɩɚɞɚɧɢɢ ɩɭɥɢ ............................................. 104 2.2.7. ɋɨɨɛɳɚɸɳɢɟɫɹ ɫɨɫɭɞɵ ...................................................................... 109 2.2.8. ɉɨɞɴɟɦ ɚɷɪɨɫɬɚɬɚ ................................................................................ 112 2.2.9. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɮɢɝɭɪ Ʌɢɫɫɚɠɭ ........................................................ 115 3

2.2.10. Ɋɨɛɨɬ ɮɭɬɛɨɥɢɫɬ ɫ ɦɹɱɨɦ ................................................................. 118 2.2.11. Ɏɢɡɢɱɟɫɤɚɹ ɡɚɪɹɞɤɚ ɞɥɹ ɪɨɛɨɬɚ........................................................ 122 2.2.12. ɉɟɪɟɯɨɞ ɄȺ ɫ ɨɞɧɨɣ ɤɪɭɝɨɜɨɣ ɨɪɛɢɬɵ ɧɚ ɞɪɭɝɭɸ ....................... 128 2.2.13. Ɍɪɟɯɦɟɪɧɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɩɨɥɟɬɚ ɄȺ .......................................... 133 2.2.14. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɬɪɚɟɤɬɨɪɢɢ ɩɨɥɟɬɚ ɷɥɟɤɬɪɨɧɚ ɦɟɠɞɭ ɡɚɪɹɠɟɧɧɵɦɢ ɩɥɚɫɬɢɧɚɦɢ ............................................................................ 138 2.2.15. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɬɪɚɟɤɬɨɪɢɢ ɩɨɥɟɬɚ ɷɥɟɤɬɪɨɧɚ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ................................................................................................................. 145 2.2.16. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɬɪɚɟɤɬɨɪɢɢ ɡɚɪɹɠɟɧɧɵɯ ɲɚɪɢɤɨɜ ........................ 149 2.2.17. Ɂɚɛɟɣ ɝɨɥ ɫ 11 ɦɟɬɪɨɜ ........................................................................ 155 2.2.18. ɂɧɬɟɪɮɟɪɟɧɰɢɹ ɞɜɭɯ ɜɨɥɧ ................................................................ 166 2.2.19. Ȼɨɦɛɨɦɟɬɚɧɢɟ ɩɨ ɧɚɡɟɦɧɨɣ ɰɟɥɢ ɫ ɫɚɦɨɥɟɬɚ .................................. 175 2.2.20. ɉɟɪɟɯɜɚɬ ɛɚɥɥɢɫɬɢɱɟɫɤɨɣ ɪɚɤɟɬɵ .................................................... 186 2.3. Ɉɩɬɢɦɢɡɚɰɢɨɧɧɵɟ ɦɨɞɟɥɢ ................................................................. 196 2.3.1. Ʉɪɚɬɱɚɣɲɢɣ ɩɭɬɶ ɦɟɠɞɭ ɩɭɧɤɬɨɦ ɨɬɩɪɚɜɥɟɧɢɹ ɢ ɧɚɡɧɚɱɟɧɢɹ ........ 196 2.3.2. Ɂɚɞɚɱɚ ɤɨɦɦɢɜɨɹɠɟɪɚ ......................................................................... 204 2.3.3. ɉɟɪɟɱɟɧɶ ɩɨɤɭɩɚɟɦɨɣ ɩɪɨɞɭɤɰɢɢ ɩɪɢ ɭɫɥɨɜɢɢ ɦɢɧɢɦɢɡɚɰɢɢ ɫɭɦɦɵ ɨɩɥɚɬɵ ................................................................................................ 208 2.4. Ɂɚɳɢɬɚ ɢɧɮɨɪɦɚɰɢɢ ............................................................................ 213 2.4.1. Ɂɚɲɢɮɪɨɜɚɧɧɨɟ ɩɢɫɶɦɨ ...................................................................... 213 2.4.2. ɋɬɟɝɚɧɨɝɪɚɮɢɱɟɫɤɨɟ ɩɢɫɶɦɨ ɫ ɬɚɛɭɥɢɪɨɜɚɧɧɨɣ ɮɭɧɤɰɢɟɣ ............. 214 2.4.3. ɋɬɟɝɚɧɨɝɪɚɮɢɱɟɫɤɨɟ ɩɢɫɶɦɨ ɫ ɰɜɟɬɨɜɨɣ ɡɚɥɢɜɤɨɣ ɹɱɟɟɤ................. 216 2.4.4. ɗɥɟɤɬɪɨɧɧɚɹ ɩɨɞɩɢɫɶ .......................................................................... 218 2.5. Ⱦɪɭɝɢɟ ɦɨɞɟɥɢ ....................................................................................... 222 2.5.1. ɉɪɨɫɬɟɣɲɢɣ ɛɥɨɤɧɨɬ .......................................................................... 222 2.5.2. Ʉɭɪɢɰɚ, ɤɨɬɨɪɚɹ ɩɶɟɬ ɜɨɞɭ.................................................................. 226 2.5.3. ɉɨɫɬɪɨɟɧɢɹ ɦɚɪɲɪɭɬɚ ɞɜɢɠɟɧɢɹ ɧɚ ɤɚɪɬɟ ........................................ 231 2.5.4. ɑɚɫɵ ...................................................................................................... 234 2.5.5. Ⱥɥɮɚɜɢɬɧɵɣ ɯɨɪɨɜɨɞ .......................................................................... 237 2.5.6. ɍɝɚɞɚɣ ɦɵɲɢɧɭɸ ɧɨɪɤɭ ..................................................................... 240 2.5.7. ɉɨɣɦɚɣ ɦɭɯɭ ....................................................................................... 246 Ʌɢɬɟɪɚɬɭɪɚ ................................................................................................... 256

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ɉɪɟɞɢɫɥɨɜɢɟ ȼ ɤɧɢɝɟ ɪɚɫɤɪɵɬɵ ɜɨɡɦɨɠɧɨɫɬɢ MS Excel, ɫ ɤɨɬɨɪɵɟ ɨɛɵɱɧɨ ɧɟ ɪɚɫɫɦɚɬɪɢɜɚɸɬɫɹ ɩɪɢ ɬɪɚɞɢɰɢɨɧɧɨɦ ɢɡɭɱɟɧɢɢ ɩɪɢɥɨɠɟɧɢɹ. ɗɬɢ ɜɨɡɦɨɠɧɨɫɬɢ ɩɨɡɜɨɥɹɸɬ ɫɨɡɞɚɜɚɬɶ ɞɢɧɚɦɢɱɟɫɤɢɟ ɦɨɞɟɥɢ ɢ ɢɥɥɸɫɬɪɢɪɨɜɚɬɶ ɪɟɲɟɧɢɟ ɡɚɞɚɱ. Ⱦɥɹ ɧɚɝɥɹɞɧɨɝɨ ɢɡɨɛɪɚɠɟɧɢɹ ɩɪɨɰɟɫɫɚ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɡɚɞɚɱ ɪɚɫɫɦɨɬɪɟɧɵ ɩɪɚɤɬɢɱɟɫɤɢ ɜɫɟ ɜɨɡɦɨɠɧɵɟ ɫɩɨɫɨɛɵ ɪɚɛɨɬɵ ɫ ɞɢɚɝɪɚɦɦɚɦɢ ɢ ɢɯ ɷɥɟɦɟɧɬɚɦɢ. ȼ ɤɧɢɝɟ ɩɪɟɞɫɬɚɜɥɟɧɚ ɩɨɞɛɨɪɤɚ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ɢ ɦɨɞɟɥɟɣ ɢɡ ɪɚɡɥɢɱɧɵɯ ɪɚɡɞɟɥɨɜ ɟɫɬɟɫɬɜɟɧɧɵɯ ɞɢɫɰɢɩɥɢɧ. ɇɚɞɟɟɦɫɹ, ɱɬɨ ɷɬɨ ɩɨɦɨɠɟɬ ɛɨɥɟɟ ɝɥɭɛɨɤɨ ɢɡɭɱɢɬɶ ɜɨɡɦɨɠɧɨɫɬɢ MS Excel ɢ VBA, ɩɪɢɨɛɪɟɫɬɢ ɧɚɜɵɤɢ ɦɨɞɟɥɢɪɨɜɚɧɢɹ, ɚ ɬɚɤɠɟ ɨɬɨɣɬɢ ɨɬ ɤɥɚɫɫɢɱɟɫɤɨɝɨ ɩɨɫɬɪɨɟɧɢɹ ɝɪɚɮɢɤɨɜ, ɪɚɫɱɟɬɨɜ ɜ ɬɚɛɥɢɰɚɯ, ɮɨɪɦɚɬɢɪɨɜɚɧɢɹ ɪɟɡɭɥɶɬɚɬɨɜ ɜɵɱɢɫɥɟɧɢɣ. Ɋɚɡɪɚɛɨɬɤɚ ɦɨɞɟɥɟɣ ɡɧɚɱɢɬɟɥɶɧɨ ɪɚɫɲɢɪɹɟɬ ɩɟɪɟɱɟɧɶ ɩɪɢɦɟɧɹɟɦɵɯ ɮɭɧɤɰɢɣ, ɤɨɬɨɪɵɟ ɨɛɵɱɧɨ ɨɝɪɚɧɢɱɢɜɚɸɬɫɹ ɨɫɧɨɜɧɵɦɢ ɦɚɬɟɦɚɬɢɱɟɫɤɢɦɢ, ɥɨɝɢɱɟɫɤɢɦɢ ɢ ɫɬɚɬɢɫɬɢɱɟɫɤɢɦɢ ɮɭɧɤɰɢɹɦɢ. ɋɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɮɢɡɢɤɚ ɮɨɪɦɭɥ, ɩɪɢɦɟɧɹɟɦɵɯ ɜ ɦɨɞɟɥɹɯ, ɧɟ ɪɚɫɤɪɵɜɚɟɬɫɹ, ɚ ɞɚɸɬɫɹ ɨɩɪɟɞɟɥɟɧɧɵɟ ɩɨɹɫɧɟɧɢɹ. ɇɚɞɟɟɦɫɹ, ɱɬɨ ɩɨɥɶɡɨɜɚɬɟɥɢ ɜɥɚɞɟɸɬ ɧɭɠɧɵɦɢ ɡɧɚɧɢɹɦɢ ɢ ɫɦɨɝɭɬ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨ ɩɨɡɧɚɬɶ ɧɟɨɛɯɨɞɢɦɨɟ ɱɟɪɟɡ ɢɧɬɟɪɧɟɬ ɞɥɹ ɭɹɫɧɟɧɢɹ ɫɭɳɧɨɫɬɢ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ɢ ɦɨɞɟɥɟɣ. ɉɪɢ ɫɨɡɞɚɧɢɢ ɦɨɞɟɥɟɣ ɨɛɭɱɚɟɦɵɟ ɨɜɥɚɞɟɜɚɸɬ ɧɚɜɵɤɚɦɢ ɪɚɡɪɚɛɨɬɤɢ ɚɥɝɨɪɢɬɦɨɜ ɢ ɨɫɧɨɜɚɦɢ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ. Ⱦɥɹ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɩɪɨɰɟɫɫɚ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɢ ɢɡ-ɡɚ ɢɦɟɸɳɢɯɫɹ ɨɝɪɚɧɢɱɟɧɢɣ ɩɪɢ ɩɪɢɦɟɧɟɧɢɢ ɜɫɬɪɨɟɧɧɵɯ ɮɭɧɤɰɢɣ ɜ ɩɪɢɦɟɪɚɯ ɢɫɩɨɥɶɡɭɸɬɫɹ ɩɨɥɶɡɨɜɚɬɟɥɶɫɤɢɟ ɮɭɧɤɰɢɢ, ɭɩɪɚɜɥɹɸɳɢɟ ɷɥɟɦɟɧɬɵ, ɮɨɪɦɵ, ɨɛɴɟɤɬɵ ɞɢɚɝɪɚɦɦɵ, ɩɪɨɰɟɞɭɪɵ ɢ ɦɟɬɨɞɵ VBA. ȼɧɚɱɚɥɟ ɤɧɢɝɢ ɩɪɢɜɟɞɟɧɵ ɫɩɪɚɜɨɱɧɵɟ ɞɚɧɧɵɟ ɩɨ ɨɫɧɨɜɧɵɦ ɩɨɥɨɠɟɧɢɹɦ MS Excel ɢ VBA ɫ ɩɪɢɦɟɪɚɦɢ. ȼɫɟ ɷɬɨ ɩɨɡɜɨɥɢɬ ɪɚɡɨɛɪɚɬɶɫɹ ɫ ɩɪɟɞɫɬɚɜɥɟɧɧɵɦɢ ɦɨɞɟɥɹɦɢ ɡɚɞɚɱ ɢ ɜ ɞɚɥɶɧɟɣɲɟɦ ɥɟɝɤɨ ɨɫɜɨɢɬɶ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɟ ɧɚ ɪɚɡɥɢɱɧɵɯ ɹɡɵɤɚɯ ɢɥɢ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨ ɪɚɡɪɚɛɚɬɵɜɚɬɶ ɩɪɢɥɨɠɟɧɢɹ. ȼ ɷɬɨɦ ɢ ɡɚɤɥɸɱɚɟɬɫɹ ɰɟɥɶ ɤɧɢɝɢ.

5

1. Ɉ ɦɨɞɟɥɢɪɨɜɚɧɢɢ, ɪɟɲɟɧɢɢ ɡɚɞɚɱ, ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɢ ɢ MS Excel 1.1. Ɉ ɪɟɲɟɧɢɢ ɡɚɞɚɱ ɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ ȼ ɠɢɡɧɢ ɜɫɟ ɩɨɫɬɨɹɧɧɨ ɪɟɲɚɸɬ ɡɚɞɚɱɢ ɢ ɦɨɞɟɥɢɪɭɸɬ. Ɋɟɲɟɧɢɟ ɡɚɞɚɱ ɫɜɹɡɚɧɨ ɫ ɤɨɧɤɪɟɬɧɵɦɢ ɢɫɯɨɞɧɵɦɢ ɞɚɧɧɵɦɢ ɢ ɭɫɥɨɜɢɹɦɢ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɩɨɥɭɱɚɟɦ ɤɨɧɤɪɟɬɧɵɟ ɞɚɧɧɵɟ. ɉɪɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ ɢɫɯɨɞɧɵɟ ɞɚɧɧɵɟ ɢ ɭɫɥɨɜɢɹ ɨɛɵɱɧɨ ɢɡɦɟɧɹɸɬɫɹ ɜ ɨɩɪɟɞɟɥɟɧɧɵɯ ɞɢɚɩɚɡɨɧɚɯ, ɚ ɜ ɪɟɡɭɥɶɬɚɬɟ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɩɨɥɭɱɚɟɦ ɞɚɧɧɵɟ, ɤɨɬɨɪɵɟ ɪɚɫɩɨɥɚɝɚɸɬɫɹ ɜ ɨɩɪɟɞɟɥɟɧɧɵɯ ɞɢɚɩɚɡɨɧɚɯ, ɡɚɜɢɫɹɳɢɯ ɨɬ ɪɚɡɥɢɱɧɵɯ ɧɚɱɚɥɶɧɵɯ ɭɫɥɨɜɢɣ. ɉɨɫɥɟ ɩɪɨɜɟɞɟɧɢɹ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɨɛɵɱɧɨ ɩɪɨɜɨɞɹɬ ɚɧɚɥɢɡ ɢ ɩɪɢɧɢɦɚɸɬ ɤɨɧɤɪɟɬɧɨɟ ɪɟɲɟɧɢɟ, ɨɫɧɨɜɚɧɧɨɟ ɧɚ ɢɡɭɱɟɧɢɢ ɩɨɥɭɱɟɧɧɵɯ ɞɚɧɧɵɯ ɢ ɨɰɟɧɤɢ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɪɚɡɥɢɱɧɵɯ ɜɚɪɢɚɧɬɨɜ ɦɨɞɟɥɢ. ȼɫɩɨɦɧɢɦ ɨ ɤɥɚɫɫɢɱɟɫɤɢɯ ɩɨɞɯɨɞɚɯ ɜ ɪɚɡɴɹɫɧɟɧɢɹɯ ɩɨɧɹɬɢɣ ɨ ɪɟɲɟɧɢɢ ɡɚɞɚɱ ɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ. Ɋɟɲɟɧɢɟ ɡɚɞɚɱɢ - ɜɵɩɨɥɧɟɧɢɟ ɞɟɣɫɬɜɢɣ ɢɥɢ ɦɵɫɥɢɬɟɥɶɧɵɯ ɨɩɟɪɚɰɢɣ, ɧɚɩɪɚɜɥɟɧɧɵɯ ɧɚ ɞɨɫɬɢɠɟɧɢɟ ɰɟɥɢ ɩɪɢ ɡɚɞɚɧɧɨɣ ɩɪɨɛɥɟɦɧɨɣ ɫɢɬɭɚɰɢɢ. Ⱦɚɧɧɨɟ ɩɨɧɹɬɢɟ ɢɦɟɟɬ ɨɱɟɧɶ ɲɢɪɨɤɢɣ ɫɦɵɫɥ. ɇɚɦ ɠɟɥɚɬɟɥɶɧɨ ɟɝɨ ɫɭɡɢɬɶ ɢ ɤɨɧɤɪɟɬɢɡɢɪɨɜɚɬɶ. ɋɭɳɟɫɬɜɭɸɬ ɪɚɡɥɢɱɧɵɟ ɦɟɬɨɞɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ, ɜ ɤɨɬɨɪɵɟ ɜɤɥɸɱɟɧ ɢ ɦɟɬɨɞ ɦɨɞɟɥɢɪɨɜɚɧɢɹ. Ʉɪɭɝ ɤɚɠɟɬɫɹ, ɡɚɦɤɧɭɥɫɹ. ɑɬɨɛɵ ɜɫɟ-ɬɚɤɢ ɟɝɨ ɪɚɡɨɪɜɚɬɶ ɨɫɬɚɧɨɜɢɦɫɹ ɧɚ ɪɟɲɟɧɢɢ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɡɚɞɚɱɚɯ, ɦɚɬɟɦɚɬɢɱɟɫɤɨɦ ɢ ɤɨɦɩɶɸɬɟɪɧɨɦ ɦɨɞɟɥɢɪɨɜɚɧɢɢ. Ɉɛɳɢɦ ɞɥɹ ɧɢɯ ɹɜɥɹɟɬɫɹ ɬɨ, ɱɬɨ ɨɧɢ ɨɫɧɨɜɵɜɚɸɬɫɹ ɧɚ ɩɪɢɦɟɧɟɧɢɢ ɨɩɪɟɞɟɥɟɧɧɨɝɨ ɹɡɵɤɚ, ɫɢɦɜɨɥɨɜ, ɨɛɴɟɤɬɨɜ ɢ ɦɟɬɨɞɨɜ ɦɚɬɟɦɚɬɢɤɢ. Ɍɟɩɟɪɶ ɫɞɟɥɚɟɦ ɟɳɟ ɨɞɢɧ ɲɚɝ ɞɥɹ ɤɨɧɤɪɟɬɢɡɚɰɢɢ. Ɉɫɬɚɧɨɜɢɦɫɹ ɧɚ ɪɚɫɫɦɨɬɪɟɧɢɢ ɡɚɞɚɱ ɢ ɦɨɞɟɥɟɣ, ɤɨɬɨɪɵɟ ɨɛɵɱɧɨ ɢɡɭɱɚɸɬɫɹ ɜ ɭɱɟɛɧɵɯ ɡɚɜɟɞɟɧɢɹɯ ɧɚ ɭɪɨɤɚɯ ɩɨ ɟɫɬɟɫɬɜɟɧɧɵɦ ɞɢɫɰɢɩɥɢɧɚɦ (ɦɚɬɟɦɚɬɢɤɢ, ɮɢɡɢɤɢ, ɢɧɮɨɪɦɚɬɢɤɢ ɢ ɬ.ɩ.). ȿɫɬɶ ɡɚɞɚɱɚ ɨ ɜɵɯɨɞɟ ɩɭɬɧɢɤɚ ɢɡ ɩɭɧɤɬɚ Ⱥ. ɇɟɨɛɯɨɞɢɦɨ ɜɵɱɢɫɥɢɬɶ ɜɪɟɦɹ, ɤɨɝɞɚ ɩɭɬɧɢɤ ɩɪɢɛɭɞɟɬ ɜ ɩɭɧɤɬ ȼ ɩɪɢ ɡɚɞɚɧɧɵɯ ɭɫɥɨɜɢɹɯ. ɗɬɨ ɟɫɬɶ ɤɥɚɫɫɢɱɟɫɤɢɣ ɩɪɢɦɟɪ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɡɚɞɚɱɢ, ɤɨɝɞɚ ɜ ɪɟɡɭɥɶɬɚɬɟ ɪɟɲɟɧɢɹ ɩɨɥɭɱɚɟɦ ɜɪɟɦɹ ɩɪɢɛɵɬɢɹ ɩɭɬɧɢɤɚ ɜ ɩɭɧɤɬ ȼ. ɇɨ ɟɫɥɢ ɬɪɟɛɭɟɬɫɹ ɩɨɫɬɪɨɢɬɶ 6

1.1. Ɉ ɪɟɲɟɧɢɢ ɡɚɞɚɱ ɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ

ɝɪɚɮɢɤ ɞɜɢɠɟɧɢɹ ɩɭɬɧɢɤɚ, ɬɨ ɭɦɟɫɬɧɨ ɝɨɜɨɪɢɬɶ ɨ ɦɨɞɟɥɢ ɩɟɪɟɦɟɳɟɧɢɹ ɩɭɬɧɢɤɚ ɢɡ ɩɭɧɤɬɚ Ⱥ ɜ ȼ. Ɂɞɟɫɶ ɧɭɠɧɨ ɭɱɟɫɬɶ ɜɨɡɦɨɠɧɭɸ ɫɤɨɪɨɫɬɶ ɩɟɪɟɞɜɢɠɟɧɢɹ ɩɭɬɧɢɤɚ ɤɚɤ ɫɜɨɣɫɬɜɨ ɨɛɴɟɤɬɚ. Ɍɨ ɟɫɬɶ ɢɦɟɟɦ ɷɥɟɦɟɧɬɚɪɧɭɸ ɦɨɞɟɥɶ ɩɟɪɟɦɟɳɟɧɢɹ ɩɭɬɧɢɤɚ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ. ȿɫɥɢ ɡɧɚɧɢɣ ɨ ɫɤɨɪɨɫɬɢ ɧɟɞɨɫɬɚɬɨɱɧɨ, ɬɨ ɦɨɠɧɨ ɜɜɟɫɬɢ ɜ ɦɨɞɟɥɶ ɞɨɩɨɥɧɢɬɟɥɶɧɵɟ ɞɚɧɧɵɟ ɨ ɤɚɱɟɫɬɜɟ ɞɨɪɨɝɢ, ɨɫɬɚɧɨɜɤɚɯ ɧɚ ɨɬɞɵɯ, ɫɪɟɞɫɬɜɚɯ ɢ ɫɩɨɫɨɛɚɯ ɩɟɪɟɞɜɢɠɟɧɢɹ, ɡɚɩɚɫɚɯ ɬɨɩɥɢɜɚ ɢ ɬ.ɩ. ɗɬɨ ɩɨɡɜɨɥɢɬ ɭɫɥɨɠɧɢɬɶ ɦɨɞɟɥɶ ɢ ɩɪɢ ɷɬɨɦ ɭɬɨɱɧɢɬɶ ɬɨɱɧɨɫɬɶ ɩɪɢɧɹɬɢɹ ɪɟɲɟɧɢɹ ɩɪɢ ɚɧɚɥɢɡɟ ɩɨɥɭɱɟɧɧɵɯ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɞɚɧɧɵɯ. ɇɨ ɧɟ ɜɫɟɝɞɚ ɜ ɦɨɞɟɥɢ ɦɨɠɧɨ ɭɱɟɫɬɶ ɜɫɟ ɞɚɧɧɵɟ. Ɉɞɧɢ ɞɚɧɧɵɟ ɧɟɢɡɜɟɫɬɧɵ, ɞɪɭɝɢɟ ɧɟ ɧɭɠɧɵ, ɬɪɟɬɶɢ – ɧɟɥɶɡɹ ɭɱɟɫɬɶ ɜ ɦɨɞɟɥɢ ɢɡ-ɡɚ ɪɚɡɥɢɱɧɵɯ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɢɥɢ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɬɪɭɞɧɨɫɬɟɣ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɪɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ ɭɱɢɬɵɜɚɸɬɫɹ ɫɭɳɟɫɬɜɟɧɧɵɟ ɫɜɨɣɫɬɜɚ ɢ ɩɚɪɚɦɟɬɪɵ ɨɛɴɟɤɬɨɜ (ɹɜɥɟɧɢɣ ɩɪɢɪɨɞɵ, ɫɨɛɵɬɢɢ ɢ ɬ.ɩ.). ȼɵɛɨɪ ɫɜɨɣɫɬɜ ɨɛɴɟɤɬɨɜ ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɨɫɬɚɜɥɟɧɧɵɦɢ ɰɟɥɹɦɢ ɢɫɫɥɟɞɨɜɚɧɢɹ ɢɥɢ ɜɨɡɦɨɠɧɨɫɬɹɦɢ ɢɯ ɭɱɟɬɚ ɜ ɦɨɞɟɥɢ. ɋɜɨɣɫɬɜɚ ɦɨɝɭɬ ɛɵɬɶ ɜɧɟɲɧɢɦɢ ɢ ɜɧɭɬɪɟɧɧɢɦɢ ɩɨ ɨɬɧɨɲɟɧɢɸ ɨɛɴɟɤɬɚ. ȼɧɟɲɧɢɟ ɫɜɨɣɫɬɜɚ ɫɜɹɡɚɧɵ ɫ ɨɤɪɭɠɚɸɳɟɣ ɫɪɟɞɨɣ, ɚ ɜɧɭɬɪɟɧɧɢɟ – ɫ ɫɭɳɧɨɫɬɶɸ ɨɛɴɟɤɬɚ. ɉɪɢ ɷɬɨɦ ɜɫɟ ɫɜɨɣɫɬɜɚ ɦɨɝɭɬ ɢɡɦɟɧɹɬɶɫɹ ɩɪɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ. Ɍɚɤɠɟ ɫɜɨɣɫɬɜɚ ɞɟɥɹɬɫɹ ɧɚ ɜɯɨɞɧɵɟ ɢ ɜɵɯɨɞɧɵɟ. Ɉɛɵɱɧɨ ɜɵɯɨɞɧɵɟ ɫɜɨɣɫɬɜɚ ɡɚɜɢɫɹɬ ɨɬ ɜɯɨɞɧɵɯ. ɉɪɢ ɷɬɨɦ ɜɯɨɞɧɵɟ ɫɜɨɣɫɬɜɚ ɡɚɞɚɸɬɫɹ ɜ ɯɨɞɟ ɦɨɞɟɥɢɪɨɜɚɧɢɹ, ɚ ɜɵɯɨɞɧɵɟ ɩɨɥɭɱɚɟɦ ɜ ɪɟɡɭɥɶɬɚɬɟ ɜɨɡɞɟɣɫɬɜɢɹ ɜɯɨɞɧɵɯ ɫɜɨɣɫɬɜ ɧɚ ɨɛɴɟɤɬ. Ⱦɥɹ ɛɨɥɟɟ ɩɨɥɧɨɝɨ ɢɡɭɱɟɧɢɹ ɨɛɴɟɤɬɚ ɜɯɨɞɧɵɟ ɫɜɨɣɫɬɜɚ ɡɚɞɚɸɬɫɹ ɜ ɜɢɞɟ ɞɢɚɩɚɡɨɧɚ ɞɚɧɧɵɯ. ɏɨɬɹ ɨɧɢ ɦɨɝɭɬ ɡɚɞɚɜɚɬɶɫɹ ɤɚɤ ɤɨɧɫɬɚɧɬɵ ɢɥɢ ɢɡɦɟɧɹɟɦɵɟ ɩɚɪɚɦɟɬɪɵ ɨɬ ɞɪɭɝɢɯ ɜɯɨɞɧɵɯ ɫɜɨɣɫɬɜ. ɋɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɩɪɟɠɞɟ ɱɟɦ ɧɚɱɚɬɶ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɨɛɴɟɤɬɚ ɪɟɲɚɸɬɫɹ ɡɚɞɚɱɢ ɩɪɢ ɤɨɧɤɪɟɬɧɵɯ ɡɧɚɱɟɧɢɣ ɫɜɨɣɫɬɜ (ɞɚɧɧɵɯ) ɞɥɹ ɨɬɥɚɞɤɢ ɢɥɢ ɩɪɨɜɟɪɤɢ ɩɪɚɜɢɥɶɧɨɫɬɢ ɦɨɞɟɥɢ. ɇɟ ɫɭɳɟɫɬɜɭɸɬ ɦɨɞɟɥɢ ɛɟɡ ɷɬɚɩɚ ɪɟɲɟɧɢɹ ɡɚɞɚɱ. Ʉɨɧɬɪɨɥɶɧɵɟ ɩɪɨɫɱɟɬɵ ɧɭɠɧɵ ɧɟ ɬɨɥɶɤɨ ɧɚ ɷɬɚɩɟ ɫɨɡɞɚɧɢɹ, ɨɬɥɚɞɤɢ ɦɨɞɟɥɢ, ɧɨ ɢ ɞɥɹ ɩɪɨɜɟɪɤɢ ɞɨɫɬɨɜɟɪɧɨɫɬɢ ɩɨɥɭɱɟɧɧɵɯ ɞɚɧɧɵɯ ɩɪɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ ɪɚɡɥɢɱɧɵɯ ɫɢɬɭɚɰɢɣ. Ʉɥɚɫɫɢɮɢɤɚɰɢɹ ɦɨɞɟɥɟɣ ɪɚɡɧɨɨɛɪɚɡɧɚ, ɧɨ ɧɚɫ ɢɧɬɟɪɟɫɭɸɬ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɢ ɤɨɦɩɶɸɬɟɪɧɵɟ ɦɨɞɟɥɢ. Ʉɨɦɩɶɸɬɟɪɧɭɸ ɦɨɞɟɥɶ ɧɟɥɶɡɹ ɫɨɡɞɚɬɶ ɛɟɡ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɦɨɞɟɥɢ. Ɇɚɬɟɦɚɬɢɱɟɫɤɚɹ ɦɨɞɟɥɶ - ɷɬɨ ɩɪɢɛɥɢɠɺɧɧɨɟ ɨɩɢɫɚɧɢɟ ɤɚɤɨɝɨ-ɥɢɛɨ ɤɥɚɫɫɚ ɹɜɥɟɧɢɣ ɜɧɟɲɧɟɝɨ ɦɢɪɚ, ɜɵɪɚɠɟɧɧɨɟ ɫ ɩɨɦɨɳɶɸ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɫɢɦ7

1. Ɉ ɦɨɞɟɥɢɪɨɜɚɧɢɢ, ɪɟɲɟɧɢɢ ɡɚɞɚɱ, ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɢ ɢ MS Excel

ɜɨɥɢɤɢ. ɉɨɱɟɦɭ ɩɪɢɛɥɢɠɟɧɧɨɟ? Ɍɚɤ ɤɚɤ ɜ ɦɨɞɟɥɢ ɜɫɟ ɭɱɟɫɬɶ ɧɟɥɶɡɹ! ɋɬɚɪɚɸɬɫɹ ɭɱɟɫɬɶ ɜ ɩɟɪɜɭɸ ɨɱɟɪɟɞɶ ɬɨɥɶɤɨ ɫɭɳɟɫɬɜɟɧɧɨɟ ɢ ɧɟɨɛɯɨɞɢɦɨɟ. ɇɚ ɨɫɧɨɜɟ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɨɩɢɫɚɧɢɹ ɪɚɡɪɚɛɚɬɵɜɚɟɬɫɹ ɚɥɝɨɪɢɬɦ ɦɨɞɟɥɢ. Ⱦɚɥɟɟ ɪɚɡɪɚɛɚɬɵɜɚɟɬɫɹ ɩɪɨɝɪɚɦɦɚ ɦɨɞɟɥɢ ɜ ɨɩɪɟɞɟɥɟɧɧɨɣ ɫɪɟɞɟ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ. ɉɪɨɝɪɚɦɦɚ ɪɚɡɦɟɳɚɟɬɫɹ ɜ ɤɨɦɩɶɸɬɟɪɟ, ɡɚɧɨɫɹɬɫɹ ɢɫɯɨɞɧɵɟ ɞɚɧɧɵɟ ɢ ɡɚɩɭɫɤɚɟɬɫɹ ɩɪɨɝɪɚɦɦɚ ɧɚ ɜɵɩɨɥɧɟɧɢɟ. Ʉɨɦɩɶɸɬɟɪ ɧɚɱɢɧɚɟɬ ɮɭɧɤɰɢɨɧɢɪɨɜɚɬɶ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɩɪɨɝɪɚɦɦɨɣ ɦɨɞɟɥɢ, ɨɛɪɚɛɚɬɵɜɚɸɬɫɹ ɞɚɧɧɵɟ ɢ ɜɵɞɚɸɬɫɹ ɜɵɯɨɞɧɵɟ ɞɚɧɧɵɟ ɜ ɜɢɞɟ ɝɪɚɮɢɤɨɜ ɢɥɢ ɬɚɛɥɢɰ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɤɨɦɩɶɸɬɟɪɧɚɹ ɦɨɞɟɥɶ ɟɫɬɶ ɩɪɨɝɪɚɦɦɚ ɚɥɝɨɪɢɬɦɚ, ɤɨɬɨɪɵɣ ɪɚɡɪɚɛɨɬɚɧ ɧɚ ɨɫɧɨɜɟ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɨɩɢɫɚɧɢɹ ɦɨɞɟɥɢ. ɑɟɦ ɩɪɢɜɥɟɤɚɬɟɥɶɧɵ ɤɨɦɩɶɸɬɟɪɧɵɟ ɦɨɞɟɥɢ? ȼɨ-ɩɟɪɜɵɯ, ɦɨɠɧɨ ɜ ɥɸɛɨɟ ɜɪɟɦɹ ɩɪɨɜɨɞɢɬɶ ɢɫɫɥɟɞɨɜɚɧɢɟ ɪɟɚɥɶɧɵɯ ɨɛɴɟɤɬɨɜ ɧɟɨɛɯɨɞɢɦɨɟ ɱɢɫɥɨ ɪɚɡ. ȼɨ-ɜɬɨɪɵɯ, ɫɦɟɥɨ ɢɡɦɟɧɹɬɶ ɢɫɯɨɞɧɵɟ ɞɚɧɧɵɟ ɢ ɩɨɥɭɱɚɬɶ ɪɟɡɭɥɶɬɚɬɵ, ɤɨɬɨɪɵɟ ɞɥɹ ɪɟɚɥɶɧɵɯ ɨɛɴɟɤɬɨɜ ɛɵɥɢ ɛɵ «ɝɭɛɢɬɟɥɶɧɵ». ȼ-ɬɪɟɬɶɢɯ, ɫɩɨɤɨɣɧɨ ɜɧɨɫɢɬɶ ɢɡɦɟɧɟɧɢɹ ɞɥɹ ɭɥɭɱɲɟɧɢɹ ɦɨɞɟɥɢ ɢɥɢ ɢɫɩɪɚɜɥɟɧɢɹ ɨɲɢɛɨɤ. ɋɨɜɪɟɦɟɧɧɵɣ ɫɩɟɰɢɚɥɢɫɬ ɞɨɥɠɟɧ ɢɦɟɬɶ ɧɚɜɵɤɢ ɦɨɞɟɥɢɪɨɜɚɧɢɹ. Ⱦɥɹ ɷɬɨɝɨ ɨɧ ɞɨɥɠɟɧ ɡɧɚɬɶ ɫɜɨɸ ɩɪɟɞɦɟɬɧɭɸ ɨɛɥɚɫɬɶ, ɢɦɟɬɶ ɡɧɚɧɢɹ ɜ ɨɛɥɚɫɬɢ ɦɚɬɟɦɚɬɢɤɢ, ɭɦɟɬɶ ɫɨɫɬɚɜɥɹɬɶ ɚɥɝɨɪɢɬɦɵ, ɡɧɚɬɶ ɨɫɧɨɜɵ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ. ȼ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɫɩɟɰɢɮɢɤɢ ɪɚɛɨɬɵ ɨɛɴɟɦ ɡɧɚɧɢɣ, ɭɦɟɧɢɣ ɢ ɧɚɜɵɤɨɜ ɩɨ ɩɪɟɞɫɬɚɜɥɟɧɧɵɦ ɫɨɫɬɚɜɥɹɸɳɢɦ ɦɨɠɟɬ ɛɵɬɶ ɪɚɡɥɢɱɧɵɦ. ȼɨɩɪɨɫɵ ɚɥɝɨɪɢɬɦɢɡɚɰɢɢ ɢ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ ɪɚɫɫɦɚɬɪɢɜɚɸɬɫɹ ɜ ɞɢɫɰɢɩɥɢɧɟ ɢɧɮɨɪɦɚɬɢɤɚ. Ɂɞɟɫɶ ɯɨɱɟɬɫɹ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɜ ɢɧɮɨɪɦɚɬɢɤɭ ɜɯɨɞɹɬ ɜɨɩɪɨɫɵ ɢɧɮɨɪɦɚɰɢɨɧɧɵɯ ɬɟɯɧɨɥɨɝɢɣ. Ɇɧɨɝɢɟ ɱɚɫɬɨ ɩɪɢɧɢɠɚɸɬ ɪɨɥɶ ɢɧɮɨɪɦɚɬɢɤɢ ɢ ɜɵɞɜɢɝɚɸɬ ɧɚ ɩɟɪɜɵɣ ɩɥɚɧ ɞɢɫɰɢɩɥɢɧɭ ɢɧɮɨɪɦɚɰɢɨɧɧɵɟ ɬɟɯɧɨɥɨɝɢɢ. Ʉɚɤ ɭɱɢɬɶ ɢ ɱɬɨ ɢɡɭɱɚɬɶ ɧɚ ɭɪɨɤɚɯ ɢɧɮɨɪɦɚɬɢɤɢ? ɇɚ ɷɬɢ ɜɨɩɪɨɫɵ ɱɟɬɤɨ ɢ ɨɞɧɨɡɧɚɱɧɨ ɧɟɥɶɡɹ ɨɬɜɟɬɢɬɶ ɜ ɫɢɥɭ ɨɝɪɚɧɢɱɟɧɧɨɫɬɢ ɜɪɟɦɟɧɢ ɢ ɨɬɫɭɬɫɬɜɢɹ ɧɟɨɛɯɨɞɢɦɵɯ ɜɵɱɢɫɥɢɬɟɥɶɧɵɯ ɫɪɟɞɫɬɜ ɢ ɩɪɨɝɪɚɦɦɧɨɝɨ ɨɛɟɫɩɟɱɟɧɢɹ. Ɉɫɧɨɜɧɵɦɢ ɢɡɭɱɚɟɦɵɦɢ ɬɟɦɚɦɢ ɜ ɭɱɟɛɧɵɯ ɡɚɜɟɞɟɧɢɹɯ ɹɜɥɹɸɬɫɹ ɩɪɢɥɨɠɟɧɢɹ ɢ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɟ. ɉɪɢɱɟɦ ɫɟɣɱɚɫ ɜɚɠɧɨ ɧɟ ɬɨɥɶɤɨ ɡɧɚɬɶ ɜɨɡɦɨɠɧɨɫɬɢ ɩɪɢɥɨɠɟɧɢɣ, ɧɨ ɢ ɭɦɟɬɶ ɩɪɨɝɪɚɦɦɢɪɨɜɚɬɶ. ɋ ɩɨɦɨɳɶɸ ɩɪɢɥɨɠɟɧɢɹ MS Excel ɦɨɠɧɨ ɢɡɭɱɢɬɶ ɨɛɚ ɜɨɩɪɨɫɚ ɢ ɡɚɬɟɦ ɫɩɨɤɨɣɧɨ ɩɟɪɟɣɬɢ ɤ ɢɡɭɱɟɧɢɸ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ ɧɚ ɥɸɛɨɦ ɹɡɵɤɟ.

8

1.1. Ɉ ɪɟɲɟɧɢɢ ɡɚɞɚɱ ɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ

ɉɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɩɪɢɥɨɠɟɧɢɹ MS Excel ɨɛɵɱɧɨ ɪɟɲɚɸɬ ɪɚɡɥɢɱɧɵɟ ɪɚɫɱɟɬɧɵɟ ɡɚɞɚɱɢ. Ɋɚɫɱɟɬɧɵɟ ɡɚɞɚɱɢ ɯɚɪɚɤɬɟɪɢɡɭɸɬɫɹ ɧɚɥɢɱɢɟɦ ɤɨɧɤɪɟɬɧɵɯ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ ɢ ɧɟɢɡɦɟɧɧɵɦɢ ɭɫɥɨɜɢɹɦɢ, ɨ ɱɟɦ ɝɨɜɨɪɢɥɨɫɶ ɜɵɲɟ. Ɉɞɧɚɤɨ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɩɪɢ ɢɡɭɱɟɧɢɢ ɩɪɢɥɨɠɟɧɢɹ ɩɨɡɜɨɥɢɬ ɛɨɥɟɟ ɝɥɭɛɨɤɨ ɭɡɧɚɬɶ ɜɨɡɦɨɠɧɨɫɬɢ MS Excel ɢ ɨɫɧɨɜɵ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ. ɉɪɢɥɨɠɟɧɢɟ MS Excel ɢɦɟɟɬ ɪɹɞ ɨɫɨɛɟɧɧɨɫɬɟɣ. ɇɨ ɫɚɦɨɟ ɝɥɚɜɧɨɟ ɧɚ ɥɸɛɨɦ ɉɄ ɜɫɟɝɞɚ ɩɪɢɫɭɬɫɬɜɭɟɬ ɫɬɚɧɞɚɪɬɧɵɣ ɩɚɤɟɬ MS Office c ɩɪɢɥɨɠɟɧɢɟɦ MS Excel. ɇɟ ɧɭɠɧɨ ɜɵɛɢɪɚɬɶ ɹɡɵɤ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ, ɭɫɬɚɧɚɜɥɢɜɚɬɶ ɞɨɩɨɥɧɢɬɟɥɶɧɨ ɫɪɟɞɭ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ. ɇɭɠɧɨ ɬɨɥɶɤɨ ɢɦɟɬɶ ɉɄ, ɢɧɬɟɪɟɫ, ɧɚɫɬɨɣɱɢɜɨɫɬɶ ɢ ɭɫɢɞɱɢɜɨɫɬɶ. ȼ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɫɭɳɟɫɬɜɭɸɬ ɪɚɡɥɢɱɧɵɟ ɦɨɞɢɮɢɤɚɰɢɢ ɩɪɢɥɨɠɟɧɢɹ MS Excel, ɧɨ ɩɨɥɶɡɨɜɚɬɟɥɶɫɤɢɣ ɢɧɬɟɪɮɟɣɫ ɢɡɦɟɧɹɥɫɹ ɧɟ ɨɱɟɧɶ ɫɢɥɶɧɨ. ɉɨɷɬɨɦɭ ɜɫɟɝɞɚ ɩɪɢ ɪɟɚɥɢɡɚɰɢɢ ɩɪɢɜɟɞɟɧɧɵɯ ɩɪɢɦɟɪɨɜ ȼɵ ɧɚɣɞɟɬɟ ɧɭɠɧɵɣ ɩɭɧɤɬ ɞɥɹ ɪɟɚɥɢɡɚɰɢɢ ɦɟɬɨɞɢɤɢ ɦɨɞɟɥɢ.

9

1. Ɉ ɦɨɞɟɥɢɪɨɜɚɧɢɢ, ɪɟɲɟɧɢɢ ɡɚɞɚɱ, ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɢ ɢ MS Excel

1.2. Ɉ ɩɪɟɢɦɭɳɟɫɬɜɚɯ MS Excel ɩɪɢ ɢɡɭɱɟɧɢɢ ɨɫɧɨɜ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ Ɉɬɦɟɬɢɦ ɫɥɟɞɭɸɳɢɟ ɩɪɟɢɦɭɳɟɫɬɜɚ ɩɪɢɥɨɠɟɧɢɹ MS Excel ɫ ɬɨɱɤɢ ɡɪɟɧɢɹ ɩɪɢɨɛɪɟɬɟɧɢɹ ɧɚɜɵɤɨɜ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ ɢ ɪɚɡɪɚɛɨɬɤɢ ɦɨɞɟɥɟɣ: x MS Excel ɜɫɟɝɞɚ ɜɤɥɸɱɟɧɨ ɜ ɫɨɫɬɚɜ ɩɚɤɟɬɚ MS Office. x MS Excel ɢɦɟɟɬ ɞɨɫɬɚɬɨɱɧɨ ɛɨɥɶɲɨɣ ɧɚɛɨɪ ɪɚɡɥɢɱɧɵɯ ɮɭɧɤɰɢɣ. x MS Excel ɩɪɟɞɫɬɚɜɥɹɟɬ ɜɨɡɦɨɠɧɨɫɬɶ ɩɨ ɫɨɡɞɚɧɢɸ ɫɜɨɢɯ ɩɨɥɶɡɨɜɚɬɟɥɶɫɤɢɯ ɮɭɧɤɰɢɣ. x MS Excel ɢɦɟɟɬ ɩɨɧɹɬɧɭɸ ɫɢɫɬɟɦɭ ɢɧɞɢɤɚɰɢɢ ɨɲɢɛɨɤ. x MS Excel ɩɨɡɜɨɥɹɟɬ ɢɡɦɟɧɹɬɶ ɮɨɪɦɚɬ ɪɟɡɭɥɶɬɚɬɨɜ ɜɵɱɢɫɥɟɧɢɣ, ɚ ɬɚɤɠɟ ɫɨɡɞɚɜɚɬɶ ɫɜɨɣ ɩɨɥɶɡɨɜɚɬɟɥɶɫɤɢɣ ɮɨɪɦɚɬ. x MS Excel ɢɦɟɟɬ ɩɪɨɫɬɵɟ ɩɪɚɜɢɥɚ ɫɨɫɬɚɜɥɟɧɢɹ ɜɵɪɚɠɟɧɢɣ ɞɥɹ ɜɵɱɢɫɥɟɧɢɣ, ɤɨɬɨɪɵɟ ɢɡɭɱɚɸɬɫɹ ɜ ɲɤɨɥɟ. x ȼɵɱɢɫɥɟɧɢɹ ɜɵɩɨɥɧɹɸɬɫɹ ɚɜɬɨɦɚɬɢɱɟɫɤɢ ɩɨɫɥɟ ɢɡɦɟɧɟɧɢɹ ɞɚɧɧɵɯ ɢɥɢ ɪɚɫɱɟɬɧɵɯ ɜɵɪɚɠɟɧɢɣ, ɤɨɬɨɪɵɟ ɜɜɨɞɹɬɫɹ ɩɨɫɥɟ ɳɟɥɱɤɚ ɩɨ ɤɥɚɜɢɲɟ Enter. x ɉɨɥɶɡɨɜɚɬɟɥɶ «ɜɢɞɢɬ» ɧɟ ɬɨɥɶɤɨ ɝɪɚɮɢɤɭ, ɧɨ ɢ ɪɟɡɭɥɶɬɚɬɵ ɜɵɱɢɫɥɟɧɢɣ ɩɨ ɯɨɞɭ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɢɥɢ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ. x ɉɨɥɶɡɨɜɚɬɟɥɶ ɦɨɠɟɬ ɧɚ ɥɸɛɨɦ ɷɬɚɩɟ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɩɪɨɫɦɨɬɪɟɬɶ ɪɚɫɱɟɬɧɵɟ ɜɵɪɚɠɟɧɢɹ, ɩɨ ɤɨɬɨɪɵɦ ɩɪɨɢɡɜɨɞɹɬɫɹ ɜɵɱɢɫɥɟɧɢɹ, ɚ ɬɚɤɠɟ ɜɤɥɸɱɢɬɶ ɪɟɠɢɦ ɉɨɤɚɡɵɜɚɬɶ ɮɨɪɦɭɥɵ, ɚ ɧɟ ɢɯ ɡɧɚɱɟɧɢɹ. x ɉɨɥɶɡɨɜɚɬɟɥɶ ɦɨɠɟɬ ɫɮɨɪɦɢɪɨɜɚɬɶ ɩɪɨɦɟɠɭɬɨɱɧɵɟ ɜɵɱɢɫɥɟɧɢɹ, ɤɨɬɨɪɵɟ ɨɬɪɚɠɚɸɬ ɤɨɥɢɱɟɫɬɜɟɧɧɵɟ ɩɚɪɚɦɟɬɪɵ ɦɨɞɟɥɢ ɢ ɧɚɛɥɸɞɚɬɶ ɡɚ ɢɯ ɢɡɦɟɧɟɧɢɹɦɢ. x MS Excel ɩɨɡɜɨɥɹɟɬ ɨɫɭɳɟɫɬɜɥɹɬɶ ɜɥɨɠɟɧɢɹ, ɤɨɥɢɱɟɫɬɜɨ ɤɨɬɨɪɵɯ ɞɨɫɬɚɬɨɱɧɨ ɞɥɹ ɪɟɚɥɢɡɚɰɢɢ ɛɨɥɶɲɢɧɫɬɜɚ ɜɵɱɢɫɥɟɧɢɣ ɢ ɫɨɩɨɫɬɚɜɢɦɨ ɫ ɤɨɥɢɱɟɫɬɜɨɦ ɜɥɨɠɟɧɢɣ ɜ ɞɪɭɝɢɯ ɫɪɟɞɚɯ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ. x Ɍɚɤ ɤɚɤ MS Excel ɹɜɥɹɟɬɫɹ ɬɚɛɥɢɱɧɵɦ ɩɪɨɰɟɫɫɨɪɨɦ, ɬɨ ɩɨɥɶɡɨɜɚɬɟɥɶ ɞɨɥɠɟɧ ɞɥɹ ɜɵɱɢɫɥɟɧɢɣ ɫɨɡɞɚɜɚɬɶ ɪɚɫɱɟɬɧɵɟ ɜɵɪɚɠɟɧɢɹ (ɮɨɪɦɭɥɵ) ɜ ɤɚɠɞɨɣ ɹɱɟɣɤɟ. ɑɬɨ ɨɱɟɧɶ ɩɨɥɟɡɧɨ ɜ ɩɥɚɧɟ ɡɚɩɨɦɢɧɚɧɢɹ ɫɬɚɧɞɚɪɬɧɵɯ ɮɭɧɤɰɢɣ MS Excel.

10

1.2. Ɉ ɩɪɟɢɦɭɳɟɫɬɜɚɯ MS Excel ɩɪɢ ɢɡɭɱɟɧɢɢ ɨɫɧɨɜ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ 

x ɉɨɥɶɡɨɜɚɬɟɥɶ ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɫɱɟɬɱɢɤɨɜ ɦɨɠɟɬ ɧɚɛɥɸɞɚɬɶ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɟ ɦɨɞɟɥɢ ɧɚ ɥɸɛɨɦ ɧɭɠɧɨɦ ɷɬɚɩɟ. x MS Excel ɢɦɟɟɬ ɫɪɟɞɭ ɪɚɡɪɚɛɨɬɤɢ MS Visual Basic Application, ɤɨɬɨɪɚɹ ɡɧɚɱɢɬɟɥɶɧɨ ɨɛɥɟɝɱɚɟɬ ɪɟɲɟɧɢɟ ɡɚɞɚɱ ɩɭɬɟɦ ɤɨɦɩɨɧɟɧɬɧɨɝɨ ɫɩɨɫɨɛɚ ɫɨɡɞɚɧɢɹ ɩɪɨɝɪɚɦɦ. ɗɬɢ ɩɪɟɢɦɭɳɟɫɬɜɚ ɩɨɡɜɨɥɹɸɬ ɨɜɥɚɞɟɬɶ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨ ɧɚɜɵɤɚɦɢ ɪɚɡɪɚɛɨɬɤɢ ɚɥɝɨɪɢɬɦɨɜ ɢ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ ɧɚ ɛɨɥɟɟ ɤɨɦɮɨɪɬɧɨɦ ɭɪɨɜɧɟ, ɤɨɬɨɪɵɣ ɡɚɧɢɦɚɟɬ ɩɪɨɦɟɠɭɬɨɱɧɨɟ ɩɨɥɨɠɟɧɢɟ ɦɟɠɞɭ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɟɦ ɩɪɹɦɵɦɢ ɤɨɞɚɦɢ ɢ ɨɛɴɟɤɬɧɨ-ɨɪɢɟɧɬɢɪɨɜɚɧɧɵɦ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɟɦ. ɉɪɢ ɷɬɨɦ ɪɚɡɜɢɜɚɬɶ «ɢɡɜɨɪɨɬɥɢɜɨɫɬɶ» ɢ ɭɦɟɧɢɟ ɧɚɯɨɞɢɬɶ ɜɵɯɨɞɵ ɢɡ ɬɪɭɞɧɨɫɬɟɣ ɩɪɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ ɢɡ-ɡɚ ɨɝɪɚɧɢɱɟɧɧɵɯ ɜɨɡɦɨɠɧɨɫɬɟɣ ɪɹɞɚ ɮɭɧɤɰɢɣ MS Excel. ɇɟɤɨɬɨɪɵɟ ɩɪɟɩɨɞɚɜɚɬɟɥɢ ɪɚɬɭɸɬ ɡɚ ɩɨɞɯɨɞɵ ɤ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɸ ɫ ɬɨɱɤɢ ɡɪɟɧɢɹ ɢɫɩɨɥɶɡɨɜɚɧɢɹ «ɤɭɛɢɤɨɜ», ɤɨɬɨɪɵɟ ɫɨɛɢɪɚɸɬɫɹ ɜ ɨɩɪɟɞɟɥɟɧɧɨɦ ɩɨɪɹɞɤɟ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɢɥɢ ɦɨɞɟɥɢɪɨɜɚɧɢɹ. ȼ ɪɨɥɢ «ɤɭɛɢɤɨɜ» ɜɵɫɬɭɩɚɸɬ ɝɨɬɨɜɵɟ ɩɨɞɩɪɨɝɪɚɦɦɵ (ɮɭɧɤɰɢɢ, ɩɪɨɰɟɞɭɪɵ), ɤɨɬɨɪɵɟ ɜɵɩɨɥɧɹɸɬ ɨɩɪɟɞɟɥɟɧɧɵɟ ɞɟɣɫɬɜɢɹ. ɉɪɢ ɷɬɨɦ ɧɟ ɜɚɠɧɨ, ɱɬɨ ɭ ɧɢɯ ɜɧɭɬɪɢ. ɇɟɨɛɯɨɞɢɦɨ ɬɨɥɶɤɨ ɡɧɚɬɶ, ɱɬɨ ɧɭɠɧɨ ɩɨɞɚɬɶ ɧɚ ɜɯɨɞ ɢ ɱɬɨ ɩɨɥɭɱɚɟɬɫɹ ɧɚ ɜɵɯɨɞɟ «ɤɭɛɢɤɚ». Ɍɚɤɨɣ ɩɨɞɯɨɞ ɰɟɥɟɫɨɨɛɪɚɡɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɩɪɢ ɪɚɡɪɚɛɨɬɤɟ ɨɱɟɧɶ ɫɥɨɠɧɵɯ ɢ ɛɨɥɶɲɢɯ ɩɨ ɨɛɴɟɦɭ ɩɪɨɝɪɚɦɦ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ɢɥɢ ɦɨɞɟɥɢɪɨɜɚɧɢɹ. ɗɬɨɬ ɩɨɞɯɨɞ ɹɜɥɹɟɬɫɹ ɪɟɚɥɢɡɚɰɢɟɣ ɩɪɢɧɰɢɩɚ ɫɬɪɭɤɬɭɪɢɪɨɜɚɧɧɨɝɨ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ. Ɉɞɧɚɤɨ ɧɚ ɩɟɪɜɨɧɚɱɚɥɶɧɵɯ ɷɬɚɩɚɯ ɨɛɭɱɟɧɢɹ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɸ ɪɟɚɥɢɡɚɰɢɹ ɬɚɤɨɝɨ ɩɨɞɯɨɞɚ ɩɚɝɭɛɧɚ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɭɱɚɬɫɹ ɩɨɥɶɡɨɜɚɬɶɫɹ ɝɨɬɨɜɵɦ «ɤɚɥɶɤɭɥɹɬɨɪɨɦ». Ɍɨ ɟɫɬɶ ɧɚɠɢɦɚɬɶ ɧɚ ɤɧɨɩɤɢ ɢ ɧɟ ɜɞɚɜɚɬɶɫɹ ɜ ɩɨɞɪɨɛɧɨɫɬɢ ɜɵɱɢɫɥɟɧɢɣ. ȼ ɫɥɭɱɚɟ ɧɟɢɫɩɪɚɜɧɨɫɬɢ «ɤɚɥɶɤɭɥɹɬɨɪɚ» ɧɟ ɛɭɞɟɬ ɜɨɡɦɨɠɧɨɫɬɢ ɟɝɨ ɢɫɩɪɚɜɢɬɶ, ɬɚɤ ɤɚɤ ɨɛɭɱɚɟɦɵɟ ɧɟ ɢɦɟɸɬ ɩɪɟɞɫɬɚɜɥɟɧɢɹ ɨ ɟɝɨ «ɧɚɱɢɧɤɟ». ɉɨɷɬɨɦɭ ɧɭɠɧɨ ɧɚɱɢɧɚɬɶ ɩɪɨɝɪɚɦɦɢɪɨɜɚɬɶ ɫ ɤɨɞɨɜ ɢɥɢ, ɜ ɤɪɚɣɧɟɦ ɫɥɭɱɚɟ, ɢɫɩɨɥɶɡɨɜɚɬɶ ɷɥɟɦɟɧɬɚɪɧɵɟ ɮɭɧɤɰɢɢ, ɫɭɳɧɨɫɬɶ ɤɨɬɨɪɵɯ ɹɫɧɚ. ɇɚɩɪɢɦɟɪ, ɮɭɧɤɰɢɹ SIN() ɢɥɢ ɋɍɆɆ() ɩɪɢɥɨɠɟɧɢɹ MS Excel. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɨɛɭɱɚɟɦɵɣ ɩɪɢɨɛɪɟɬɚɟɬ ɪɹɞ ɱɟɪɬ, ɤɨɬɨɪɵɟ ɧɭɠɧɵ ɩɪɨɝɪɚɦɦɢɫɬɭ: x ɋɨɫɬɚɜɥɹɬɶ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨ ɢɥɢ «ɱɢɬɚɬɶ» ɱɭɠɢɟ ɚɥɝɨɪɢɬɦɵ. x «ȼɢɞɟɬɶ» ɢ «ɱɭɜɫɬɜɨɜɚɬɶ» ɩɪɨɝɪɚɦɦɭ.

11

1. Ɉ ɦɨɞɟɥɢɪɨɜɚɧɢɢ, ɪɟɲɟɧɢɢ ɡɚɞɚɱ, ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɢ ɢ MS Excel

x ɍɦɟɬɶ ɪɚɡɛɢɜɚɬɶ ɚɥɝɨɪɢɬɦ ɧɚ «ɤɭɫɤɢ», ɤɨɬɨɪɵɟ ɧɟɫɭɬ ɨɩɪɟɞɟɥɟɧɧɵɣ ɮɢɡɢɱɟɫɤɢɣ ɫɦɵɫɥ. x Ɉɩɪɟɞɟɥɹɬɶ ɩɪɨɦɟɠɭɬɨɱɧɵɟ ɩɚɪɚɦɟɬɪɵ ɩɪɢ ɜɵɱɢɫɥɟɧɢɹɯ ɞɥɹ ɭɩɪɨɳɟɧɢɹ ɱɬɟɧɢɹ ɩɪɨɝɪɚɦɦɵ ɢɥɢ ɨɛɥɟɝɱɟɧɢɹ ɤɨɧɬɪɨɥɹ ɩɪɨɝɪɚɦɦɵ. x ȼɵɛɢɪɚɬɶ ɢɡ ɡɚɞɚɧɧɨɝɨ ɞɢɚɩɚɡɨɧɚ ɞɚɧɧɵɟ, ɤɨɬɨɪɵɟ ɢɫɩɨɥɶɡɭɸɬɫɹ ɞɥɹ ɩɪɨɜɟɪɤɢ ɩɪɚɜɢɥɶɧɨɫɬɢ ɩɪɨɝɪɚɦɦɵ. x ɉɪɢ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɩɨɢɫɤɚ ɨɲɢɛɨɤ «ɠɟɜɚɬɶ ɩɪɨɝɪɚɦɦɭ», ɚ ɧɟ ɝɥɨɬɚɬɶ ɟɟ ɤɭɫɤɢ. x ȼɵɞɟɥɹɬɶ ɤɭɫɤɢ ɩɪɨɝɪɚɦɦɵ ɞɥɹ ɧɚɯɨɠɞɟɧɢɹ ɨɲɢɛɨɤ ɢɥɢ ɩɪɨɜɟɪɤɢ ɩɪɚɜɢɥɶɧɨɫɬɢ ɢɯ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ. x ɉɨɞɛɢɪɚɬɶ ɧɭɠɧɵɟ ɞɚɧɧɵɟ ɞɥɹ ɜɵɜɨɞɚ ɧɚɝɥɹɞɧɨɝɨ ɨɬɨɛɪɚɠɟɧɢɹ ɪɟɡɭɥɶɬɚɬɨɜ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɩɪɨɝɪɚɦɦɵ ɢɥɢ ɩɪɨɜɟɪɤɢ ɟɟ ɩɪɚɜɢɥɶɧɨɫɬɢ. x Ɉɛɟɫɩɟɱɢɜɚɬɶ ɫɨɯɪɚɧɧɨɫɬɶ ɩɨɥɭɱɟɧɧɵɯ ɞɚɧɧɵɯ ɞɥɹ ɞɚɥɶɧɟɣɲɟɝɨ ɚɧɚɥɢɡɚ. ɉɪɢ ɪɚɡɪɚɛɨɬɤɟ ɚɥɝɨɪɢɬɦɚ ɦɨɞɟɥɢ (ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ) ɝɥɚɜɧɨɟ ɧɟ ɬɨɥɶɤɨ ɨɩɪɟɞɟɥɢɬɶɫɹ ɫ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶɸ ɜɵɱɢɫɥɟɧɢɣ ɢ ɩɪɢɦɟɧɹɟɦɵɦɢ ɮɨɪɦɭɥɚɦɢ, ɧɨ ɢ ɱɟɬɤɨ ɜɵɞɟɥɢɬɶ ɜɯɨɞɧɵɟ ɢ ɜɵɯɨɞɧɵɟ ɜɟɥɢɱɢɧɵ. ȼɵɹɫɧɢɬɶ ɡɚɜɢɫɹɬ ɥɢ ɜɟɥɢɱɢɧɵ ɨɬ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɯ ɤɨɨɪɞɢɧɚɬ, ɜɪɟɦɟɧɢ ɢɥɢ ɞɪɭɝɢɯ ɜɟɥɢɱɢɧ. ɗɬɨ ɜɚɠɧɨ ɞɥɹ ɨɪɝɚɧɢɡɚɰɢɢ ɮɢɤɫɚɰɢɢ ɢɯ ɢɡɦɟɧɟɧɢɣ, ɧɚɝɥɹɞɧɨɝɨ ɩɪɟɞɫɬɚɜɥɟɧɢɹ ɪɟɡɭɥɶɬɚɬɨɜ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɢ ɨɩɪɟɞɟɥɟɧɢɹ ɨɛɴɟɦɚ ɜɵɯɨɞɧɵɯ ɦɚɫɫɢɜɨɜ. ɉɪɢ ɷɬɨɦ ɠɟɥɚɬɟɥɶɧɨ ɫɪɚɡɭ ɨɩɪɟɞɟɥɢɬɶɫɹ ɫ ɤɨɧɫɬɚɧɬɚɦɢ ɢ ɩɚɪɚɦɟɬɪɚɦɢ. Ɉɛɵɱɧɨ ɤɨɧɫɬɚɧɬɵ ɹɜɥɹɸɬɫɹ ɮɢɡɢɱɟɫɤɢɦɢ ɜɟɥɢɱɢɧɚɦɢ, ɤɨɬɨɪɵɟ ɢɦɟɸɬ ɤɨɧɤɪɟɬɧɵɟ ɪɚɡɦɟɪɧɨɫɬɢ. ɉɨɷɬɨɦɭ ɧɭɠɧɨ ɫɨɝɥɚɫɨɜɚɬɶ ɪɚɡɦɟɪɧɨɫɬɢ ɤɨɧɫɬɚɧɬ ɫ ɜɟɥɢɱɢɧɚɦɢ, ɤɨɬɨɪɵɟ ɢɫɩɨɥɶɡɭɸɬɫɹ ɜ ɮɨɪɦɭɥɚɯ (ɜɵɪɚɠɟɧɢɹɯ) ɩɪɢ ɜɵɱɢɫɥɟɧɢɹɯ. ɉɚɪɚɦɟɬɪɵ ɦɨɝɭɬ ɛɵɬɶ ɫɜɹɡɚɧɵ ɧɟ ɬɨɥɶɤɨ ɫ ɮɢɡɢɤɨɣ ɦɨɞɟɥɢ, ɧɨ ɢ ɢɫɩɨɥɶɡɭɸɬɫɹ ɞɥɹ ɤɨɧɬɪɨɥɹ ɨɬɞɟɥɶɧɵɯ ɷɬɚɩɨɜ ɜɵɱɢɫɥɟɧɢɣ ɩɪɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ. ɉɪɨɝɪɚɦɦɢɫɬ ɞɨɥɠɟɧ ɭɦɟɬɶ ɪɟɚɥɢɡɨɜɵɜɚɬɶ ɩɪɟɞɫɬɚɜɥɟɧɧɵɣ ɟɦɭ ɚɥɝɨɪɢɬɦ ɧɚ ɤɨɧɤɪɟɬɧɨɦ ɹɡɵɤɟ ɢ ɡɧɚɬɶ ɨɫɨɛɟɧɧɨɫɬɢ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ. Ɉɞɧɚɤɨ ɩɪɨɝɪɚɦɦɢɫɬ ɜɫɟɝɞɚ ɫɨɡɞɚɟɬ ɫɜɨɢ «ɦɚɥɟɧɶɤɢɟ ɚɥɝɨɪɢɬɦɵ» ɩɪɢ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɢ ɡɚɞɚɱɢ. ȼ ɠɢɡɧɢ ɱɚɫɬɨ ɩɪɨɝɪɚɦɦɢɫɬɵ ɧɟ ɨɫɬɚɸɬɫɹ ɜ ɫɬɨɪɨɧɟ ɨɬ ɜɨɩɪɨɫɨɜ ɚɥɝɨɪɢɬɦɢɡɚɰɢɢ. ɗɬɨ ɧɭɠɧɨ ɭɱɢɬɵɜɚɬɶ ɧɚ ɫɬɚɞɢɢ ɢɡɭɱɟɧɢɹ ɩɪɨɝɪɚɦɦɢɪɨ12

1.2. Ɉ ɩɪɟɢɦɭɳɟɫɬɜɚɯ MS Excel ɩɪɢ ɢɡɭɱɟɧɢɢ ɨɫɧɨɜ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ 

ɜɚɧɢɹ. ɇɟɨɛɯɨɞɢɦɨ ɭɦɟɬɶ ɪɚɡɪɚɛɚɬɵɜɚɬɶ ɚɥɝɨɪɢɬɦɵ ɫ ɭɱɟɬɨɦ ɨɫɨɛɟɧɧɨɫɬɟɣ ɤɨɧɤɪɟɬɧɨɣ ɫɪɟɞɵ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ, ɨɫɧɨɜɧɵɯ ɩɨɥɨɠɟɧɢɣ ɩɪɟɞɦɟɬɧɨɣ ɨɛɥɚɫɬɢ ɢ ɩɨɫɬɚɜɥɟɧɧɵɯ ɰɟɥɟɣ ɢɫɫɥɟɞɨɜɚɧɢɹ. ɂɬɚɤ, ɩɪɨɝɪɚɦɦɢɫɬ ɩɪɢ ɫɨɡɞɚɧɢɢ ɤɨɦɩɶɸɬɟɪɧɨɣ ɦɨɞɟɥɢ ɞɨɥɠɟɧ: x ɍɹɫɧɢɬɶ ɰɟɥɶ ɢɫɫɥɟɞɨɜɚɧɢɹ. x ȼɵɹɜɢɬɶ ɨɫɨɛɟɧɧɨɫɬɢ ɦɨɞɟɥɢ. x Ɋɚɡɨɛɪɚɬɶɫɹ ɫ ɚɥɝɨɪɢɬɦɨɦ ɦɨɞɟɥɢ. x ɋɨɡɞɚɬɶ ɩɪɨɝɪɚɦɦɭ. x Ɉɫɭɳɟɫɬɜɢɬɶ ɤɨɧɬɪɨɥɶɧɵɣ ɩɪɨɫɱɟɬ ɧɚ ɩɪɨɝɪɚɦɦɟ. x ɍɛɟɞɢɬɶɫɹ ɜ ɪɚɛɨɬɨɫɩɨɫɨɛɧɨɫɬɢ ɩɪɨɝɪɚɦɦɵ ɜ ɡɚɞɚɧɧɨɦ ɞɢɚɩɚɡɨɧɟ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ. x Ɉɪɝɚɧɢɡɨɜɚɬɶ ɮɢɤɫɚɰɢɸ ɜɵɯɨɞɧɵɯ ɞɚɧɧɵɯ. x ɍɫɬɪɚɧɢɬɶ ɜɵɹɜɥɟɧɧɵɟ ɨɲɢɛɤɢ ɜ ɩɪɨɝɪɚɦɦɟ ɢɥɢ ɚɥɝɨɪɢɬɦɟ. x ɉɪɨɜɟɫɬɢ ɧɟɨɛɯɨɞɢɦɵɟ ɭɥɭɱɲɟɧɢɹ ɩɪɨɝɪɚɦɦɵ ɢɥɢ ɚɥɝɨɪɢɬɦɚ. x ɇɚɩɢɫɚɬɶ ɢɧɫɬɪɭɤɰɢɸ ɷɤɫɩɥɭɚɬɚɰɢɢ ɩɪɨɝɪɚɦɦɵ ɦɨɞɟɥɢ ɢ ɩɪɨɜɟɪɢɬɶ ɟɟ ɩɪɚɜɢɥɶɧɨɫɬɶ. x ɋɨɯɪɚɧɢɬɶ ɩɪɨɝɪɚɦɦɭ ɦɨɞɟɥɢ ɧɚ ɡɚɞɚɧɧɵɯ ɧɨɫɢɬɟɥɹɯ.

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1. Ɉ ɦɨɞɟɥɢɪɨɜɚɧɢɢ, ɪɟɲɟɧɢɢ ɡɚɞɚɱ, ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɢ ɢ MS Excel

1.3. Ɉɫɧɨɜɧɵɟ ɨɫɨɛɟɧɧɨɫɬɢ ɢɫɩɨɥɶɡɨɜɚɧɢɹ MS Excel ɩɪɢ ɪɟɲɟɧɢɢ ɡɚɞɚɱ ɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ Ʌɸɛɨɣ ɩɪɨɞɭɤɬ, ɫɨɡɞɚɜɚɟɦɵɣ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ MS Excel, ɫɨɞɟɪɠɢɬ ɬɪɢ ɤɨɦɩɨɧɟɧɬɚ: x ɬɚɛɥɢɰɭ ɜɯɨɞɧɵɯ ɞɚɧɧɵɯ; x ɬɚɛɥɢɰɭ ɜɵɯɨɞɧɵɯ ɞɚɧɧɵɯ; x ɝɪɚɮɢɱɟɫɤɭɸ ɤɨɦɩɨɧɟɧɬɭ. ȼ ɬɚɛɥɢɰɟ ɜɯɨɞɧɵɯ ɞɚɧɧɵɯ ɧɚɯɨɞɹɬɫɹ ɢɫɯɨɞɧɵɟ ɞɚɧɧɵɟ, ɤɨɬɨɪɵɟ ɦɨɝɭɬ ɢɦɟɬɶ ɪɚɡɥɢɱɧɵɟ ɮɨɪɦɚɬɵ. ɂɫɯɨɞɧɵɦɢ ɞɚɧɧɵɦɢ ɦɨɝɭɬ ɛɵɬɶ ɱɢɫɥɚ, ɬɟɤɫɬ (ɫɢɦɜɨɥɵ), ɞɚɬɵ, ɜɪɟɦɹ ɢ ɬ.ɩ. ɇɨ ɫɚɦɨɟ ɝɥɚɜɧɨɟ ɜ ɢɫɯɨɞɧɵɯ ɬɚɛɥɢɰɚɯ ɧɟ ɩɪɨɢɡɜɨɞɹɬ ɜɵɱɢɫɥɟɧɢɣ. ɂɫɯɨɞɧɵɟ ɞɚɧɧɵɟ ɦɨɝɭɬ ɛɵɬɶ ɩɪɟɞɫɬɚɜɥɟɧɵ ɜ ɬɚɛɥɢɰɟ ɜ ɜɢɞɟ ɨɞɧɨɝɨ ɢɥɢ ɧɟɫɤɨɥɶɤɢɯ ɫɬɨɥɛɰɨɜ (ɫɬɪɨɤ), ɚ ɬɚɤɠɟ ɜ ɜɢɞɟ ɫɨɜɨɤɭɩɧɨɫɬɢ ɢɥɢ ɨɞɢɧɨɱɧɵɯ ɩɚɪɚɦɟɬɪɨɜ. ȼ ɬɚɛɥɢɰɚɯ ɜɵɯɨɞɧɵɯ ɞɚɧɧɵɯ ɞɨɥɠɧɵ ɩɪɢɫɭɬɫɬɜɨɜɚɬɶ ɜɵɱɢɫɥɟɧɢɹ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ. ɉɪɢ ɷɬɨɦ ɜ ɬɚɛɥɢɰɚɯ ɩɪɨɢɡɜɨɞɹɬɫɹ ɤɚɤ ɢɬɨɝɨɜɵɟ, ɬɚɤ ɢ ɩɪɨɦɟɠɭɬɨɱɧɵɟ ɜɵɱɢɫɥɟɧɢɹ. Ƚɪɚɮɢɱɟɫɤɚɹ ɤɨɦɩɨɧɟɧɬɚ ɩɨɡɜɨɥɹɟɬ ɧɚɝɥɹɞɧɨ ɢɡɨɛɪɚɠɚɬɶ ɪɟɡɭɥɶɬɚɬɵ ɜɵɱɢɫɥɟɧɢɣ, ɡɚɜɢɫɢɦɨɫɬɢ ɜɵɯɨɞɧɵɯ ɞɚɧɧɵɯ ɨɬ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ ɢɥɢ ɩɚɪɚɦɟɬɪɨɜ, ɚ ɬɚɤɠɟ ɢɡɦɟɧɟɧɢɹ ɞɢɧɚɦɢɤɢ ɪɚɡɥɢɱɧɵɯ ɜɟɥɢɱɢɧ. Ɉɫɬɚɧɨɜɢɦɫɹ ɧɚ ɬɚɛɥɢɰɚɯ ɜɯɨɞɧɵɯ ɞɚɧɧɵɯ. ȼ ɹɱɟɣɤɢ ɬɚɛɥɢɰɵ ɦɨɝɭɬ ɛɵɬɶ ɜɧɟɫɟɧɵ ɱɢɫɥɨɜɵɟ ɢɥɢ ɬɟɤɫɬɨɜɵɟ ɞɚɧɧɵɟ. Ɍɟɤɫɬɨɜɵɟ ɞɚɧɧɵɟ ɦɨɝɭɬ ɫɨɫɬɨɹɬɶ ɢɡ ɛɭɤɜ ɢɥɢ ɫɢɦɜɨɥɨɜ. ɑɢɫɥɨɜɵɟ ɞɚɧɧɵɟ ɦɨɝɭɬ ɢɦɟɬɶ ɪɚɡɦɟɪɧɨɫɬɢ. Ɉɞɧɚɤɨ ɞɥɹ ɢɫɤɥɸɱɟɧɢɹ ɧɟɩɪɢɹɬɧɨɫɬɟɣ ɩɪɢ ɪɚɫɱɟɬɚɯ ɰɟɥɟɫɨɨɛɪɚɡɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɱɢɫɥɨɜɵɟ ɞɚɧɧɵɟ ɛɟɡ ɪɚɡɦɟɪɧɨɫɬɟɣ. Ɋɚɡɦɟɪɧɨɫɬɢ ɧɭɠɧɨ ɭɤɚɡɵɜɚɬɶ ɜ ɡɚɝɨɥɨɜɤɚɯ ɫɬɨɥɛɨɜ (ɫɬɪɨɤ) ɬɚɛɥɢɰɵ. ɋɥɟɞɭɟɬ ɩɨɦɧɢɬɶ, ɱɬɨ ɜɫɟ ɫɢɦɜɨɥɵ ɢɦɟɸɬ ɱɢɫɥɨɜɵɟ ɤɨɞɵ, ɤɨɬɨɪɵɟ ɦɨɠɧɨ ɭɜɢɞɟɬɶ ɜ ɨɤɧɟ ɋɢɦɜɨɥɵ ɩɪɢ ɜɵɛɨɪɟ ɫɢɦɜɨɥɚ ɞɥɹ ɜɫɬɚɜɤɢ (ɜɧɢɡɭ ɨɤɧɚ). ɉɪɢ ɡɚɩɢɫɢ ɬɟɤɫɬɚ ɢɥɢ ɫɢɦɜɨɥɚ ɨɧɢ ɩɪɢɠɢɦɚɸɬɫɹ ɤ ɥɟɜɨɦɭ ɤɪɚɸ ɹɱɟɣɤɢ ɩɨ ɭɦɨɥɱɚɧɢɸ (Ⱥ1, Ⱥ3). ɑɢɫɥɚ ɜɫɟɝɞɚ ɩɪɢɠɢɦɚɸɬɫɹ ɤ ɩɪɚɜɨɦɭ ɤɪɚɸ ɹɱɟɣɤɢ (Ⱥ2). ȼ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ ɜɫɟɝɞɚ ɧɭɠɧɨ ɨɛɪɚɬɢɬɶ ɜɧɢɦɚɧɢɟ ɧɚ ɪɚɡɞɟɥɢɬɟɥɶɧɵɣ ɡɧɚɤ ɰɟɥɨɣ ɢ ɞɪɨɛɧɨɣ ɱɚɫɬɢ ɱɢɫɥɚ (ȼ2). ɉɪɢ ɮɨɪɦɚɬɢɪɨɜɚɧɢɢ ɱɢɫɥɨɜɵɯ ɞɚɧɧɵɯ ɧɭɠɧɨ ɨɛɪɚɬɢɬɶɫɹ ɤ Ɏɨɪɦɚɬ ɹɱɟɟɤ, ɞɚɥɟɟ ɜ ɨɤɧɟ ɜɵɛɪɚɬɶ ɡɚɤɥɚɞɤɭ ɑɢɫɥɨ ɢ ɚɤɬɢɜɢɪɨɜɚɬɶ ɧɭɠɧɵɣ ɮɨɪɦɚɬ ɢɡ ɫɩɢɫɤɚ ɑɢɫɥɨɜɨɣ ɮɨɪɦɚɬ. ȿɫɥɢ ɨɬɫɭɬɫɬɜɭɟɬ ɧɭɠɧɵɣ ɮɨɪɦɚɬ, ɬɨ ɦɨɠɧɨ ɫɨɡɞɚɬɶ ɫɜɨɣ ɩɨɥɶɡɨɜɚɬɟɥɶɫɤɢɣ ɮɨɪɦɚɬ. Ɉɞɧɚɤɨ ɩɨɥɶɡɨɜɚɬɟɥɶɫɤɢɣ ɮɨɪɦɚɬ ɰɟɥɟɫɨɨɛɪɚɡɧɨ ɮɨɪɦɢɪɨɜɚɬɶ ɞɥɹ ɜɵɯɨɞɧɵɯ ɞɚɧɧɵɯ. 14

1.2. Ɉ ɩɪɟɢɦɭɳɟɫɬɜɚɯ MS Excel ɩɪɢ ɢɡɭɱɟɧɢɢ ɨɫɧɨɜ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ 

ɉɪɢ ɜɧɟɫɟɧɢɢ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ ɦɨɠɟɬ ɜɨɡɧɢɤɧɭɬɶ ɫɢɬɭɚɰɢɹ, ɤɨɝɞɚ ɜɦɟɫɬɨ ɱɢɫɟɥ ɜ ɹɱɟɣɤɟ ɛɭɞɟɬ ɜɢɞɧɚ ɬɨɥɶɤɨ ɪɟɲɟɬɤɚ (Ⱥ1). ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɧɭɠɧɨ ɭɜɟɥɢɱɢɬɶ ɲɢɪɢɧɭ ɫɬɨɥɛɰɚ Ⱥ1. Ɍɚɤ ɤɚɤ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ ɦɨɠɟɬ ɛɵɬɶ ɞɨɫɬɚɬɨɱɧɨ ɦɧɨɝɨ, ɬɨ ɩɪɢ ɢɯ ɡɚɧɟɫɟɧɢɢ ɧɭɠɧɨ ɩɨɥɶɡɨɜɚɬɶɫɹ ɦɟɯɚɧɢɡɦɨɦ ɚɜɬɨɡɚɩɨɥɧɟɧɢɹ. ɉɪɨɫɬɟɣɲɢɣ ɫɥɭɱɚɣ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɩɪɨɫɬɨɦ ɤɨɩɢɪɨɜɚɧɢɢ ɞɚɧɧɵɯ ɡɚɧɟɫɟɧɧɵɯ ɜ ɨɞɧɭ ɢɡ ɹɱɟɟɤ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɜɵɞɟɥɹɟɬɫɹ ɹɱɟɣɤɚ (Ⱥ1), ɤɭɪɫɨɪ ɧɚɜɨɞɢɬɫɹ ɧɚ ɩɪɚɜɵɣ ɧɢɠɧɢɣ ɭɝɨɥ ɹɱɟɣɤɢ ɞɨ ɩɨɹɜɥɟɧɢɹ ɦɚɪɤɟɪɚ ɚɜɬɨɡɚɩɨɥɧɟɧɢɹ ɜ ɜɢɞɟ ɤɪɟɫɬɚ, ɧɚɠɢɦɚɟɬɫɹ ɥɟɜɚɹ ɤɥɚɜɢɲɚ ɦɵɲɢ ɢ ɩɪɨɬɹɠɤɨɣ ɡɚɩɨɥɧɹɟɦ ɞɪɭɝɢɟ ɹɱɟɣɤɢ (Ⱥ1:Ⱥ3). Ɇɨɠɧɨ ɩɨɫɥɟ ɚɤɬɢɜɢɡɚɰɢɢ ɹɱɟɣɤɢ (Ⱥ1) ɩɪɨɬɹɠɤɭ ɨɫɭɳɟɫɬɜɢɬɶ ɩɪɚɜɨɣ ɤɥɚɜɢɲɟɣ. Ɂɚɬɟɦ ɟɟ ɨɬɩɭɫɬɢɬɶ ɢ ɜ ɤɨɧɬɟɤɫɬɧɨɦ ɦɟɧɸ ɜɵɛɪɚɬɶ ɩɭɧɤɬ ɉɪɨɝɪɟɫɫɢɹ. ȼ ɩɨɹɜɢɜɲɟɦɫɹ ɨɤɧɟ ɭɫɬɚɧɨɜɢɬɶ ɩɚɪɚɦɟɬɪɵ ɞɥɹ ɡɚɩɨɥɧɟɧɢɹ ɹɱɟɟɤ ɞɚɧɧɵɦɢ. ɇɨ ɟɫɬɶ ɛɨɥɟɟ ɩɪɨɫɬɨɣ ɢ ɭɞɨɛɧɵɣ ɫɩɨɫɨɛ, ɤɨɬɨɪɵɣ ɩɨɡɜɨɥɹɟɬ ɤɨɧɬɪɨɥɢɪɨɜɚɬɶ ɡɧɚɱɟɧɢɹ ɞɚɧɧɵɯ ɜ ɯɨɞɟ ɚɜɬɨɡɚɩɨɥɧɟɧɢɹ. Ɂɚɧɨɫɢɦ ɜ ɩɟɪɜɵɟ ɞɜɟ ɹɱɟɣɤɢ (Ⱥ1, Ⱥ2) ɞɚɧɧɵɟ ɢ ɜɵɞɟɥɹɟɦ ɢɯ. Ʉɭɪɫɨɪ ɭɫɬɚɧɚɜɥɢɜɚɟɦ ɜ ɧɢɠɧɢɣ ɩɪɚɜɵɣ ɭɝɨɥ ɜɬɨɪɨɣ ɹɱɟɣɤɢ ɢ ɥɟɜɨɣ ɤɥɚɜɢɲɟɣ ɡɚɩɨɥɧɹɟɦ ɩɪɨɬɹɠɤɨɣ ɧɭɠɧɵɟ ɹɱɟɣɤɢ. ɉɪɨɝɪɚɦɦɚ ɩɨɤɚɡɵɜɚɟɬ ɡɧɚɱɟɧɢɟ ɬɟɤɭɳɟɣ ɩɨɫɥɟɞɧɟɣ ɹɱɟɣɤɢ ɩɪɢ ɩɪɨɬɹɠɤɟ (Ⱥ5). ɉɨ ɩɟɪɜɵɦ ɞɜɭɦ ɡɧɚɱɟɧɢɹɦ ɞɚɧɧɵɯ ɚɜɬɨɦɚɬɢɱɟɫɤɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɲɚɝ ɢɯ ɢɡɦɟɧɟɧɢɹ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɩɨɥɭɱɚɟɦ ɩɹɬɶ ɡɧɚɱɟɧɢɣ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ (Ⱥ1:Ⱥ5) ɜ ɜɢɞɟ ɚɪɢɮɦɟɬɢɱɟɫɤɨɣ ɩɪɨɝɪɟɫɫɢɢ ɨɬ 2 ɞɨ 6. ȼ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɩɟɪɜɵɯ ɞɜɭɯ ɡɧɚɱɟɧɢɣ ɩɪɨɝɪɟɫɫɢɢ ɩɪɢ ɩɪɨɬɹɠɤɟ ɜɧɢɡ ɢ ɜɩɪɚɜɨ ɩɪɨɢɫɯɨɞɢɬ ɭɜɟɥɢɱɟɧɢɟ (ɭɦɟɧɶɲɟɧɢɟ) ɡɧɚɱɟɧɢɣ ɩɪɨɝɪɟɫɫɢɢ, ɚ ɩɪɢ ɩɪɨɬɹɠɤɟ ɜɜɟɪɯ ɢɥɢ ɜɥɟɜɨ – ɭɦɟɧɶɲɟɧɢɟ (ɭɜɟɥɢɱɟɧɢɟ). ɑɚɫɬɨ ɜ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ ɧɭɠɧɨ ɨɬɦɟɬɢɬɶ ɞɧɢ ɧɟɞɟɥɢ, ɦɟɫɹɰɚ ɝɨɞɚ ɢ ɬ.ɩ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɦɨɠɧɨ ɫ ɩɨɦɨɳɶɸ ɦɟɯɚɧɢɡɦɚ ɚɜɬɨɡɚɩɨɥɧɟɧɢɹ ɫɮɨɪɦɢɪɨɜɚɬɶ ɢɫɯɨɞɧɵɟ ɞɚɧɧɵɟ. Ⱦɥɹ ɷɬɨɝɨ ɧɭɠɧɨ ɡɚɧɟɫɬɢ ɧɚɡɜɚɧɢɹ ɞɧɹ ɧɟɞɟɥɢ ɢɥɢ ɦɟɫɹɰɚ, ɚ ɡɚɬɟɦ ɚɧɚɥɨɝɢɱɧɨ, ɫ ɩɨɦɨɳɶɸ ɥɟɜɨɣ ɤɥɚɜɢɲɟɣ ɡɚɩɨɥɧɢɬɶ ɹɱɟɣɤɢ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɵɦɢ ɢɦɟɧɚɦɢ ɞɧɟɣ ɧɟɞɟɥɢ ɢɥɢ ɦɟɫɹɰɟɜ ɢɡ ɜɫɬɪɨɟɧɧɵɯ ɫɩɢɫɤɨɜ.

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1. Ɉ ɦɨɞɟɥɢɪɨɜɚɧɢɢ, ɪɟɲɟɧɢɢ ɡɚɞɚɱ, ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɢ ɢ MS Excel

ɉɪɢ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɦɨɠɧɨ ɫɮɨɪɦɢɪɨɜɚɬɶ ɫɜɨɢ ɩɨɥɶɡɨɜɚɬɟɥɶɫɤɢɟ ɫɩɢɫɤɢ, ɫɨɫɬɨɹɳɢɟ ɢɡ ɬɟɤɫɬɚ. Ⱦɥɹ ɷɬɨɝɨ ɫɧɚɱɚɥɚ ɮɨɪɦɢɪɭɟɦ ɧɚ ɥɢɫɬɟ ɩɨɥɶɡɨɜɚɬɟɥɶɫɤɢɣ ɫɩɢɫɨɤ, ɤɨɬɨɪɵɣ ɩɨɥɧɨɫɬɶɸ ɜɵɞɟɥɹɟɦ. Ɂɚɬɟɦ ɱɟɪɟɡ ɩɚɪɚɦɟɬɪɵ ɩɪɢɥɨɠɟɧɢɹ ɜɵɯɨɞɢɦ ɧɚ ɂɡɦɟɧɢɬɶ ɫɩɢɫɤɢ. ȼ ɩɨɹɜɢɜɲɟɦɫɹ ɨɤɧɟ ɋɩɢɫɤɢ ɳɟɥɤɚɟɦ ɧɚ ɤɧɨɩɤɟ ɂɦɩɨɪɬ ɢ ɤɧɨɩɤɟ ɈɄ. ɉɨɫɥɟ ɡɚɩɨɥɧɟɧɢɹ ɬɚɛɥɢɰɵ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ ɦɨɠɧɨ ɨɫɭɳɟɫɬɜɢɬɶ ɮɨɪɦɚɬɢɪɨɜɚɧɢɟ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɝɪɭɩɩ ɒɪɢɮɬ, ȼɵɪɚɜɧɢɜɚɧɢɟ ɢ ɑɢɫɥɨ ɧɚ ɡɚɤɥɚɞɤɟ Ƚɥɚɜɧɚɹ. ɉɪɢ ɮɨɪɦɚɬɢɪɨɜɚɧɢɢ ɠɟɥɚɬɟɥɶɧɨ ɞɟɥɚɬɶ ɬɚɤ ɱɬɨɛɵ ɧɟ ɢɡɦɟɧɹɥɢɫɶ ɲɢɪɢɧɚ ɫɬɨɥɛɰɚ ɢ ɜɵɫɨɬɚ ɫɬɪɨɤ. ɗɬɨ ɩɨɡɜɨɥɢɬ ɢɫɤɥɸɱɢɬɶ ɢɡɦɟɧɟɧɢɹ ɜ ɞɪɭɝɢɯ ɬɚɛɥɢɰɚɯ, ɤɨɬɨɪɵɟ ɛɭɞɭɬ ɪɚɫɩɨɥɚɝɚɬɶɫɹ ɧɚ ɥɢɫɬɟ. ɉɪɢ ɢɡɦɟɧɟɧɢɢ ɪɚɡɦɟɪɨɜ ɹɱɟɟɤ ɫ ɢɫɯɨɞɧɵɦɢ ɞɚɧɧɵɦɢ ɰɟɥɟɫɨɨɛɪɚɡɧɟɟ ɜ ɩɟɪɜɭɸ ɨɱɟɪɟɞɶ ɭɦɟɧɶɲɢɬɶ ɜɟɥɢɱɢɧɭ ɢɫɩɨɥɶɡɭɟɦɨɝɨ ɲɪɢɮɬɚ. ȼ ɬɚɛɥɢɰɚɯ ɜɵɯɨɞɧɵɯ ɞɚɧɧɵɯ ɞɨɥɠɧɵ ɜɫɟɝɞɚ ɩɪɢɫɭɬɫɬɜɨɜɚɬɶ ɪɚɫɱɟɬɧɵɟ ɜɵɪɚɠɟɧɢɹ. ȿɫɥɢ ɜɵɱɢɫɥɟɧɢɹ ɨɬɫɭɬɫɬɜɭɸɬ, ɬɨ ɧɭɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɩɪɢɥɨɠɟɧɢɟ MS Word. ȼɫɟ ɪɚɫɱɟɬɧɵɟ ɜɵɪɚɠɟɧɢɹ ɧɚɱɢɧɚɸɬɫɹ ɫɨ ɡɧɚɤɚ ɪɚɜɟɧɫɬɜɚ. ɉɪɢ ɜɧɟɫɟɧɢɢ ɡɧɚɤɚ ɪɚɜɟɧɫɬɜɚ ɜ ɹɱɟɣɤɭ ɚɤɬɢɜɢɡɢɪɭɟɬɫɹ ɫɩɢɫɨɤ ɮɨɪɦɭɥ ɜ ɨɤɧɟ ɂɦɹ. ɉɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɮɭɧɤɰɢɣ ɧɭɠɧɨ ɩɨɦɧɢɬɶ ɨ ɪɚɡɪɟɲɟɧɧɨɦ ɱɢɫɥɟ ɜɥɨɠɟɧɢɣ. Ɉɞɧɚɤɨ ɜɥɨɠɟɧɢɹɦɢ ɧɟ ɧɭɠɧɨ ɭɜɥɟɤɚɬɶɫɹ. Ʌɭɱɲɟ ɫɮɨɪɦɢɪɨɜɚɬɶ ɩɪɨɦɟɠɭɬɨɱɧɵɟ ɜɵɱɢɫɥɟɧɢɹ ɜ ɜɢɞɟ ɩɚɪɚɦɟɬɪɨɜ. ȼ ɤɚɱɟɫɬɜɟ ɚɪɝɭɦɟɧɬɨɜ ɰɟɥɟɫɨɨɛɪɚɡɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɫɫɵɥɤɢ (ɚɞɪɟɫɚ) ɧɚ ɞɚɧɧɵɟ. ɗɬɨ ɩɨɡɜɨɥɹɟɬ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ ɚɜɬɨɦɚɬɢɱɟɫɤɢ ɩɨɥɭɱɚɬɶ ɪɟɡɭɥɶɬɚɬɵ. ɉɪɢ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɜɫɟɝɞɚ ɧɭɠɧɨ ɫɨɡɞɚɜɚɬɶ ɬɚɛɥɢɰɵ ɩɚɪɚɦɟɬɪɨɜ, ɤɨɧɫɬɚɧɬ ɢ ɤɨɷɮɮɢɰɢɟɧɬɨɜ, ɤɨɬɨɪɵɟ ɢɫɩɨɥɶɡɭɸɬɫɹ ɜ ɪɚɫɱɟɬɧɵɯ ɜɵɪɚɠɟɧɢɹɯ. ɉɪɢ ɜɧɟɫɟɧɢɢ ɜ ɮɨɪɦɭɥɵ ɜ ɤɚɱɟɫɬɜɟ ɚɪɝɭɦɟɧɬɨɜ ɫɫɵɥɤɢ ɧɚ ɤɨɧɫɬɚɧɬɵ (ɤɨɷɮɮɢɰɢɟɧɬɵ) ɫɪɚɡɭ ɢɯ ɞɟɥɚɬɶ ɚɛɫɨɥɸɬɧɵɦɢ ɫ ɩɨɦɨɳɶɸ ɤɥɚɜɢɲɢ F4. ȿɫɥɢ ɧɭɠɧɨ ɫɞɟɥɚɬɶ ɚɛɫɨɥɸɬɧɵɦ ɚɞɪɟɫ ɫɬɨɥɛɰɚ ɢɥɢ ɫɬɪɨɤɢ, ɬɨ ɧɭɠɧɨ ɳɟɥɤɧɭɬɶ ɩɨ ɤɥɚɜɢɲɟ F4 ɧɟɫɤɨɥɶɤɨ ɪɚɡ ɞɥɹ ɫɧɹɬɢɹ ɫɢɦɜɨɥɚ $ ɫ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɱɚɫɬɢ ɚɞɪɟɫɚ. ɂɫɩɨɥɶɡɨɜɚɧɢɟ ɚɛɫɨɥɸɬɧɵɯ ɚɞɪɟɫɨɜ ɩɨɡɜɨɥɹɟɬ ɩɪɢ ɩɪɢɦɟɧɟɧɢɢ ɚɜɬɨɡɚɩɨɥɧɟɧɢɹ ɞɥɹ ɞɪɭɝɢɯ ɡɧɚɱɟɧɢɣ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ ɫɨɯɪɚɧɹɬɶ ɧɟɢɡɦɟɧɧɵɦɢ ɚɞɪɟɫɚ ɤɨɧɫɬɚɧɬ ɜ ɪɚɫɱɟɬɧɵɯ ɜɵɪɚɠɟɧɢɹɯ. ȿɫɥɢ ɜ ɜɵɪɚɠɟɧɢɢ ɧɭɠɧɨ, ɧɚɩɪɢɦɟɪ, ɜɨɡɜɟɫɬɢ ɜ ɫɬɟɩɟɧɶ ɮɭɧɤɰɢɸ, ɬɨ ɫɥɟɞɭɟɬ ɩɨɦɧɢɬɶ ɨ ɬɨɦ, ɱɬɨ ɤɨɧɫɬɪɭɤɰɢɹ ɮɭɧɤɰɢɢ ɫ ɚɪɝɭɦɟɧɬɨɦ ɧɟɞɟɥɢɦɚ. Ɍɨ ɟɫɬɶ ɩɪɢ ɬɚɛɭɥɹɰɢɢ ɮɭɧɤɰɢɢ ‫ ݕ‬ൌ ‫݊݅ݏ‬ଶ ሺ‫ݔ‬ሻ ɜ ɪɚɫɱɟɬɧɨɟ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɤɨɧɤɪɟɬɧɨɝɨ ɡɧɚɱɟɧɢɹ, ɡɚɩɢɫɚɧɧɨɝɨ ɜ ɹɱɟɣɤɟ Ⱥ1, ɞɨɥɠɧɨ ɜɵɝɥɹɞɟɬɶ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ ൌ •‹ሺ‫ͳܣ‬ሻ̰ ʹ. ɂɧɨɝɞɚ ɧɟɨɛɯɨɞɢɦɨ ɫɨɡɞɚɬɶ ɮɭɧɤɰɢɸ, ɤɨɬɨɪɨɣ ɧɟɬ ɜ ɫɩɢɫɤɟ. Ɍɨɝɞɚ ɦɨɠɧɨ ɜɨɫɩɨɥɶɡɨɜɚɬɶɫɹ ɦɟɯɚɧɢɡɦɨɦ ɫɨɡɞɚɧɢɹ ɩɨɥɶɡɨɜɚɬɟɥɶɫɤɨɣ ɮɭɧɤɰɢɢ. ɉɨɥɶ16

1.2. Ɉ ɩɪɟɢɦɭɳɟɫɬɜɚɯ MS Excel ɩɪɢ ɢɡɭɱɟɧɢɢ ɨɫɧɨɜ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ 

ɡɨɜɚɬɟɥɶɫɤɭɸ ɮɭɧɤɰɢɸ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɩɪɢ ɜɤɥɸɱɟɧɢɢ ɪɚɡɪɟɲɟɧɢɹ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɦɚɤɪɨɫɨɜ ɢɥɢ ɩɪɢ ɫɨɯɪɚɧɟɧɢɢ ɮɚɣɥɚ ɫ ɩɨɞɞɟɪɠɤɨɣ ɦɚɤɪɨɫɨɜ. ɋɨɡɞɚɞɢɦ ɮɭɧɤɰɢɸ ɫ 3-ɦɹ ɩɚɪɚɦɟɬɪɚɦɢ (ɤɨɷɮɮɢɰɢɟɧɬɚɦɢ) ɫɥɟɞɭɸɳɟɝɨ ɜɢɞɚ ‫ ݕ‬ൌ ܽ ‫ ݔ כ‬൅ ܾ ‫݊݅ݏ כ‬ଶ ሺܿ ‫ݔ כ‬ሻɞɥɹ ɪɚɫɱɟɬɚ ɩɪɢ ɡɚɞɚɧɧɵɯ ɡɧɚɱɟɧɢɹɯ ‫ݔ‬. Ɉɛɪɚɬɢɦɫɹ ɱɟɪɟɡ ɡɚɤɥɚɞɤɭ Ɋɚɡɪɚɛɨɬɱɢɤ ɤ ɤɧɨɩɤɟ Visual Basic ɢ ɜɵɡɨɜɟɦ ɨɤɧɨ ɪɟɞɚɤɬɨɪɚ VBA. ȼɵɛɢɪɚɟɦ ɩɭɧɤɬ ɫɨɡɞɚɧɢɹ ɧɨɜɨɝɨ ɦɨɞɭɥɹ Module ɜ ɦɟɧɸ Insert. ɋɧɚɱɚɥɚ ɜɧɨɫɢɦ ɫɥɨɜɨ Function, ɞɚɥɟɟ ɢɦɹ ɧɚɲɟɣ ɮɭɧɤɰɢɢ Polzfun ɢ ɨɛɨɡɧɚɱɟɧɢɟ ɜɯɨɞɧɵɯ ɩɟɪɟɦɟɧɧɵɯ, ɧɟɨɛɯɨɞɢɦɵɯ ɞɥɹ ɪɚɫɱɟɬɚ ɡɧɚɱɟɧɢɹ ɮɭɧɤɰɢɢ. Ɏɨɪɦɚɬ ɚɪɝɭɦɟɧɬɨɜ ɞɟɥɚɟɦ ɩɨ ɭɦɨɥɱɚɧɢɸ. Ⱥɜɬɨɦɚɬɢɱɟɫɤɢ ɮɨɪɦɢɪɭɟɬɫɹ ɬɟɤɫɬ ɨɤɨɧɱɚɧɢɟ ɮɭɧɤɰɢɢ. Ɉɫɬɚɥɨɫɶ ɜɧɟɫɬɢ ɬɟɤɫɬ ɩɪɨɝɪɚɦɦɵ ɫɚɦɨɣ ɮɭɧɤɰɢɢ, ɤɨɬɨɪɵɣ ɩɨɧɹɬɟɧ ɛɟɡ ɨɛɴɹɫɧɟɧɢɣ. Ɂɚɤɪɵɜɚɟɦ ɨɤɧɚ ɪɟɞɚɤɬɨɪɚ, ɫɨɯɪɚɧɹɟɦ ɮɚɣɥ ɫ ɩɨɞɞɟɪɠɤɨɣ ɦɚɤɪɨɫɨɜ. Ɍɟɩɟɪɶ ɫɨɡɞɚɧɧɚɹ ɮɭɧɤɰɢɹ ɧɚɯɨɞɢɬɫɹ ɜ Ɇɚɫɬɟɪɟ ɮɭɧɤɰɢɣ ɜ ɤɚɬɟɝɨɪɢɢ Ɉɩɪɟɞɟɥɟɧɧɵɟ ɩɨɥɶɡɨɜɚɬɟɥɟɦ. ɉɪɢ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɜɫɬɚɜɤɢ ɮɭɧɤɰɢɢ ɜ ɪɚɫɱɟɬɧɭɸ ɮɨɪɦɭɥɭ ɨɛɪɚɳɚɟɦɫɹ ɤ Ɇɚɫɬɟɪɭ ɮɭɧɤɰɢɣ ɢ ɜɵɞɟɥɹɟɦ ɟɟ ɢɡ ɫɩɢɫɤɚ. Ɂɚɪɚɧɟɟ ɫɨɡɞɚɟɦ ɬɚɛɥɢɰɵ ɜɯɨɞɧɵɯ ɞɚɧɧɵɯ ɞɥɹ ɚɪɝɭɦɟɧɬɚ ɢ ɩɚɪɚɦɟɬɪɨɜ (ɤɨɷɮɮɢɰɢɟɧɬɨɜ) ɮɭɧɤɰɢɢ. ɉɪɢ ɜɧɟɫɟɧɢɢ ɚɞɪɟɫɨɜ ɩɚɪɚɦɟɬɪɨɜ ɫ ɩɨɦɨɳɶɸ ɤɥɚɜɢɲɢ F4 ɞɟɥɚɟɦ ɢɯ ɚɞɪɟɫɚ ɚɛɫɨɥɸɬɧɵɦɢ. ɉɨɫɥɟ ɩɨɥɭɱɟɧɢɹ ɪɟɡɭɥɶɬɚɬɨɜ ɞɥɹ ɡɧɚɱɟɧɢɹ ‫ ݔ‬ൌ െͳ ɫ ɩɨɦɨɳɶɸ ɦɟɯɚɧɢɡɦɚ ɚɜɬɨɡɚɩɨɥɧɟɧɢɹ ɬɚɛɭɥɢɪɭɟɦ ɡɧɚɱɟɧɢɹ ɮɭɧɤɰɢɢ ɞɥɹ ɞɪɭɝɢɯ ɞɚɧɧɵɯ. ȼ ɫɥɭɱɚɟ ɨɬɫɭɬɫɬɜɢɹ ɩɟɪɟɫɱɟɬɚ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɩɨɥɶɡɨɜɚɬɟɥɶɫɤɨɣ ɮɭɧɤɰɢɢ ɞɥɹ ɞɪɭɝɢɯ ɡɧɚɱɟɧɢɣ ɚɪɝɭɦɟɧɬɚ ɧɭɠɧɨ ɨɛɪɚɬɢɬɶɫɹ ɤ ɉɚɪɚɦɟɬɪɵ Excel, ɜɵɛɪɚɬɶ ɩɭɧɤɬ Ɏɨɪɦɭɥɵ ɢ ɜ ɉɚɪɚɦɟɬɪɵ ɜɵɱɢɫɥɟɧɢɣ ɜɤɥɸɱɢɬɶ ɚɜɬɨɦɚɬɢɱɟɫɤɢ. Ⱦɚɥɟɟ ɮɨɪɦɚɬɢɪɭɟɦ ɬɚɛɥɢɰɵ ɢ ɫɨɡɞɚɟɦ ɩɪɢɦɟɱɚɧɢɟ ɫ ɪɚɫɱɟɬɧɨɣ ɮɨɪɦɭɥɨɣ ɱɟɪɟɡ ɤɨɧɬɟɤɫɬɧɨɟ ɦɟɧɸ ɞɥɹ ɜɬɨɪɨɝɨ ɡɧɚɱɟɧɢɹ ɬɚɛɭɥɢɪɨɜɚɧɧɨɣ ɮɭɧɤɰɢɢ. Ɏɨɪɦɭɥɭ ɤɨɩɢɪɭɟɦ ɢɡ ɋɬɪɨɤɢ ɮɨɪɦɭɥɵ ɢ ɜɫɬɚɜɥɹɟɦ ɜ ɩɪɢɦɟɱɚɧɢɟ. ɂɡ ɩɪɢɦɟɱɚɧɢɹ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨ ɭɞɚɥɹɟɦ ɜɫɬɚɜɤɭ ɫɜɟɞɟɧɢɹ ɨ ɩɨɥɶɡɨɜɚɬɟɥɟ, ɤɨɬɨɪɚɹ ɹɜɥɹɟɬɫɹ ɱɚɫɬɨ ɥɢɲɧɟɣ. ɇɟ ɡɚɛɵɜɚɟɦ ɩɪɢ ɷɬɨɦ ɜɤɥɸɱɢɬɶ ɪɟɠɢɦ ɩɨɤɚɡɚ ɩɪɢɦɟɱɚɧɢɹ ɱɟɪɟɡ ɤɨɧɬɟɤɫɬɧɨɟ ɦɟɧɸ ɹɱɟɣɤɢ. ɑɚɫɬɨ ɩɪɢ ɩɟɱɚɬɢ ɩɪɢɦɟɱɚɧɢɹ ɧɟ ɩɟɱɚɬɚɸɬɫɹ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɧɟɨɛɯɨɞɢɦɨ ɜɤɥɸɱɢɬɶ ɪɚɡ17

1. Ɉ ɦɨɞɟɥɢɪɨɜɚɧɢɢ, ɪɟɲɟɧɢɢ ɡɚɞɚɱ, ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɢ ɢ MS Excel

ɪɟɲɟɧɢɟ ɩɟɱɚɬɢ ɩɪɢɦɟɱɚɧɢɣ. Ⱦɥɹ ɷɬɨɝɨ ɧɚ ɜɤɥɚɞɤɟ Ɋɚɡɦɟɬɤɚ ɫɬɪɚɧɢɰɵ ɨɬɤɪɵɬɶ ɨɤɧɨ ɉɚɪɚɦɟɬɪɵ ɩɟɱɚɬɢ ɢ ɧɚ ɡɚɤɥɚɞɤɟ Ʌɢɫɬ ɜ ɫɩɢɫɤɟ ɩɪɢɦɟɱɚɧɢɟ ɜɵɛɪɚɬɶ Ʉɚɤ ɧɚ ɥɢɫɬɟ. ɉɪɢ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨɦ ɩɪɨɫɦɨɬɪɟ ɭɜɢɞɢɦ ɫɨɡɞɚɧɧɵɟ ɩɪɢɦɟɱɚɧɢɹ. Ɍɚɛɥɢɰɵ ɬɚɛɭɥɢɪɨɜɚɧɧɨɣ ɮɭɧɤɰɢɢ ɜ ɞɚɥɶɧɟɣɲɟɦ ɢɫɩɨɥɶɡɭɟɦ ɩɪɢ ɪɚɫɫɦɨɬɪɟɧɢɢ ɝɪɚɮɢɱɟɫɤɨɣ ɤɨɦɩɨɧɟɧɬɵ. Ɍɚɤ ɤɚɤ ɡɞɟɫɶ ɭɩɨɦɹɧɭɥɢ ɨ ɩɟɱɚɬɢ ɬɨ, ɱɬɨɛɵ ɬɚɛɥɢɰɵ ɧɟ «ɪɚɡɜɚɥɢɜɚɥɢɫɶ» ɩɨ ɪɚɡɧɵɦ ɥɢɫɬɚɦ ɜ ɧɚɱɚɥɟ ɪɚɛɨɬɵ ɧɟɨɛɯɨɞɢɦɨ ɪɚɡɛɢɜɚɬɶ ɥɢɫɬɵ ɧɚ ɮɨɪɦɚɬɵ ɱɟɪɟɡ ɡɚɤɥɚɞɤɭ ȼɢɞ ɢ ɤɧɨɩɤɭ Ɋɚɡɦɟɬɤɚ ɫɬɪɚɧɢɰɵ. Ⱦɚɥɟɟ ɥɭɱɲɟ ɜɟɪɧɭɬɶɫɹ ɤ ɪɟɠɢɦɭ Ɉɛɵɱɧɵɣ ɢ ɬɚɛɥɢɰɵ (ɝɪɚɮɢɤɢ) ɪɚɫɩɨɥɚɝɚɬɶ ɜ ɨɛɨɡɧɚɱɟɧɧɵɯ ɝɪɚɧɢɰɚɯ ɥɢɫɬɨɜ, ɤɨɬɨɪɵɟ ɩɨ ɭɦɨɥɱɚɧɢɸ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɮɨɪɦɚɬɭ Ⱥ4. ȼɚɠɧɨ ɧɟ ɬɨɥɶɤɨ ɨɛɟɫɩɟɱɢɬɶ ɩɪɚɜɢɥɶɧɵɟ ɪɚɫɱɟɬɵ, ɧɨ ɢ ɧɚɝɥɹɞɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɪɟɡɭɥɶɬɚɬɵ. ɉɪɢ ɷɬɨɦ ɧɭɠɧɨ ɬɨɱɧɨ ɭɤɚɡɚɬɶ ɪɚɡɦɟɪɧɨɫɬɢ ɩɨɥɭɱɟɧɧɵɯ ɱɢɫɟɥ. ɋɬɚɧɞɚɪɬɧɵɟ ɮɨɪɦɚɬɵ ɱɢɫɟɥ ɧɟ ɜɫɟɝɞɚ ɩɨɡɜɨɥɹɸɬ ɷɬɨ ɫɞɟɥɚɬɶ. ɉɨɷɬɨɦɭ ɫɨɡɞɚɸɬ ɩɨɥɶɡɨɜɚɬɟɥɶɫɤɢɟ ɮɨɪɦɚɬɵ. Ⱦɥɹ ɫɨɡɞɚɧɢɹ ɩɨɥɶɡɨɜɚɬɟɥɶɫɤɨɝɨ ɮɨɪɦɚɬɚ ɧɭɠɧɨ ɜɵɡɜɚɬɶ ɨɤɧɨ Ɏɨɪɦɚɬ ɹɱɟɟɤ. ȼ ɨɤɧɟ ɧɚ ɡɚɤɥɚɞɤɟ ɑɢɫɥɨ ɜɵɛɢɪɚɟɦ ɩɭɧɤɬ ȼɫɟ ɮɨɪɦɚɬɵ. ȼ ɨɤɧɟ Ɍɢɩ ɜɵɞɟɥɹɟɦ ɮɨɪɦɚɬ 0,00 ɢɥɢ ɤɚɤɨɣ-ɬɨ ɞɪɭɝɨɣ ɢ ɞɨɩɢɫɵɜɚɟɦ ɜ ɚɩɨɫɬɪɨɮɚɯ, ɧɚɩɪɢɦɟɪ, “ɤɦ”. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɩɨɥɭɱɚɟɦ ɱɢɫɥɨɜɨɣ ɮɨɪɦɚɬ ɫ ɞɜɭɦɹ ɡɧɚɤɚɦɢ ɩɨɫɥɟ ɡɚɩɹɬɨɣ ɢ ɩɨɞɩɢɫɶɸ «ɤɦ». ɇɚ ɪɢɫɭɧɤɟ ɩɨɤɚɡɚɧ ɩɪɢɦɟɪ ɩɪɢɦɟɧɟɧɢɹ ɫɨɡɞɚɧɧɨɝɨ ɩɨɥɶɡɨɜɚɬɟɥɶɫɤɨɝɨ ɮɨɪɦɚɬɚ. ɉɪɢ ɷɬɨɦ ɫɧɚɱɚɥɚ ɜɵɞɟɥɢɥɢ ɧɭɠɧɵɟ ɹɱɟɣɤɢ, ɚ ɡɚɬɟɦ ɜ ɫɩɢɫɤɟ ȼɫɟ ɮɨɪɦɚɬɵ ɧɚɲɥɢ ɫɨɡɞɚɧɧɵɣ, ɜɵɞɟɥɢɥɢ ɟɝɨ ɢ ɳɟɥɤɧɭɥɢ ɧɚ ɤɧɨɩɤɟ ɈɄ. Ƚɪɚɮɢɱɟɫɤɚɹ ɤɨɦɩɨɧɟɧɬɚ ɧɟɨɛɯɨɞɢɦɚ ɞɥɹ ɧɚɝɥɹɞɧɨɝɨ ɨɬɨɛɪɚɠɟɧɢɹ ɪɟɡɭɥɶɬɚɬɨɜ ɪɚɫɱɟɬɨɜ ɢɥɢ ɩɪɨɜɟɞɟɧɢɹ ɦɨɞɟɥɢɪɨɜɚɧɢɹ. ɇɚ ɝɪɚɮɢɤɚɯ ɦɨɠɧɨ ɬɚɤɠɟ ɨɩɪɟɞɟɥɢɬɶ ɭɪɚɜɧɟɧɢɟ ɪɟɝɪɟɫɫɢɢ ɢ ɩɨɫɬɪɨɢɬɶ ɥɢɧɢɸ ɬɪɟɧɞɚ ɤɚɤ ɫ ɩɪɨɝɧɨɡɨɦ ɜɩɟɪɟɞ, ɬɚɤ ɢ ɧɚɡɚɞ ɧɚ ɡɚɞɚɧɧɵɟ ɢɧɬɟɪɜɚɥɵ. ɉɪɢ ɩɨɫɬɪɨɟɧɢɢ ɝɪɚɮɢɤɨɜ (ɞɢɚɝɪɚɦɦ) ɫɧɚɱɚɥɚ ɜɵɞɟɥɢɬɶ ɫɬɨɥɛɰɵ (ɫɬɪɨɤɢ) ɜ ɬɚɛɥɢɰɟ ɢɫɯɨɞɧɵɯ ɢ (ɢɥɢ) ɜɵɯɨɞɧɵɯ ɞɚɧɧɵɯ. ɉɪɢ ɷɬɨɦ ɨɛɵɱɧɨ ɜɵɞɟɥɟɧɢɟ ɩɪɨɢɡɜɨɞɢɬɫɹ ɩɪɨɬɹɠɤɨɣ ɤɭɪɫɨɪɚ ɩɨ ɧɭɠɧɵɦ ɹɱɟɣɤɚɦ, ɚ ɡɚɬɟɦ ɧɭɠɧɨ ɨɛɪɚɬɢɬɶɫɹ ɤ ɝɪɭɩɩɟ Ⱦɢɚɝɪɚɦɦɚ ɧɚ ɡɚɤɥɚɞɤɟ ȼɫɬɚɜɤɚ ɞɥɹ ɨɛɪɚɳɟɧɢɹ ɤ ɧɭɠɧɨɦɭ ɬɢɩɭ ɝɪɚɮɢɤɚ (ɞɢɚɝɪɚɦɦɵ). ɑɚɫɬɨ ɧɭɠɧɵɟ ɞɥɹ ɜɵɞɟɥɟɧɢɹ ɫɬɨɥɛɰɵ (ɫɬɪɨɤɢ) ɧɟ ɪɚɫɩɨɥɨɠɟɧɵ ɪɹɞɨɦ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɞɥɹ ɜɵɞɟɥɟɧɢɹ ɧɟɫɦɟɠɧɵɯ ɫɬɨɥɛɰɨɜ (ɫɬɪɨɤ) ɧɭɠɧɨ ɧɚɠɚɬɶ ɧɚ ɝɪɭɩɩɨɜɭɸ ɤɥɚɜɢɲɭ Ctrl ɢ ɩɪɨɞɨɥɠɢɬɶ ɜɵɞɟɥɟɧɢɟ. Ⱦɥɹ ɝɪɚɮɢɱɟɫɤɨɣ ɢɥɥɸɫɬɪɚɰɢɢ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ɢ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɜ ɨɫɧɨɜɧɨɦ ɛɭɞɟɦ ɢɫɩɨɥɶɡɨɜɚɬɶ ɬɨɱɟɱɧɵɣ ɬɢɩ ɞɢɚɝɪɚɦɦɵ. ɉɪɢ ɷɬɨɦ ɛɭɞɟɦ ɜɵɛɢɪɚɬɶ ɫɥɟɞɭɸɳɢɟ ɜɢɞɵ: ɬɨɱɟɱɧɚɹ ɫ ɨɬɪɟɡɤɚɦɢ ɢɥɢ ɝɥɚɞɤɢɦɢ ɤɪɢɜɵɦɢ, ɫ ɦɚɪɤɟɪɚɦɢ, ɛɟɡ ɦɚɪɤɟɪɨɜ ɢɥɢ ɬɨɥɶɤɨ ɦɚɪɤɟɪɵ. Ɍɨɝɞɚ ɞɚɧɧɵɟ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɚɪɝɭɦɟɧɬɚɦ, 18

1.2. Ɉ ɩɪɟɢɦɭɳɟɫɬɜɚɯ MS Excel ɩɪɢ ɢɡɭɱɟɧɢɢ ɨɫɧɨɜ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ 

ɛɭɞɭɬ ɪɚɫɩɨɥɚɝɚɬɶɫɹ ɩɨ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɨɫɢ ɤɨɨɪɞɢɧɚɬ, ɚ ɞɚɧɧɵɟ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɮɭɧɤɰɢɢ – ɩɨ ɜɟɪɬɢɤɚɥɶɧɨɣ ɨɫɢ ɤɨɨɪɞɢɧɚɬ. Ⱦɥɹ ɩɨɜɵɲɟɧɢɹ ɤɨɧɬɪɚɫɬɧɨɫɬɢ ɢ ɬɨɱɧɨɫɬɢ ɢɡɨɛɪɚɠɟɧɢɹ ɩɪɨɢɡɜɨɞɢɦ ɮɨɪɦɚɬɢɪɨɜɚɧɢɟ ɨɬɞɟɥɶɧɵɯ ɷɥɟɦɟɧɬɨɜ ɝɪɚɮɢɤɨɜ ɱɟɪɟɡ ɢɯ ɤɨɧɬɟɤɫɬɧɨɟ ɦɟɧɸ ɢ ɨɛɪɚɳɟɧɢɹ ɤ ɩɭɧɤɬɭ Ɏɨɪɦɚɬ ɪɹɞɚ ɞɚɧɧɵɯ, ɨɛɥɚɫɬɢ ɞɢɚɝɪɚɦɦɵ, ɬɨɱɤɢ ɞɚɧɧɵɯ ɢ ɬ.ɩ. Ⱦɥɹ ɮɨɪɦɚɬɢɪɨɜɚɧɢɹ ɬɨɱɤɢ ɞɚɧɧɵɯ ɧɭɠɧɨ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨ ɧɚ ɧɟɣ ɞɜɚɠɞɵ ɳɟɥɤɧɭɬɶ, ɚ ɡɚɬɟɦ ɜɵɡɵɜɚɬɶ ɤɨɧɬɟɤɫɬɧɨɟ ɦɟɧɸ. ȼ ɤɚɱɟɫɬɜɟ ɩɪɢɦɟɪɚ ɩɪɢɜɟɞɟɦ ɝɪɚɮɢɤ ɬɚɛɭɥɢɪɨɜɚɧɧɨɣ ɮɭɧɤɰɢɢ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɩɨɥɶɡɨɜɚɬɟɥɶɫɤɨɣ ɮɭɧɤɰɢɢ ɢ ɞɨɩɨɥɧɢɬɟɥɶɧɨɝɨ ɫɬɨɥɛɰɚ ɫ ɫɨɫɬɚɜɥɟɧɧɵɦ ɪɚɫɱɟɬɧɵɦ ɜɵɪɚɠɟɧɢɟɦ (ɮɨɪɦɭɥɨɣ) ɫɨ ɫɬɚɧɞɚɪɬɧɨɣ ɮɭɧɤɰɢɟɣ. ɉɟɪɟɞ ɮɨɪɦɢɪɨɜɚɧɢɟɦ ɞɨɩɨɥɧɢɬɟɥɶɧɨɝɨ ɫɬɨɥɛɰɚ ɜɫɬɚɜɢɥɢ ɫɬɨɥɛɟɰ ɞɥɹ ɨɬɞɟɥɟɧɢɹ ɟɝɨ ɨɬ ɬɚɛɥɢɰɵ ɤɨɷɮɮɢɰɢɟɧɬɨɜ. ɋɨɡɞɚɟɦ ɮɨɪɦɭɥɭ ɞɥɹ ɪɚɫɱɟɬɨɜ ɡɧɚɱɟɧɢɹ ɮɭɧɤɰɢɢ ɞɥɹ ɩɟɪɜɨɝɨ ɡɧɚɱɟɧɢɹ ‫ݔ‬. ɉɪɢ ɷɬɨɦ ɚɞɪɟɫɚ (ɫɫɵɥɤɢ) ɞɚɧɧɵɯ ɮɨɪɦɢɪɭɟɦ ɳɟɥɱɤɚɦɢ ɩɨ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦ ɹɱɟɣɤɚɦ. ȿɫɥɢ ɚɞɪɟɫ ɞɨɥɠɟɧ ɛɵɬɶ ɚɛɫɨɥɸɬɧɵɦ, ɬɨ ɳɟɥɤɚɟɦ ɧɚ ɤɥɚɜɢɲɟ F4. ȼ ɤɨɧɰɟ ɮɨɪɦɢɪɨɜɚɧɢɹ ɳɟɥɤɚɟɦ ɧɚ ɤɥɚɜɢɲɟ Enter. ȿɫɥɢ ɷɬɨɝɨ ɧɟ ɞɟɥɚɬɶ, ɬɨ ɜ ɪɚɫɱɟɬɧɨɟ ɜɵɪɚɠɟɧɢɟ ɛɭɞɭɬ ɡɚɩɢɫɵɜɚɬɶɫɹ ɚɞɪɟɫɚ ɚɤɬɢɜɧɵɯ ɹɱɟɟɤ. ɍɛɟɠɞɚɟɦɫɹ, ɱɬɨ ɪɟɡɭɥɶɬɚɬɵ ɜɵɱɢɫɥɟɧɢɣ ɫɨɜɩɚɞɚɸɬ ɢ, ɢɫɩɨɥɶɡɭɹ ɚɜɬɨɡɚɩɨɥɧɟɧɢɟ, ɮɨɪɦɢɪɭɟɦ ɮɨɪɦɭɥɵ ɞɥɹ ɨɫɬɚɥɶɧɵɯ ɡɧɚɱɟɧɢɣ ‫ݔ‬. ɉɨɫɥɟ ɞɨɩɨɥɧɢɬɟɥɶɧɨɝɨ ɮɨɪɦɚɬɢɪɨɜɚɧɢɹ ɢ ɜɵɞɟɥɟɧɢɹ ɫɬɨɥɛɰɨɜ ɚɪɝɭɦɟɧɬɚ ɢ ɮɭɧɤɰɢɢ ɨɛɪɚɳɚɟɦɫɹ ɤ ɝɪɚɮɢɤɭ Ɍɨɱɟɱɧɚɹ ɫ ɝɥɚɞɤɢɦɢ ɤɪɢɜɵɦɢ ɢ ɦɚɪɤɟɪɚɦɢ. Ⱦɨɛɚɜɥɹɟɦ ɨɫɧɨɜɧɵɟ ɥɢɧɢɢ ɫɟɬɤɢ ɞɥɹ ɨɫɢ ɚɪɝɭɦɟɧɬɚ ɱɟɪɟɡ ɟɟ ɤɨɧɬɟɤɫɬɧɨɟ ɦɟɧɸ. ɂɫɩɨɥɶɡɭɹ Ɇɚɤɟɬɵ ɞɢɚɝɪɚɦɦ ɜɫɬɚɜɥɹɟɦ ɧɚɡɜɚɧɢɟ ɨɫɟɣ ɢ ɞɢɚɝɪɚɦɦɵ. ɍɞɚɥɹɟɦ ɧɟɧɭɠɧɵɟ ɷɥɟɦɟɧɬɵ. ȿɫɥɢ ɜɨ ɜɬɨɪɨɦ ɫɬɨɥɛɰɟ ɬɚɛɭɥɢɪɨɜɚɧɧɵɣ ɮɭɧɤɰɢɢ ɫɞɟɥɚɥɢ ɪɚɫɱɟɬɵ ɩɨ ɞɪɭɝɨɣ ɮɨɪɦɭɥɟ, ɬɨ ɩɪɢ ɜɵɞɟɥɟɧɢɢ ɬɪɟɯ ɫɬɨɥɛɰɨɜ ɩɨɥɭɱɢɥɢ ɝɪɚɮɢɱɟɫɤɨɟ ɢɡɨɛɪɚɠɟɧɢɟ ɞɜɭɯ ɪɚɡɧɵɯ ɤɪɢɜɵɯ ɝɪɚɮɢɤɨɜ. ɏɨɬɟɥɨɫɶ ɧɚɩɨɦɧɢɬɶ ɨɛ ɨɞɧɨɣ ɯɚɪɚɤɬɟɪɧɨɣ ɨɲɢɛɤɟ. ɉɪɢ ɨɛɪɚɳɟɧɢɢ ɤ ɬɢɩɭ Ƚɪɚɮɢɤ ɜ ɩɨɫɥɟɞɧɟɦ ɫɥɭɱɚɟ ɩɨɥɭɱɢɥɢ ɛɵ ɬɪɢ ɤɪɢɜɵɟ, ɚ ɩɨ ɨɫɢ ɚɪɝɭɦɟɧɬɨɜ ɛɵɥɢ ɛɵ ɫɮɨɪɦɢɪɨɜɚɧɵ ɧɨɦɟɪɚ ɫɬɪɨɤ ɬɚɛɥɢɰ ɨɬ 1 ɞɨ 21, ɚ ɧɟ ɡɧɚɱɟɧɢɹ ɚɪɝɭɦɟɧɬɚ ‫ݔ‬. Ɋɚɫɫɦɨɬɪɢɦ ɦɟɬɨɞɢɤɭ ɩɨɫɬɪɨɟɧɢɹ ɩɪɨɫɬɟɣɲɢɯ ɝɟɨɦɟɬɪɢɱɟɫɤɢɯ ɮɢɝɭɪ, ɤɨɬɨɪɚɹ ɩɨɧɚɞɨɛɢɬɶɫɹ ɩɪɢ ɪɟɲɟɧɢɢ ɡɚɞɚɱ. ɉɪɨɫɬɟɣɲɢɦ ɷɥɟɦɟɧɬɨɦ ɮɢɝɭɪɵ ɞɥɹ ɧɚɫ ɛɭɞɟɬ ɩɪɹɦɚɹ ɥɢɧɢɹ. ɉɪɹɦɚɹ ɥɢɧɢɹ ɡɚɞɚɟɬɫɹ ɞɜɭɦɹ ɤɨɨɪɞɢɧɚɬɚɦɢ ɟɟ ɤɨɧɰɨɜ. Ɉɛɨɡɧɚɱɢɦ ɡɚɝɨɥɨɜɤɢ ɫɬɨɥɛɰɨɜ ɬɚɛɥɢɰɵ ɤɨɨɪɞɢɧɚɬ. Ⱦɥɹ ɧɚɛɥɸɞɟɧɢɹ ɩɨɫɬɪɨɟɧɢɹ ɮɢɝɭɪ ɜɵɞɟɥɢɦ ɫ ɡɚɩɚɫɨɦ ɨɛɥɚɫɬɶ ɹɱɟɟɤ ɬɚɛɥɢɰɵ, ɜ ɤɨɬɨɪɭɸ ɛɭ19

1. Ɉ ɦɨɞɟɥɢɪɨɜɚɧɢɢ, ɪɟɲɟɧɢɢ ɡɚɞɚɱ, ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɢ ɢ MS Excel

ɞɟɦ ɡɚɩɢɫɵɜɚɬɶ ɤɨɨɪɞɢɧɚɬɵ ɷɥɟɦɟɧɬɨɜ ɮɢɝɭɪ, ɢ ɨɛɪɚɬɢɦɫɹ ɤ ɬɢɩɭ ɞɢɚɝɪɚɦɦ Ɍɨɱɟɱɧɵɣ ɝɪɚɮɢɤ ɫ ɩɪɹɦɵɦɢ ɨɬɪɟɡɤɚɦɢ ɢ ɦɚɪɤɟɪɚɦɢ. ɑɟɪɟɡ ɤɨɧɬɟɤɫɬɧɨɟ ɦɟɧɸ ɨɫɟɣ ɭɫɬɚɧɨɜɢɦ ɮɢɤɫɢɪɨɜɚɧɧɵɟ ɦɢɧɢɦɚɥɶɧɵɟ ɢ ɦɚɤɫɢɦɚɥɶɧɵɟ ɡɧɚɱɟɧɢɹ ɨɫɟɣ, ɞɨɛɚɜɢɦ ɨɫɧɨɜɧɵɟ ɥɢɧɢɢ ɫɟɬɤɢ. Ɋɚɫɬɹɧɟɦ ɨɛɥɚɫɬɶ ɞɢɚɝɪɚɦɦɵ ɬɚɤ, ɱɬɨɛɵ ɹɱɟɣɤɢ ɫɟɬɤɢ ɞɢɚɝɪɚɦɦɵ ɫɬɚɥɢ ɤɜɚɞɪɚɬɧɵɦɢ. Ɍɟɩɟɪɶ ɦɨɠɧɨ ɧɚɱɢɧɚɬɶ ɜɧɨɫɢɬɶ ɤɨɨɪɞɢɧɚɬɵ ɷɥɟɦɟɧɬɨɜ ɮɢɝɭɪ ɜ ɬɚɛɥɢɰɭ ɢ ɩɪɢ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɢɯ ɤɨɪɪɟɤɬɢɪɨɜɚɬɶ. ɉɟɪɜɵɦ ɩɨɫɬɪɨɢɦ ɬɪɟɭɝɨɥɶɧɢɤ. Ʉɨɨɪɞɢɧɚɬɵ ɛɭɞɟɦ ɩɪɢɜɹɡɵɜɚɬɶ ɤ ɭɡɥɚɦ ɫɟɬɤɢ. Ʉɨɨɪɞɢɧɚɬɵ ɜ ɧɚɲɟɦ ɫɥɭɱɚɟ ɢɦɟɸɬ ɭɫɥɨɜɧɭɸ ɪɚɡɦɟɪɧɨɫɬɶ. Ɂɚɧɟɫɟɦ ɤɨɨɪɞɢɧɚɬɵ ɥɢɧɢɣ ɞɜɭɯ ɫɬɨɪɨɧ ɬɪɟɭɝɨɥɶɧɢɤɚ. Ʉɚɤ ɜɢɞɧɨ ɤɨɨɪɞɢɧɚɬɵ ɤɨɧɰɚ ɨɞɧɨɣ ɥɢɧɢɢ ɫɨɜɩɚɞɚɸɬ ɫ ɤɨɨɪɞɢɧɚɬɚɦɢ ɧɚɱɚɥɨ ɞɪɭɝɨɣ. Ɇɟɠɞɭ ɹɱɟɣɤɚɦɢ ɤɨɨɪɞɢɧɚɬ ɥɢɧɢɣ ɨɫɬɚɜɥɹɟɦ ɩɭɫɬɭɸ ɫɬɪɨɤɭ. Ɉɫɬɚɥɨɫɶ ɫɮɨɪɦɢɪɨɜɚɬɶ ɤɨɨɪɞɢɧɚɬɵ ɬɪɟɬɟɣ ɫɬɨɪɨɧɵ ɬɪɟɭɝɨɥɶɧɢɤɚ. Ʉɨɨɪɞɢɧɚɬɚ ɧɚɱɚɥɚ ɫɨɜɩɚɞɚɟɬ ɫ ɤɨɨɪɞɢɧɚɬɨɣ ɤɨɧɰɚ ɜɬɨɪɨɣ ɥɢɧɢɢ, ɚ ɤɨɨɪɞɢɧɚɬɚ ɤɨɧɰɚ ɫɨɜɩɚɞɚɟɬ ɫ ɧɚɱɚɥɨɦ ɩɟɪɜɨɣ ɥɢɧɢɢ. ɉɨɥɭɱɢɥɢ ɢɡɨɛɪɚɠɟɧɢɟ ɬɪɟɭɝɨɥɶɧɢɤɚ. ȼ ɯɨɞɟ ɩɨɫɬɪɨɟɧɢɹ ɢɧɨɝɞɚ ɰɟɥɟɫɨɨɛɪɚɡɧɨ ɨɬɤɨɪɪɟɤɬɢɪɨɜɚɬɶ ɩɚɪɚɦɟɬɪɵ ɫɟɬɤɢ ɞɢɚɝɪɚɦɦɵ. Ⱥɧɚɥɨɝɢɱɧɨ ɡɚɞɚɟɦ ɤɨɨɪɞɢɧɚɬɵ ɞɥɹ ɩɨɫɬɪɨɟɧɢɹ ɩɪɹɦɨɭɝɨɥɶɧɢɤɚ. ɉɪɢ ɷɬɨɦ ɮɨɪɦɢɪɨɜɚɬɶ ɤɨɨɪɞɢɧɚɬɵ ɥɢɧɢɣ ɦɨɠɧɨ ɫ ɩɨɦɨɳɶɸ ɫɫɵɥɨɤ ɧɚ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɤɨɨɪɞɢɧɚɬɵ ɞɪɭɝɢɯ ɥɢɧɢɣ (ɫɦ. ɩɪɢɦɟɱɚɧɢɟ). ɗɬɨ ɭɩɪɨɳɚɟɬ ɡɚɞɚɱɭ ɩɨɫɬɪɨɟɧɢɹ ɡɚɦɤɧɭɬɵɯ ɮɢɝɭɪ. Ɍɟɩɟɪɶ ɩɨɫɬɪɨɢɦ ɩɪɚɜɢɥɶɧɵɣ ɲɟɫɬɢɝɪɚɧɧɢɤ. ȼɵɛɟɪɟɦ ɜ ɤɚɱɟɫɬɜɟ ɰɟɧɬɪɚ ɲɟɫɬɢɝɪɚɧɧɢɤɚ ɫɟɪɟɞɢɧɭ ɹɱɟɣɤɢ ɫɟɬɤɢ. Ɋɚɫɱɟɬ ɤɨɨɪɞɢɧɚɬ ɤɨɧɰɨɜ ɥɢɧɢɣ ɝɪɚɧɟɣ ɛɭɞɟɦ ɞɟɥɚɬɶ ɩɨ ɫɥɟɞɭɸɳɢɦ ɮɨɪɦɭɥɚɦ: ‫ ݔ‬ൌ ‫ݔ‬௖ ൅ ܴ ‫ ߮ݏ݋ܿ כ‬, ‫ ݕ‬ൌ ‫ݕ‬௖ ൅ ܴ ‫ ߮݊݅ݏ כ‬, ɝɞɟ‫ݔ‬௖ ǡ ‫ݕ‬௖ - ɤɨɨɪɞɢɧɚɬɵ ɰɟɧɬɪɚ ɲɟɫɬɢɭɝɨɥɶɧɢɤɚ, ܴ- ɪɚɞɢɭɫ ɨɤɪɭɠɧɨɫɬɢ, ɜ ɤɨɬɨɪɭɸ ɜɩɢɫɚɧ ɲɟɫɬɢɭɝɨɥɶɧɢɤɚ, ߮ – ɭɝɨɥ ɤɪɚɬɧɵɣ 600 ɢ ɨɬɫɱɢɬɵɜɚɟɦɵɣ ɨɬ ɨɫɢ ɨɪɞɢɧɚɬ ɩɪɨɬɢɜ ɱɚɫɨɜɨɣ ɫɬɪɟɥɤɢ.

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1.2. Ɉ ɩɪɟɢɦɭɳɟɫɬɜɚɯ MS Excel ɩɪɢ ɢɡɭɱɟɧɢɢ ɨɫɧɨɜ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ 

ȼɨɡɶɦɟɦ ɪɚɞɢɭɫ ɪɚɜɧɵɣ 10 ɭɫɥɨɜɧɵɦ ɟɞɢɧɢɰɚɦ. Ɂɚɧɟɫɟɦ ɜɟɥɢɱɢɧɭ ɪɚɞɢɭɫɚ (D25) ɢ ɤɨɨɪɞɢɧɚɬɵ ɰɟɧɬɪɚ (D23,E23) ɜ ɬɚɛɥɢɰɭ ɩɚɪɚɦɟɬɪɨɜ. ȼ ɹɱɟɣɤɭ ȿ25 ɡɚɧɟɫɟɦ ɧɚɱɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɭɝɥɚ ߮ ɞɥɹ ɪɚɫɱɟɬɚ ɧɚɱɚɥɶɧɨɣ ɤɨɨɪɞɢɧɚɬɵ ɩɟɪɜɨɣ ɝɪɚɧɢ. Ɏɨɪɦɭɥɵ ɪɚɫɱɟɬɚ ɩɪɟɞɫɬɚɜɥɟɧɵ ɜ ɩɪɢɦɟɱɚɧɢɹɯ. Ⱦɚɥɟɟ ɜ ɹɱɟɣɤɟ ȿ26 ɮɨɪɦɢɪɭɟɦ ɡɧɚɱɟɧɢɟ ɭɝɥɚ ߮ ɞɥɹ ɪɚɫɱɟɬɚ ɤɨɧɟɱɧɨɣ ɤɨɨɪɞɢɧɚɬɵ ɩɟɪɜɨɣ ɝɪɚɧɢ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɤɨɧɫɬɚɧɬɵ ʌ. ȼ ɮɭɧɤɰɢɢ ɭɝɨɥ ɩɨɞɫɬɚɜɥɹɟɦ ɜ ɪɚɡɦɟɪɧɨɫɬɢ ɪɚɞɢɚɧ. Ʉɨɨɪɞɢɧɚɬɵ ɧɚɱɚɥɚ ɜɬɨɪɨɣ ɝɪɚɧɢ ɮɨɪɦɢɪɭɟɦ ɢɡ ɤɨɨɪɞɢɧɚɬ ɤɨɧɰɚ ɩɪɟɞɵɞɭɳɟɣ. Ⱦɥɹ ɪɚɫɱɟɬɚ ɤɨɨɪɞɢɧɚɬ ɤɨɧɰɚ ɮɨɪɦɢɪɭɟɦ ɡɧɚɱɟɧɢɹ ɭɝɥɚ ߮ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɡɧɚɱɟɧɢɹ ɭɝɥɚ ɜ ɹɱɟɣɤɟ ȿ26. ȼ ɪɟɡɭɥɶɬɚɬɟ ɜɢɞɢɦ ɧɚ ɝɪɚɮɢɤɟ ɞɜɟ ɝɪɚɧɢ ɲɟɫɬɢɝɪɚɧɧɢɤɚ. Ⱥɧɚɥɨɝɢɱɧɨ ɮɨɪɦɢɪɭɟɦ ɤɨɨɪɞɢɧɚɬɵ ɞɪɭɝɢɯ ɝɪɚɧɟɣ. ɉɪɢ ɢɡɦɟɧɟɧɢɢ ɤɨɨɪɞɢɧɚɬ ɰɟɧɬɪɚ ɛɭɞɟɦ ɧɚɛɥɸɞɚɬɶ ɩɟɪɟɦɟɳɟɧɢɟ ɮɢɝɭɪɵ, ɚ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɜɟɥɢɱɢɧɵ ɪɚɞɢɭɫɚ – ɭɜɟɥɢɱɟɧɢɟ ɢɥɢ ɭɦɟɧɶɲɟɧɢɟ ɪɚɡɦɟɪɨɜ ɮɢɝɭɪɵ. ɉɪɢ ɭɜɟɥɢɱɟɧɢɢ ɱɢɫɥɚ ɝɪɚɧɟɣ ɞɨ 15-20 ɜ ɦɧɨɝɨɭɝɨɥɶɧɢɤɟ ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɯɨɪɨɲɟɟ ɢɡɨɛɪɚɠɟɧɢɟ ɨɤɪɭɠɧɨɫɬɢ. ɇɚ ɝɪɚɮɢɤɚɯ ɦɨɠɧɨ ɢɡɨɛɪɚɠɚɬɶ ɜɟɤɬɨɪɵ. ɋɨɡɞɚɞɢɦ ɬɚɛɥɢɰɭ ɤɨɨɪɞɢɧɚɬ (Ⱥ3:ȼ19), ɜɵɞɟɥɢɦ ɟɟ ɢ ɨɛɪɚɬɢɦɫɹ ɤ ɞɢɚɝɪɚɦɦɟ Ɍɨɱɟɱɧɚɹ ɫ ɩɪɹɦɵɦɢ ɨɬɪɟɡɤɚɦɢ ɢ ɦɚɪɤɟɪɚɦɢ. Ɂɚɞɚɞɢɦ ɤɨɨɪɞɢɧɚɬɵ ɥɢɧɢɣ ɜɟɤɬɨɪɨɜ. ɉɪɨɢɡɜɟɞɟɦ ɮɨɪɦɚɬɢɪɨɜɚɧɢɟ ɪɹɞɚ ɞɚɧɧɵɯ. ȼɵɡɵɜɚɟɦ ɤɨɧɬɟɤɫɬɧɨɟ ɦɟɧɸ ɥɢɧɢɢ ɥɸɛɨɝɨ ɜɟɤɬɨɪɚ ɢ ɜɵɯɨɞɢɦ ɧɚ ɩɭɧɤɬ Ɏɨɪɦɚɬ ɪɹɞɚ ɞɚɧɧɵɯ. ȼɵɛɢɪɚɟɦ ɜ ɨɤɧɟ ɩɭɧɤɬ Ɍɢɩ ɥɢɧɢɢ ɢ ɜ ɉɚɪɚɦɟɬɪɵ ɫɬɪɟɥɤɢ ɜɵɛɢɪɚɟɦ ɩɪɹɦɭɸ ɞɥɹ Ɍɢɩ ɧɚɱɚɥɚ ɢ ɫɬɪɟɥɤɭ - ɞɥɹ Ɍɢɩ ɨɤɨɧɱɚɧɢɹ. ȼ ɉɚɪɚɦɟɬɪɵ ɦɚɪɤɟɪɚ ɭɫɬɚɧɚɜɥɢɜɚɟɦ ɇɟɬ ɞɥɹ Ɍɢɩ ɦɚɪɤɟɪɚ. ɉɪɨɢɡɜɟɞɟɦ ɫɥɨɠɟɧɢɟ ɜɬɨɪɨɝɨ ɢ ɬɪɟɬɶɟɝɨ ɜɟɤɬɨɪɚ. ɉɨɥɭɱɢɦ ɬɪɟɬɢɣ ɜɟɤɬɨɪ ɫ ɤɨɨɪɞɢɧɚɬɚɦɢ ‫ݔ‬௖ଶ ൌ ‫ݔ‬ଵଵ , ‫ݔ‬௖ଵ ൌ ‫ݔ‬ଵଶ ൅ ሺ‫ݔ‬ଶଶ െ ‫ݔ‬ଶଵ ሻ , ‫ݕ‬௖ଶ ൌ ‫ݕ‬ଵଵ , ‫ݕ‬௖ଵ ൌ ‫ݕ‬ଵଶ ൅ ሺ‫ݕ‬ଶଶ െ ‫ݕ‬ଶଵ ሻ , ଵ ɝɞɟ ‫ݔ‬௖ ɢ ‫ݕ‬௖ଵ – ɤɨɨɪɞɢɧɚɬɵ ɧɚɱɚɥɚ ɜɟɤɬɨɪɚ ɫɭɦɦɵ ɜɟɤɬɨɪɨɜ, ‫ݔ‬௖ଶ ɢ ‫ݕ‬௖ଶ – ɤɨɨɪɞɢɧɚɬɵ ɤɨɧɰɚ ɜɟɤɬɨɪɚ ɫɭɦɦɵ ɜɟɤɬɨɪɨɜ, ‫ݔ‬ଵଵ ɢ ‫ݕ‬ଵଵ – ɤɨɨɪɞɢɧɚɬɵ ɧɚɱɚɥɚ ɩɟɪɜɨɝɨ ɜɟɤɬɨɪɚ ɫɭɦɦɵ, ‫ݔ‬ଵଶ ɢ ‫ݕ‬ଵଶ – ɤɨɨɪɞɢɧɚɬɵ ɤɨɧɰɚ ɩɟɪɜɨɝɨ ɜɟɤɬɨɪɚ ɫɭɦɦɵ, ‫ݔ‬ଶଵ ɢ ‫ݕ‬ଶଵ – ɤɨɨɪɞɢɧɚɬɵ ɧɚɱɚɥɚ ɜɬɨɪɨɝɨ ɜɟɤɬɨɪɚ ɫɭɦɦɵ, ‫ݔ‬ଶଶ ɢ ‫ݕ‬ଶଶ – ɤɨɨɪɞɢɧɚɬɵ ɤɨɧɰɚ ɜɬɨɪɨɝɨ ɜɟɤɬɨɪɚ ɫɭɦɦɵ. ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɩɪɢɜɟɞɟɧɧɵɦɢ ɮɨɪɦɭɥɚɦɢ, ɜɵɱɢɫɥɢɦ ɤɨɨɪɞɢɧɚɬɵ ɫɭɦɦɚɪɧɨɝɨ ɜɟɤɬɨɪɚ ɜ ɬɚɛɥɢɰɟ. 21

1. Ɉ ɦɨɞɟɥɢɪɨɜɚɧɢɢ, ɪɟɲɟɧɢɢ ɡɚɞɚɱ, ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɢ ɢ MS Excel

ɉɪɢ ɫɥɨɠɟɧɢɢ ɝɟɨɦɟɬɪɢɱɟɫɤɢ ɧɭɠɧɨ ɫɦɟɫɬɢɬɶ ɜɬɨɪɨɣ ɜɟɤɬɨɪ ɫɭɦɦɵ. Ⱦɥɹ ɷɬɨɝɨ ɩɪɟɨɛɪɚɡɭɟɦ ɤɨɨɪɞɢɧɚɬɵ ɬɪɟɬɶɟɝɨ ɜɟɤɬɨɪɚ ɜ ɬɚɛɥɢɰɟ (Ⱥ9:ȼ10) ɢ ɡɚɩɢɲɟɦ ɢɯ ɫɨ ɫɦɟɳɟɧɢɹɦɢ ɜ ɹɱɟɣɤɢ Ⱥ12:ȼ13 (ɫɦ. ɩɪɢɦɟɱɚɧɢɹ). ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɤɨɨɪɞɢɧɚɬɵ ɧɚɱɚɥɚ ɜɬɨɪɨɝɨ ɜɟɤɬɨɪɚ ɫɭɦɦɵ ɫɨɜɦɟɳɚɟɬɫɹ ɫ ɤɨɧɰɨɦ ɩɟɪɜɨɝɨ ɜɟɤɬɨɪɚ ɫɭɦɦɵ (Ⱥ6:ȼ7). Ɉɫɬɚɥɨɫɶ ɬɟɩɟɪɶ ɜɵɱɢɫɥɢɬɶ ɤɨɨɪɞɢɧɚɬɵ ɫɭɦɦɚɪɧɨɝɨ ɜɟɤɬɨɪɚ ɜ ɹɱɟɣɤɚɯ Ⱥ15:ȼ16 (ɫɦ. ɩɪɢɦɟɱɚɧɢɹ). ɇɚ ɝɪɚɮɢɤɟ ɜɢɞɢɦ ɝɟɨɦɟɬɪɢɱɟɫɤɭɸ ɢɧɬɟɪɩɪɟɬɚɰɢɸ ɫɥɨɠɟɧɢɹ ɜɟɤɬɨɪɨɜ. Ɇɨɠɧɨ ɛɟɡ ɬɪɭɞɚ ɫɨɡɞɚɬɶ ɦɨɞɟɥɶ ɪɚɡɧɨɫɬɢ ɞɜɭɯ ɜɟɤɬɨɪɨɜ. ɋɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɦɨɠɧɨ ɞɥɹ ɜɵɱɢɫɥɟɧɢɣ ɤɨɨɪɞɢɧɚɬ ɪɟɡɭɥɶɬɢɪɭɸɳɢɯ ɜɟɤɬɨɪɨɜ ɫɨɡɞɚɬɶ ɮɭɧɤɰɢɢ ɢɥɢ ɩɪɨɰɟɞɭɪɵ ɞɥɹ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɩɪɨɰɟɫɫɚ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɞɟɣɫɬɜɢɣ ɫ ɜɟɤɬɨɪɚɦɢ.

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1.4. VBA ɢ Excel

1.4. VBA ɢ Excel Visual Basic for Applications (VBA) ɩɨɡɜɨɥɹɟɬ ɚɜɬɨɦɚɬɢɡɢɪɨɜɚɬɶ ɩɪɨɰɟɫɫ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɡɚɞɚɱ ɢ ɨɛɟɫɩɟɱɢɬɶ ɜɵɩɨɥɧɟɧɢɟ ɫɥɨɠɧɵɯ ɪɚɫɱɟɬɨɜ. VBA ɨɬɧɨɫɢɬɫɹ ɤ ɨɛɴɟɤɬɧɨ-ɨɪɢɟɧɬɢɪɨɜɚɧɧɵɦ ɹɡɵɤɚɦ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ ɢ ɪɟɚɥɢɡɭɟɬ ɨɫɧɨɜɧɵɟ ɩɪɢɧɰɢɩɵ ɨɛɴɟɤɬɧɨ-ɨɪɢɟɧɬɢɪɨɜɚɧɧɨɝɨ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ. ɐɟɧɬɪɚɥɶɧɵɦ ɡɜɟɧɨɦ ɨɛɴɟɤɬɧɨ-ɨɪɢɟɧɬɢɪɨɜɚɧɧɨɝɨ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ ɹɜɥɹɟɬɫɹ ɨɛɴɟɤɬ, ɤɨɬɨɪɵɣ ɨɛɥɚɞɚɟɬ ɫɜɨɣɫɬɜɚɦɢ, ɦɟɬɨɞɚɦɢ ɢ ɪɟɚɤɰɢɹɦɢ ɧɚ ɫɨɛɵɬɢɹ. Ɉɛɴɟɤɬ – ɫɨɜɨɤɭɩɧɨɫɬɶ ɤɨɞɨɜ ɢ ɞɚɧɧɵɯ, ɤɨɬɨɪɵɟ ɦɨɠɧɨ ɨɛɪɚɛɚɬɵɜɚɬɶ ɩɪɢ ɧɚɫɬɭɩɥɟɧɢɢ ɤɚɤɢɯ-ɬɨ ɫɨɛɵɬɢɣ. ɗɬɚ ɫɨɜɨɤɭɩɧɨɫɬɶ ɩɨɡɜɨɥɹɟɬ ɨɛɟɫɩɟɱɢɬɶ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɟ ɦɨɞɟɥɟɣ ɫ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦɢ ɢ ɞɟɣɫɬɜɢɹɦɢ ɪɟɚɥɶɧɵɯ ɨɛɴɟɤɬɨɜ. ɋɜɨɣɫɬɜɚ ɟɫɬɶ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ (ɚɬɪɢɛɭɬɵ, ɩɚɪɚɦɟɬɪɵ) ɨɛɴɟɤɬɚ. Ɇɟɬɨɞ ɟɫɬɶ ɧɚɛɨɪ ɞɟɣɫɬɜɢɣ, ɤɨɬɨɪɵɟ ɦɨɠɟɬ ɜɵɩɨɥɧɹɬɶ ɨɛɴɟɤɬ. ɋɨɛɵɬɢɟ ɟɫɬɶ ɞɟɣɫɬɜɢɟ, ɤɨɬɨɪɨɟ ɪɚɫɩɨɡɧɚɟɬɫɹ ɨɛɴɟɤɬɨɦ ɢ ɞɥɹ ɤɨɬɨɪɨɝɨ ɦɨɠɧɨ ɡɚɩɪɨɝɪɚɦɦɢɪɨɜɚɬɶ ɨɬɤɥɢɤ. ɂɧɮɨɪɦɚɰɢɸ ɨɛ ɨɛɴɟɤɬɚɯ, ɢɯ ɫɜɨɣɫɬɜɚɯ, ɦɟɬɨɞɚɯ ɢ ɫɨɛɵɬɢɹɯ ɥɭɱɲɟ ɢɫɤɚɬɶ ɜ ɢɧɬɟɪɧɟɬɟ. Ɉɛɴɟɤɬɨɜ ɞɨɫɬɚɬɨɱɧɨ ɦɧɨɝɨ, ɧɨ ɜ VBA Excel ɩɪɢ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɢ ɢɫɩɨɥɶɡɭɸɬ ɫɥɟɞɭɸɳɢɟ ɨɫɧɨɜɧɵɟ ɨɛɴɟɤɬɵ: Application (ɩɪɢɥɨɠɟɧɢɟ Excel), Workbook (ɮɚɣɥ), Worksheet (ɪɚɛɨɱɢɣ ɥɢɫɬ), Range (ɞɢɚɩɚɡɨɧ), Chart (ɞɢɚɝɪɚɦɦɚ). Ɉɧɢ ɩɪɟɞɫɬɚɜɥɟɧɵ ɜ ɢɟɪɚɪɯɢɱɟɫɤɨɦ ɩɨɪɹɞɤɟ. ɉɪɢɥɨɠɟɧɢɟ Excel ɧɚɯɨɞɢɬɫɹ ɧɚ ɜɟɪɯɧɟɦ ɭɪɨɜɧɟ ɢ ɜɤɥɸɱɚɟɬ ɜ ɫɟɛɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɜɫɟ ɞɪɭɝɢɟ ɨɛɴɟɤɬɵ. ɉɪɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ ɛɭɞɟɦ ɬɚɤɠɟ ɢɫɩɨɥɶɡɨɜɚɬɶ ɨɛɴɟɤɬɵ: UserForm (ɩɨɥɶɡɨɜɚɬɟɥɶɫɤɚɹ ɮɨɪɦɚ), ɷɥɟɦɟɧɬɵ ɭɩɪɚɜɥɟɧɢɹ ɧɚ ɥɢɫɬɟ ɢ ɧɚ ɮɨɪɦɟ. Ɋɚɫɫɦɨɬɪɢɦ ɫɢɧɬɚɤɫɢɫ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɫɜɨɣɫɬɜ, ɦɟɬɨɞɨɜ ɢ ɫɨɛɵɬɢɣ ɨɛɴɟɤɬɨɜ ɩɪɢ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɢ. Ɇɨɠɧɨ ɢɡɦɟɧɢɬɶ ɡɧɚɱɟɧɢɹ ɫɜɨɣɫɬɜ ɨɛɴɟɤɬɚ ɤɚɤ Ɉɛɴɟɤɬ.ɋɜɨɣɫɬɜɨ=Ɂɧɚɱɟɧɢɟ. Ɂɧɚɱɟɧɢɟ ɦɨɠɟɬ ɢɦɟɬɶ ɤɨɧɤɪɟɬɧɨɟ ɡɧɚɱɟɧɢɟ ɢɥɢ True (False). ȿɫɥɢ ɧɭɠɧɨ ɩɨɥɭɱɢɬɶ ɡɧɚɱɟɧɢɟ ɫɜɨɣɫɬɜɚ ɨɛɴɟɤɬɚ, ɬɨ ɉɟɪɟɦɟɧɧɚɹ= Ɉɛɴɟɤɬ.ɋɜɨɣɫɬɜɨ. ɇɚɩɪɢɦɟɪ, ɢɡɦɟɧɢɦ ɧɚɡɜɚɧɢɟ ɭɩɪɚɜɥɹɸɳɟɝɨ ɷɥɟɦɟɧɬɚ Ʉɧɨɩɤɚ ɢ ɡɚɬɟɦ ɡɚɩɢɲɟɦ ɧɚɡɜɚɧɢɟ ɜ ɹɱɟɣɤɟ ɧɚ ɪɚɛɨɱɟɦ ɥɢɫɬɟ ɢ ɧɚ 2-ɦ ɥɢɫɬɟ. CommandButton1.Caption = "Ʉɧɨɩɤɚ" Cells(1, 1) = CommandButton1.Caption Worksheets("Ʌɢɫɬ2").Cells(1, 1) = CommandButton1.Caption 23

1. Ɉ ɦɨɞɟɥɢɪɨɜɚɧɢɢ, ɪɟɲɟɧɢɢ ɡɚɞɚɱ, ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɢ ɢ MS Excel

ȼ 3-ɣ ɫɬɪɨɱɤɟ ɭɤɚɡɚɥɢ ɨɛɴɟɤɬ – 2-ɣ ɥɢɫɬ, ɧɚ ɤɨɬɨɪɨɦ ɧɚɯɨɞɢɬɫɹ ɹɱɟɣɤɚ Ⱥ1. ɗɬɨɬ ɤɨɞ ɦɨɠɧɨ ɜɫɬɚɜɢɬɶ ɞɥɹ ɢɫɩɨɥɧɟɧɢɹ ɜ ɥɸɛɭɸ ɩɪɨɰɟɞɭɪɭ ɚɤɬɢɜɧɨɝɨ ɥɢɫɬɚ. Ɏɪɚɝɦɟɧɬ ɤɨɞɚ ɜɡɹɬ ɢɡ ɩɪɨɰɟɞɭɪɵ ɭɩɪɚɜɥɹɸɳɟɣ ɤɧɨɩɤɢ ɫɨɡɞɚɧɧɨɣ ɧɚ 1-ɦ ɚɤɬɢɜɧɨɦ ɥɢɫɬɟ. Ʉɚɤ ɜɢɞɧɨ ɜɨ ɜɬɨɪɨɣ ɫɬɪɨɱɤɟ ɧɟ ɭɤɚɡɚɧ ɨɛɴɟɤɬ 1-ɝɨ ɚɤɬɢɜɧɨɝɨ ɥɢɫɬɚ. ɋɭɳɟɫɬɜɭɸɬ ɧɟɫɤɨɥɶɤɨ ɫɩɨɫɨɛɨɜ ɜɵɡɨɜɨɜ ɦɟɬɨɞɨɜ. ɋɚɦɵɣ ɩɪɨɫɬɨɣ, ɤɨɝɞɚ ɜ ɦɟɬɨɞɟ ɨɬɫɭɬɫɬɜɭɸɬ ɚɪɝɭɦɟɧɬɵ Ɉɛɴɟɤɬ.Ɇɟɬɨɞ. ɉɨɫɥɟɞɧɹɹ ɬɨɱɤɚ ɜ ɩɪɨɝɪɚɦɦɟ ɧɟ ɫɬɚɜɢɬɫɹ. ɇɚɩɪɢɦɟɪ, ɟɫɥɢ ɧɭɠɧɨ ɡɚɤɪɵɬɶ ɤɧɢɝɭ (ɮɚɣɥ), ɬɨ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɦɟɬɨɞ Close ThisWorkbook. Close. ȿɫɥɢ ɧɭɠɧɨ ɩɟɪɟɞɚɜɚɬɶ ɚɪɝɭɦɟɧɬɵ (ɩɚɪɚɦɟɬɪɵ) ɦɟɬɨɞɭ, ɬɨ ɜ ɫɤɨɛɤɚɯ ɭɤɚɡɵɜɚɸɬɫɹ ɚɪɝɭɦɟɧɬɵ Ɉɛɴɟɤɬ.Ɇɟɬɨɞ (ɚɪɝɭɦɟɧɬ1, ɚɪɝɭɦɟɧɬ2,…). ɋɤɨɛɤɢ ɦɨɠɧɨ ɨɩɭɫɬɢɬɶ Ɉɛɴɟɤɬ.Ɇɟɬɨɞ ɚɪɝɭɦɟɧɬ1, ɚɪɝɭɦɟɧɬ2,…. ȿɫɥɢ ɜ ɦɟɬɨɞɟ ɭɤɚɡɵɜɚɸɬɫɹ ɮɚɤɬɢɱɟɫɤɢɟ ɩɚɪɚɦɟɬɪɵ, ɬɨ ɢɫɩɨɥɶɡɭɟɬɫɹ ɨɩɟɪɚɬɨɪ := Ɉɛɴɟɤɬ.Ɇɟɬɨɞ ɚɪɝɭɦɟɧɬ1:=ɡɧɚɱɟɧɢɟ, ɚɪɝɭɦɟɧɬ2:=ɡɧɚɱɟɧɢɟ… ɉɪɢɜɟɞɟɦ ɩɪɢɦɟɪɵ ɩɪɢɦɟɧɟɧɢɹ ɦɟɬɨɞɚ Add ɫ 4-ɦɹ ɚɪɝɭɦɟɧɬɚɦɢ. ActiveSheet.ChartObjects.Add(100, 30, 250, 200).Select 'Ⱦɨɛɚɜɥɹɟɦ ɞɢɚɝɪɚɦɦɭ ɧɚ ɚɤɬɢɜɧɵɣ ɥɢɫɬ ɢɥɢ ActiveSheet.ChartObjects.Add 100, 30, 250, 200 'Ⱦɨɛɚɜɥɹɟɦ ɞɢɚɝɪɚɦɦɭ ɧɚ ɚɤɬɢɜɧɵɣ ɥɢɫɬ ɢɥɢ ActiveSheet.ChartObjects.Add Left:=100, Top:=30, Width:=250, Height:=200 'Ⱦɨɛɚɜɥɹɟɦ ɞɢɚɝɪɚɦɦɭ ɧɚ ɚɤɬɢɜɧɵɣ ɥɢɫɬ. ɑɚɫɬɨ ɢɫɩɨɥɶɡɭɟɬɫɹ ɦɟɬɨɞ ChartWizard ɞɥɹ ɢɡɦɟɧɟɧɢɣ ɜ ɞɢɚɝɪɚɦɦɟ. Ɇɟɬɨɞ ɢɦɟɟɬ 11 ɚɪɝɭɦɟɧɬɨɜ. Ɇɨɠɧɨ ɫɨɫɬɚɜɥɹɬɶ ɨɬɞɟɥɶɧɨ ɨɩɟɪɚɬɨɪɵ ɞɥɹ ɨɩɪɟɞɟɥɟɧɧɨɝɨ ɚɪɝɭɦɟɧɬɚ ɦɟɬɨɞɚ. ActiveChart.ChartWizard Source:=Range("A1:B38") 'Ɂɚɞɚɟɬɫɹ ɦɚɫɫɢɜ ɞɚɧɧɵɯ ɞɢɚɝɪɚɦɦɵ ActiveChart.ChartWizard Gallery:=xlXYScatterLines 'Ɂɚɞɚɟɬɫɹ ɬɨɱɟɱɧɚɹ ɞɢɚɝɪɚɦɦɚ ɫ ɥɢɧɢɹɦɢ ɢɥɢ ɫɨɫɬɚɜɢɬɶ ɨɞɢɧ ɨɩɟɪɚɬɨɪ ɞɥɹ ɞɜɭɯ ɚɪɝɭɦɟɧɬɨɜ ActiveChart.ChartWizard_ Source:=Range("A1:B38"),Gallery:=xlXYScatterLines. ɑɟɪɬɨɱɤɚ ɩɨɫɥɟ ChartWizard ɭɤɚɡɵɜɚɟɬ ɧɚ ɩɟɪɟɧɨɫ ɡɚɩɢɫɢ ɨɩɟɪɚɬɨɪɚ ɧɚ ɜɬɨɪɭɸ ɫɬɪɨɱɤɭ. ɉɟɪɜɵɣ ɜɚɪɢɚɧɬ ɛɨɥɟɟ ɭɞɨɛɧɵɣ, ɚ ɜɬɨɪɨɣ – ɤɨɦɩɚɤɬɧɟɟ.

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1.4. VBA ɢ Excel

ȼ ɤɚɱɟɫɬɜɟ ɫɨɛɵɬɢɹ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɨɬɤɪɵɬɢɟ ɢɥɢ ɡɚɤɪɵɬɢɟ ɮɚɣɥɚ ɢɥɢ ɮɨɪɦɵ, ɳɟɥɱɨɤ ɦɵɲɢ, ɧɚɠɚɬɢɟ ɤɥɚɜɢɲɢ ɢ ɬ.ɩ. ɋɨɛɵɬɢɟ ɞɥɹ ɤɨɧɤɪɟɬɧɨɝɨ ɨɛɴɟɤɬɚ ɜɵɛɢɪɚɟɬɫɹ ɢɡ ɫɩɢɫɤɚ ɜ ɨɤɧɟ ɪɟɞɚɤɬɨɪɚ ɤɨɞɚ Visual Basic. ɋɥɟɞɭɟɬ ɩɨɦɧɢɬɶ, ɱɬɨ ɩɨɥɧɚɹ ɫɫɵɥɤɚ ɧɚ ɨɛɴɟɤɬ ɫɨɫɬɨɢɬ ɢɡ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɜɥɨɠɟɧɧɵɯ ɢɦɟɧ ɨɛɴɟɤɬɨɜ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɢɯ ɢɟɪɚɪɯɢɟɣ. ɗɬɚ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɜ ɨɛɳɟɦ ɫɥɭɱɚɟ ɧɚɱɢɧɚɟɬɫɹ ɫ Application ɢ ɡɚɤɚɧɱɢɜɚɟɬɫɹ ɢɦɟɧɟɦ ɩɨɫɥɟɞɧɟɝɨ ɨɛɴɟɤɬɚ. ɇɚɩɪɢɦɟɪ, Application.Workbooks("Ʉɧɢɝɚ1").Worksheets("Ʌɢɫɬ2").Range("ȼ2"). Ɉɞɧɚɤɨ, ɟɫɥɢ ɧɟɬ ɞɪɭɝɨɝɨ ɚɤɬɢɜɧɨɝɨ ɩɪɢɥɨɠɟɧɢɹ, ɬɨ ɨɛɴɟɤɬ Application ɨɩɭɫɤɚɟɬɫɹ. ȿɫɥɢ ɜɟɪɯɧɢɣ ɩɨ ɢɟɪɚɪɯɢɢ ɨɛɴɟɤɬ ɨɬɧɨɫɢɬɟɥɶɧɨ ɩɨɫɥɟɞɧɟɝɨ ɨɛɴɟɤɬɚ ɚɤɬɢɜɧɵɣ, ɬɨ ɟɝɨ ɢ ɞɪɭɝɢɟ ɜɵɫɲɢɟ ɨɛɴɟɤɬɵ ɦɨɠɧɨ ɧɟ ɭɤɚɡɵɜɚɬɶ. ȿɫɥɢ ɚɤɬɢɜɧɚ ɤɧɢɝɚ, ɬɨ Worksheets("Ʌɢɫɬ2").Range("ȼ2"). ȿɫɥɢ ɚɤɬɢɜɟɧ ɥɢɫɬ, ɬɨ Range("ȼ2"). ȼɫɟ ɷɬɨ ɦɨɠɧɨ ɩɪɢɦɟɧɹɬɶ ɩɪɢ ɪɚɡɪɚɛɨɬɤɟ ɩɪɨɟɤɬɨɜ, ɦɚɤɪɨɫɨɜ ɢ ɩɪɨɝɪɚɦɦ ɦɨɞɟɥɟɣ. Ⱦɥɹ ɷɬɨɝɨ ɧɭɠɧɨ ɱɟɪɟɡ ɜɤɥɚɞɤɭ Ɋɚɡɪɚɛɨɬɱɢɤ ɜɵɡɜɚɬɶ ɪɟɞɚɤɬɨɪ VBA ɳɟɥɤɧɭɜ ɧɚ ɤɧɨɩɤɟ Visual Basic ɜ ɝɪɭɩɩɟ Ʉɨɞ. ɉɪɟɞɜɚɪɢɬɟɥɶɧɨ ɫɨɡɞɚɬɶ ɮɚɣɥ ɫ ɪɚɫɲɢɪɟɧɢɟɦ, ɤɨɬɨɪɨɟ ɩɨɞɞɟɪɠɢɜɚɟɬ ɦɚɤɪɨɫɵ. ɉɨɹɜɢɬɶɫɹ ɨɤɧɨ ɪɟɞɚɤɬɨɪɚ Visual Basic ɫ ɦɟɧɸ, ɩɚɧɟɥɹɦɢ ɢɧɫɬɪɭɦɟɧɬɨɜ ɢ ɨɤɧɚɦɢ. Ɍɚɤɠɟ ɜɵɯɨɞɢɦ ɧɚ ɪɟɞɚɤɬɨɪ VBA ɩɪɢ ɫɨɡɞɚɧɢɢ ɷɥɟɦɟɧɬɨɜ ActiveX ɧɚ ɥɢɫɬɟ ɩɨɫɥɟ ɞɜɨɣɧɨɝɨ ɳɟɥɱɤɚ ɧɚ ɷɥɟɦɟɧɬɟ. ɉɨɫɥɟ ɪɚɫɩɨɥɨɠɟɧɢɹ ɷɥɟɦɟɧɬɚ ɧɚ ɥɢɫɬɟ ɞɥɹ ɫɨɡɞɚɧɢɹ ɟɝɨ ɩɪɨɰɟɞɭɪɵ ɧɭɠɧɨ ɜɤɥɸɱɢɬɶ Ɋɟɠɢɦ ɤɨɧɫɬɪɭɤɬɨɪɚ. Ɉɫɬɚɧɨɜɢɦɫɹ ɧɚ ɨɫɧɨɜɧɵɯ ɷɥɟɦɟɧɬɚɯ ɨɤɧɚ ɪɟɞɚɤɬɨɪɚ. ȼ ɨɤɧɟ ɩɪɨɟɤɬɚ Project-VBAProject ɧɚɛɥɸɞɚɟɦ ɫɬɪɭɤɬɭɪɭ ɩɪɨɟɤɬɚ ɫ ɨɛɴɟɤɬɚɦɢ. Ɇɨɠɧɨ ɡɚɤɪɵɬɶ ɨɤɧɨ, ɚ ɡɚɬɟɦ ɟɝɨ ɨɬɤɪɵɬɶ ɱɟɪɟɡ ɦɟɧɸ View (ȼɢɞ), ɜ ɤɨɬɨɪɨɦ ɟɫɬɶ ɩɭɧɤɬ Project Explorer (ɉɪɨɜɨɞɧɢɤ ɩɪɨɟɤɬɚ). ȼ ɫɬɪɭɤɬɭɪɟ ɩɪɨɟɤɬɚ ɧɚɯɨɞɹɬɫɹ ɨɛɴɟɤɬɵ Worksheet(s) (Ɋɚɛɨɱɢɣ ɥɢɫɬ), Workbook(s) (Ɋɚɛɨɱɚɹ ɤɧɢɝɚ) ɢ Module(s) (Ɇɨɞɭɥɶ). ɑɟɪɟɡ ɤɨɧɬɟɤɫɬɧɨɟ ɦɟɧɸ ɨɛɴɟɤɬɨɜ ɜɵɯɨɞɢɦ ɧɚ ɩɪɨɫɦɨɬɪ ɢɯ ɤɨɞɨɜ. ȼ Module ɯɪɚɧɹɬɫɹ ɤɨɞɵ ɩɪɨɰɟɞɭɪ (ɮɭɧɤɰɢɣ, ɦɚɤɪɨɫɨɜ). Module ɫɨɡɞɚɟɬɫɹ ɩɭɬɟɦ ɜɵɯɨɞɚ ɧɚ ɩɭɧɤɬ Module ɜ ɦɟɧɸ Insert (ȼɫɬɚɜɤɚ) ɢɥɢ ɩɪɢ ɫɨɡɞɚɧɢɢ ɦɚɤɪɨɫɚ. ȼ ɷɬɨɦ ɠɟ ɦɟɧɸ ɫɨɡɞɚ25 Powered by TCPDF (www.tcpdf.org)

1. Ɉ ɦɨɞɟɥɢɪɨɜɚɧɢɢ, ɪɟɲɟɧɢɢ ɡɚɞɚɱ, ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɢ ɢ MS Excel

ɟɦ ɮɨɪɦɵ ɱɟɪɟɡ ɩɭɧɤɬ UserForm (ɉɨɥɶɡɨɜɚɬɟɥɶɫɤɚɹ ɮɨɪɦɚ). ɍɞɚɥɢɬɶ ɫɨɡɞɚɧɧɵɟ ɷɥɟɦɟɧɬɵ ɩɪɨɟɤɬɚ ɦɨɠɧɨ ɱɟɪɟɡ ɢɯ ɤɨɧɬɟɤɫɬɧɨɟ ɦɟɧɸ ɢ ɩɭɧɤɬ Remove. ȼ ɨɤɧɟ Code (Ʉɨɞ) ɫɨɡɞɚɸɬɫɹ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ ɤɨɞɵ ɮɭɧɤɰɢɣ, ɩɪɨɰɟɞɭɪ, ɩɨɥɶɡɨɜɚɬɟɥɶɫɤɢɯ ɮɨɪɦ ɢ ɞɪɭɝɢɯ ɨɛɴɟɤɬɨɜ. Ɉɤɧɨ ɤɨɞɨɜ ɫɨɞɟɪɠɢɬ 2-ɚ ɫɩɢɫɤɚ General (Ɉɛɳɚɹ ɨɛɥɚɫɬɶ) ɢ Declarations (Ɉɩɢɫɚɧɢɟ). ȼ General ɩɪɟɞɫɬɚɜɥɹɸɬɫɹ ɨɛɴɟɤɬɵ, ɭ ɤɨɬɨɪɵɯ ɫɨɡɞɚɧɵ ɩɪɨɰɟɞɭɪɵ ɢɥɢ ɞɥɹ ɤɨɬɨɪɵɯ ɦɨɠɧɨ ɫɨɡɞɚɬɶ ɩɪɨɰɟɞɭɪɵ. ȼ Declarations ɩɪɟɞɫɬɚɜɥɹɸɬɫɹ ɩɟɪɟɱɟɧɶ ɫɨɛɵɬɢɣ, ɤɨɬɨɪɵɟ ɦɨɠɧɨ ɭɫɬɚɧɨɜɢɬɶ ɞɥɹ ɩɪɨɰɟɞɭɪ ɨɛɴɟɤɬɨɜ. ɑɬɨɛɵ ɡɚɤɪɵɬɶ ɨɤɧɨ ɤɨɞɨɜ ɨɛɴɟɤɬɚ ɧɭɠɧɨ ɜɵɡɜɚɬɶ ɤɨɧɬɟɤɫɬɧɨɟ ɦɟɧɸ ɨɛɴɟɤɬɚ ɢ ɳɟɥɤɧɭɬɶ ɧɚ ɩɭɧɤɬɟ Dockable. ȼ VBA ɦɨɠɧɨ ɫɨɡɞɚɜɚɬɶ ɮɭɧɤɰɢɢ ɢ ɩɪɨɰɟɞɭɪɵ. Ɏɭɧɤɰɢɢ ɛɵɜɚɸɬ ɜɫɬɪɨɟɧɧɵɦɢ ɢ ɩɨɥɶɡɨɜɚɬɟɥɶɫɤɢɦɢ. ȼ ɨɛɳɟɦ ɜɢɞɟ ɫɬɪɭɤɬɭɪɚ ɮɭɧɤɰɢɢ ɢɦɟɟɬ ɜɢɞ Public Function ɂɦɹ (ɫɩɢɫɨɤ ɚɪɝɭɦɟɧɬɨɜ ɫ ɨɛɴɹɜɥɟɧɢɟɦ ɢɯ ɬɢɩɨɜ)_ (ɨɛɴɹɜɥɟɧɢɹ ɬɢɩɚ ɮɭɧɤɰɢɢ) Ɉɛɴɹɜɥɟɧɢɟ ɜɫɩɨɦɨɝɚɬɟɥɶɧɵɯ ɩɟɪɟɦɟɧɧɵɯ Ɉɩɟɪɚɬɨɪɵ ɂɦɹ = ɜɵɪɚɠɟɧɢɟ End Function. ȼ ɮɭɧɤɰɢɢ ɜɫɟɝɞɚ ɟɟ ɢɦɟɧɢ ɩɪɢɫɜɚɢɜɚɟɬɫɹ ɜɨɡɜɪɚɳɚɟɦɨɟ ɡɧɚɱɟɧɢɟ. ȿɫɥɢ ɮɭɧɤɰɢɹ ɢɫɩɨɥɶɡɭɟɬɫɹ ɜ ɨɞɧɨɣ ɤɧɢɝɟ, ɬɨ ɦɨɠɧɨ ɧɟ ɭɤɚɡɵɜɚɬɶ ɟɟ ɨɛɥɚɫɬɶ ɜɢɞɢɦɨɫɬɢ. Ɉɛɥɚɫɬɶ ɜɢɞɢɦɨɫɬɢ ɮɭɧɤɰɢɢ ɦɨɠɟɬ ɛɵɬɶ ɥɨɤɚɥɶɧɨɣ Private (ɜ ɩɪɟɞɟɥɚɯ ɞɚɧɧɨɝɨ ɦɨɞɭɥɹ) ɢɥɢ ɝɥɨɛɚɥɶɧɨɣ Public (ɜ ɩɪɟɞɟɥɚɯ ɜɫɟɯ ɦɨɞɭɥɟɣ ɩɪɨɟɤɬɚ). ȼ ɩɨɫɥɟɞɧɟɦ ɫɥɭɱɚɟ ɩɟɪɟɞ ɢɦɟɧɟɦ ɮɭɧɤɰɢɢ ɪɚɡɦɟɳɚɟɬɫɹ ɤɥɸɱɟɜɨɟ ɫɥɨɜɨ Public. ɂɧɮɨɪɦɚɰɢɸ ɨ ɜɫɬɪɨɟɧɧɵɯ ɮɭɧɤɰɢɹɯ ɜ MS Excel ɦɨɠɧɨ ɩɨɫɦɨɬɪɟɬɶ ɜ ɪɟɞɚɤɬɨɪɟ VBA ɱɟɪɟɡ ɦɟɧɸ View ɢ ɩɭɧɤɬ Object Browser ɢɥɢ ɱɟɪɟɡ ɤɥɚɜɢɲɭ F2. ȼ ɩɨɹɜɢɜɲɟɦɫɹ ɫɩɢɫɤɟ «All Libraries» ɜɵɛɢɪɚɟɦ VBA, ɚ ɡɚɬɟɦ ɜ ɫɩɢɫɤɟ Classes ɳɟɥɤɚɟɦ ɧɚ ɢɧɬɟɪɟɫɭɸɳɟɦ ɩɭɧɤɬɟ ɢɥɢ ɜ ɩɭɧɤɬɟ ɜɵɛɢɪɚɟɦ ɩɨ ɫɩɢɫ26

1.4. VBA ɢ Excel

ɤɭ ɧɭɠɧɭɸ ɮɭɧɤɰɢɸ ɜ ɩɪɚɜɨɦ ɨɤɧɟ. ɂɧɮɨɪɦɚɰɢɹ ɨ ɮɭɧɤɰɢɢ ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ ɜɧɢɡɭ ɨɤɧɚ (ɜ ɧɚɲɟɦ ɫɥɭɱɚɟ ɜɵɞɟɥɢɥɢ ɦɚɬɟɦɚɬɢɱɟɫɤɭɸ ɮɭɧɤɰɢɸ sin). ɉɨɥɶɡɨɜɚɬɟɥɶɫɤɢɟ ɮɭɧɤɰɢɢ ɢɫɩɨɥɶɡɭɸɬɫɹ ɞɥɹ ɪɚɫɱɟɬɨɜ, ɤɨɬɨɪɵɟ ɧɟ ɨɛɟɫɩɟɱɢɜɚɸɬɫɹ ɜɫɬɪɨɟɧɧɵɦɢ ɮɭɧɤɰɢɹɦɢ. Ɉɧɢ ɩɨɡɜɨɥɹɸɬ ɡɚɦɟɧɢɬɶ ɛɨɥɶɲɢɟ ɪɚɫɱɟɬɧɵɟ ɜɵɪɚɠɟɧɢɹ ɜ ɹɱɟɣɤɚɯ ɤɨɪɨɬɤɨɣ ɢ ɹɫɧɨɣ ɡɚɩɢɫɶɸ ɢɦɟɧɢ ɮɭɧɤɰɢɢ. ɉɪɢ ɫɨɡɞɚɧɢɢ ɩɨɥɶɡɨɜɚɬɟɥɶɫɤɨɣ ɮɭɧɤɰɢɢ ɫɨɡɞɚɟɦ Module. Ⱦɥɹ ɷɬɨɝɨ ɡɚɯɨɞɢɦ ɜ ɦɟɧɸ Insert ɢ ɳɟɥɤɚɟɦ ɧɚ ɩɭɧɤɬɟ Module. Ⱦɚɥɟɟ ɜ ɦɟɧɸ Inert ɳɟɥɤɚɟɦ ɧɚ ɩɭɧɤɬɟ Procedure ɢ ɜ ɩɨɹɜɢɜɲɟɦɫɹ ɨɤɧɟ ɜɤɥɸɱɚɟɦ ɜ Type Function, ɡɚɩɢɫɵɜɚɟɦ ɢɦɹ ɮɭɧɤɰɢɢ ɢ ɈɄ. ɂɦɹ ɢ ɩɚɪɚɦɟɬɪɵ ɩɨɥɶɡɨɜɚɬɟɥɶɫɤɨɣ ɮɭɧɤɰɢɢ ɰɟɥɟɫɨɨɛɪɚɡɧɨ ɩɢɫɚɬɶ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɪɭɫɫɤɨɝɨ ɚɥɮɚɜɢɬɚ. ɋɨɡɞɚɟɦ ɜ ɨɤɧɟ ɤɨɞɨɜ ɩɪɨɝɪɚɦɦɭ ɩɨɥɶɡɨɜɚɬɟɥɶ-

ɫɤɨɣ ɮɭɧɤɰɢɢ ɉɭɬɶ, ɝɞɟ ɜɵɱɢɫɥɹɟɦ ɩɪɨɣɞɟɧɧɵɣ ɩɭɬɶ ɩɨ ɫɤɨɪɨɫɬɢ ɢ ɜɪɟɦɟɧɢ (ɟɟ ɩɚɪɚɦɟɬɪɚɦ). ɋɨɯɪɚɧɹɟɦ ɫɞɟɥɚɧɧɵɟ ɢɡɦɟɧɟɧɢɹ ɢ ɩɟɪɟɯɨɞɢɦ ɤ ɢɫɩɨɥɶɡɨɜɚɧɢɸ ɫɨɡɞɚɧɧɨɣ ɮɭɧɤɰɢɢ. ȼ ɫɨɡɞɚɧɧɨɣ ɬɚɛɥɢɰɟ ɜ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɹɱɟɣɤɟ ɜɫɬɚɜɥɹɟɦ ɡɧɚɤ ɪɚɜɟɧɫɬɜɚ, ɨɛɪɚɳɚɟɦɫɹ ɤ ȼɫɬɚɜɢɬɶ ɮɭɧɤɰɢɸ, ɜ ɨɤɧɟ Ɇɚɫɬɟɪ ɮɭɧɤɰɢɣ ɜ ɤɚɬɟɝɨɪɢɢ Ɉɩɪɟɞɟɥɟɧɧɭɸ ɩɨɥɶɡɨɜɚɬɟɥɟɦ ɜɵɛɢɪɚɟɦ ɮɭɧɤɰɢɸ ɉɭɬɶ. Ɏɨɪɦɢɪɭɟɦ ɚɪɝɭɦɟɧɬɵ ɮɭɧɤɰɢɢ ɢ ɈɄ. ɂɫɩɨɥɶɡɭɟɦ ɦɟɯɚɧɢɡɦ ɚɜɬɨɡɚɩɨɥɧɟɧɢɹ ɞɥɹ ɪɚɫɱɟɬɨɜ ɩɪɨɣɞɟɧɧɨɝɨ ɩɭɬɢ ɜɨ ɜɫɟɣ ɬɚɛɥɢɰɟ. Ʉɚɤ ɜɢɞɧɨ, ɭ ɫɨɡɞɚɧɧɨɣ ɩɨɥɶɡɨɜɚɬɟɥɶɫɤɨɣ ɮɭɧɤɰɢɢ ɨɬɫɭɬɫɬɜɭɟɬ ɟɟ ɨɩɢɫɚɧɢɟ. Ʉɚɤ ɫɨɡɞɚɟɬɫɹ ɨɩɢɫɚɧɢɟ ɦɨɠɧɨ ɧɚɣɬɢ ɜ ɢɧɬɟɪɧɟ27

1. Ɉ ɦɨɞɟɥɢɪɨɜɚɧɢɢ, ɪɟɲɟɧɢɢ ɡɚɞɚɱ, ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɢ ɢ MS Excel

ɬɟ. ɋɥɟɞɭɟɬ ɩɨɦɧɢɬɶ, ɱɬɨ ɮɭɧɤɰɢɹ ɜɨɡɜɪɚɳɚɟɬ ɨɞɧɨ ɡɧɚɱɟɧɢɟ, ɤɨɬɨɪɨɟ ɨɛɵɱɧɨ ɩɪɢɫɜɚɢɜɚɟɬɫɹ ɤɚɤɨɣ-ɬɨ ɩɟɪɟɦɟɧɧɨɣ. ȼɵɡɨɜ ɮɭɧɤɰɢɣ ɢɦɟɟɬ ɫɥɟɞɭɸɳɢɣ ɜɢɞ ɂɦɹ ɩɟɪɟɦɟɧɧɨɣ = ɂɦɹ ɮɭɧɤɰɢɢ (ɫɩɢɫɨɤ ɮɚɤɬɢɱɟɫɤɢɯ ɚɪɝɭɦɟɧɬɨɜ). Ɏɨɪɦɚɥɶɧɵɟ ɚɪɝɭɦɟɧɬɵ ɢɫɩɨɥɶɡɭɸɬɫɹ ɩɪɢ ɨɩɢɫɚɧɢɢ ɮɭɧɤɰɢɢ. Ɏɚɤɬɢɱɟɫɤɢɟ ɚɪɝɭɦɟɧɬɵ – ɷɬɨ ɚɪɝɭɦɟɧɬɵ, ɤɨɬɨɪɵɟ ɢɫɩɨɥɶɡɭɸɬɫɹ ɩɪɢ ɜɵɡɨɜɟ ɮɭɧɤɰɢɢ.

ȼɵɡɜɚɬɶ ɮɭɧɤɰɢɸ ɦɨɠɧɨ ɜ ɞɪɭɝɨɣ ɮɭɧɤɰɢɢ ɢɥɢ ɜ ɩɪɨɰɟɞɭɪɟ. ɉɟɪɟɞɚɱɚ ɩɚɪɚɦɟɬɪɨɜ ɮɭɧɤɰɢɢ ɩɪɨɢɡɜɨɞɢɬɫɹ ɩɨ ɫɫɵɥɤɟ ɢɥɢ ɩɨ ɡɧɚɱɟɧɢɸ. ɉɪɢɦɟɧɹɬɶ ɮɭɧɤɰɢɸ ɦɨɠɧɨ ɩɪɢ ɪɚɫɱɟɬɚɯ ɜ ɹɱɟɣɤɚɯ ɥɢɫɬɚ. ɋɨɡɞɚɞɢɦ ɮɭɧɤɰɢɸ ɪɚɫɱɟɬɚ ɩɟɪɢɦɟɬɪɚ ɬɪɟɭɝɨɥɶɧɢɤɚ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɮɭɧɤɰɢɢ ɪɚɫɱɟɬɚ ɝɢɩɨɬɟɧɭɡɵ. ȼ ɩɪɢɦɟɱɚɧɢɹɯ ɹɱɟɟɤ ɜɢɞɢɦ ɡɚɞɚɧɢɟ ɩɚɪɚɦɟɬɪɨɜ ɩɨ ɫɫɵɥɤɟ ɢ ɩɨ ɡɧɚɱɟɧɢɹɦ. ɉɪɢɦɟɪɵ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɮɭɧɤɰɢɣ ɜ ɩɪɨɰɟɞɭɪɚɯ ɩɪɢɜɟɞɟɦ ɧɢɠɟ. ɉɪɨɰɟɞɭɪɵ ɛɵɜɚɸɬ ɨɛɳɢɟ ɩɪɨɰɟɞɭɪɵ ɢ ɫɨɛɵɬɢɣɧɵɟ ɩɪɨɰɟɞɭɪɵ. ɉɪɨɰɟɞɭɪɵ ɩɪɟɞɧɚɡɧɚɱɟɧɵ ɞɥɹ ɨɫɭɳɟɫɬɜɥɟɧɢɹ ɤɚɤɢɯ-ɥɢɛɨ ɞɟɣɫɬɜɢɣ (ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ, ɪɟɚɥɢɡɚɰɢɹ ɚɥɝɨɪɢɬɦɚ). ɋɨɛɵɬɢɣɧɵɟ ɩɪɨɰɟɞɭɪɵ ɨɫɭɳɟɫɬɜɥɹɸɬɫɹ ɩɪɢ ɜɨɡɧɢɤɧɨɜɟɧɢɢ ɡɚɞɚɧɧɵɯ ɫɨɛɵɬɢɣ. ɋɬɪɭɤɬɭɪɚ ɨɛɳɟɣ ɩɪɨɰɟɞɭɪɵ Sub ɂɦɹɉɪɨɰɟɞɭɪɵ (ɋɩɢɫɨɤ ɚɪɝɭɦɟɧɬɨɜ ɢɥɢ ɩɚɪɚɦɟɬɪɨɜ) Ɉɩɟɪɚɬɨɪɵ Ɉɛɴɟɤɬ1.ɋɜɨɣɫɬɜɨ=Ɂɧɚɱɟɧɢɟɋɜɨɣɫɬɜɚ ɈɛɴɟɤɬN.ɋɜɨɣɫɬɜɨ=Ɂɧɚɱɟɧɢɟɋɜɨɣɫɬɜɚ Ɉɛɴɟɤɬ1.Ɇɟɬɨɞ Ⱥɪɝɭɦɟɧɬ1: =Ɂɧɚɱɟɧɢɟ, Ⱥɪɝɭɦɟɧɬ2=Ɂɧɚɱɟɧɢɟ ɈɛɴɟɤɬM.Ɇɟɬɨɞ Ⱥɪɝɭɦɟɧɬ1: =Ɂɧɚɱɟɧɢɟ, Ⱥɪɝɭɦɟɧɬ2=Ɂɧɚɱɟɧɢɟ 28

1.4. VBA ɢ Excel

ɉɟɪɟɦɟɧɧɚɹ1=ɜɵɪɚɠɟɧɢɟ1 ɉɟɪɟɦɟɧɧɚɹL=ɜɵɪɚɠɟɧɢɟN End Sub. ɂɦɹ ɫɨɛɵɬɢɣɧɨɣ ɩɪɨɰɟɞɭɪɵ ɜɤɥɸɱɚɟɬ ɜ ɫɟɛɹ ɢɦɹ ɨɛɴɟɤɬɚ ɢ ɢɦɹ ɫɨɛɵɬɢɹ ɂɦɹ_ɨɛɴɟɤɬɚ_ ɂɦɹ_ɫɨɛɵɬɢɹ. ɉɪɨɰɟɞɭɪɚ ɦɨɠɟɬ ɫɨɞɟɪɠɚɬɶ ɩɭɫɬɵɟ ɫɤɨɛɤɢ ɛɟɡ ɩɚɪɚɦɟɬɪɨɜ. ȼɵɡɨɜ ɨɛɳɟɣ ɩɪɨɰɟɞɭɪɵ ɩɪɨɢɡɜɨɞɢɬɫɹ ɫ ɩɨɦɨɳɶɸ ɨɩɟɪɚɬɨɪɚ Call ɢɥɢ ɩɨ ɢɦɟɧɢ. ȼɵɡɵɜɚɟɬɫɹ ɩɪɨɰɟɞɭɪɚ ɬɚɤɠɟ ɢɡ ɞɪɭɝɢɯ ɩɪɨɰɟɞɭɪ. ɋɬɪɭɤɬɭɪɚ ɜɵɡɨɜɚ ɫ ɩɨɦɨɳɶɸ Call Call ɂɦɹɉɪɨɰɟɞɭɪɵ (ɋɩɢɫɨɤ ɚɪɝɭɦɟɧɬɨɜ). ȿɫɥɢ ɜɵɡɨɜ ɩɪɨɰɟɞɭɪɵ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɩɨ ɢɦɟɧɢ, ɬɨ ɫɩɢɫɨɤ ɩɚɪɚɦɟɬɪɨɜ ɧɟ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɫɤɨɛɤɢ ɂɦɹɉɪɨɰɟɞɭɪɵ ɋɩɢɫɨɤ ɚɪɝɭɦɟɧɬɨɜ. ȼɵɡɨɜ ɫɨɛɵɬɢɣɧɨɣ ɩɪɨɰɟɞɭɪɵ ɫɜɹɡɚɧ ɫ ɧɚɫɬɭɩɥɟɧɢɟ ɤɚɤɨɝɨ-ɬɨ ɫɨɛɵɬɢɹ (ɨɬɤɪɵɬɢɟɦ ɤɧɢɝɢ, ɜɵɡɨɜɚ ɮɨɪɦɵ, ɳɟɥɱɤɨɦ ɧɚ ɤɧɨɩɤɟ). ɉɪɨɰɟɞɭɪɵ ɦɨɝɭɬ ɛɵɬɶ ɥɨɤɚɥɶɧɵɦɢ (Private) ɢɥɢ ɝɥɨɛɚɥɶɧɵɦɢ (Public). Ʌɨɤɚɥɶɧɚɹ ɩɪɨɰɟɞɭɪɚ ɞɨɫɬɭɩɧɚ ɬɨɥɶɤɨ ɜ ɫɜɨɟɦ ɩɪɨɝɪɚɦɦɧɨɦ ɦɨɞɭɥɟ, ɚ ɝɥɨɛɚɥɶɧɚɹ ɩɪɨɰɟɞɭɪɚ ɦɨɠɟɬ ɛɵɬɶ ɜɵɡɜɚɧɵ ɢɡ ɜɫɟɯ ɩɪɨɝɪɚɦɦɧɵɯ ɦɨɞɭɥɟɣ. ɋɨɡɞɚɞɢɦ ɨɛɳɢɟ ɩɪɨɰɟɞɭɪɵ ɞɥɹ ɡɚɩɨɥɧɟɧɢɹ ɫɬɨɥɛɰɚ ɹɱɟɟɤ ɧɚ ɥɢɫɬɟ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶɸ ɱɢɫɟɥ ɢ ɮɨɪɦɢɪɨɜɚɧɢɹ ɡɚɝɨɥɨɜɤɚ ɫɬɨɥɛɰɚ. ȼ ɦɟɧɸ Insert ɳɟɥɤɚɟɦ ɧɚ ɩɭɧɤɬɟ Procedure ɢ ɜ ɩɨɹɜɢɜɲɟɦɫɹ ɨɤɧɟ ɜɤɥɸɱɚɟɦ ɜ Type Sub, ɡɚɩɢɫɵɜɚɟɦ ɢɦɹ ɩɪɨɰɟɞɭɪɵ ɢ ɈɄ. ɋɨɡɞɚɟɦ ɤɨɞ ɩɪɨɰɟɞɭɪɵ. ȼ ɤɚɱɟɫɬɜɟ ɩɚɪɚɦɟɬɪɨɜ ɡɚɞɚɟɦ ɧɨɦɟɪ ɫɬɪɨɤɢ ɢ ɫɬɨɥɛɰɚ ɩɟɪɜɨɣ ɹɱɟɣɤɢ, ɚ ɬɚɤɠɟ ɤɨɥɢɱɟɫɬɜɨ ɫɬɪɨɤ ɞɥɹ ɡɚɩɨɥɧɟɧɢɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶɸ ɱɢɫɟɥ ɨɬ 1 ɞɨ Ʉɨɥɢɱɟɫɬɜɚ. Ʉɨɞɵ ɩɪɨɰɟɞɭɪ ɫ ɤɨɦɦɟɧɬɚɪɢɹɦɢ ɩɪɟɞɫɬɚɜɥɟɧɵ ɧɢɠɟ. ɇɚɞɩɢɫɶ ɫɬɨɥɛɰɚ ɮɨɪɦɢɪɭɟɬɫɹ ɜ ɞɜɟ ɫɬɪɨɤɢ. Ⱦɥɹ ɩɟɪɟɯɨɞɚ ɧɚ ɜɬɨɪɭɸ ɫɬɪɨɤɭ ɢɫɩɨɥɶɡɭɟɦ ɮɭɧɤɰɢɸ Chr(10). Ʉɨɦɦɟɧɬɚɪɢɢ ɧɚɱɢɧɚɸɬɫɹ ɫ ɚɩɨɫɬɪɨɮɚ. Ʉɨɞɵ ɩɪɨɰɟɞɭɪ ɡɚɩɢɫɚɧɵ ɜ 1-ɦ ɦɨɞɭɥɟ.

29

1. Ɉ ɦɨɞɟɥɢɪɨɜɚɧɢɢ, ɪɟɲɟɧɢɢ ɡɚɞɚɱ, ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɢ ɢ MS Excel

ɋɨɡɞɚɞɢɦ ɫɨɛɵɬɢɣɧɭɸ ɩɪɨɰɟɞɭɪɭ ɭɩɪɚɜɥɹɸɳɟɣ ɤɧɨɩɤɢ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ ɧɚ ɥɢɫɬɟ. ɉɪɢ ɳɟɥɱɤɟ ɧɚ ɤɧɨɩɤɟ ɛɭɞɟɬ ɮɨɪɦɢɪɨɜɚɬɶɫɹ ɫɬɨɥɛɟɰ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɱɢɫɟɥ ɢ ɡɚɝɨɥɨɜɨɤ. ɇɚɱɚɥɶɧɵɟ ɤɨɨɪɞɢɧɚɬɵ ɫɬɨɥɛɰɚ ɢ ɤɨɥɢɱɟɫɬɜɨ ɱɢɫɟɥ ɡɚɩɢɫɵɜɚɟɦ ɜ ɹɱɟɣɤɢ ɥɢɫɬɚ. ɇɚ ɜɤɥɚɞɤɟ Ɋɚɡɪɚɛɨɬɱɢɤ ɜ ɝɪɭɩɩɟ ɗɥɟɦɟɧɬɵ ɭɩɪɚɜɥɟɧɢɹ ɢ ɜɵɛɢɪɚɟɦ ɜ ɗɥɟɦɟɧɬɵ ActiveX ɤɧɨɩɤɭ ɢ ɩɪɨɬɹɠɤɨɣ ɪɚɡɦɟɳɚɟɦ ɧɚ ɥɢɫɬɟ. ȼɤɥɸɱɚɟɦ Ɋɟɠɢɦ ɤɨɧɫɬɪɭɤɬɨɪɚ. ȼɵɡɵɜɚɟɦ ɤɨɧɬɟɤɫɬɧɨɟ ɦɟɧɸ ɤɧɨɩɤɢ, ɜɵɛɢɪɚɟɦ ɩɭɧɤɬ ɋɜɨɣɫɬɜɚ. ȼ ɨɤɧɟ Properties ɜ ɩɭɧɤɬɟ Caption ɫɨɡɞɚɟɦ ɧɚɡɜɚɧɢɟ ɤɧɨɩɤɢ «ɉɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ». Ⱦɜɚɠɞɵ ɳɟɥɤɧɭɜ ɧɚ ɤɧɨɩɤɟ ɫɨɡɞɚɟɦ ɤɨɞ ɫɨɛɵɬɢɣɧɨɣ ɩɪɨɰɟɞɭɪɵ ɜ ɨɤɧɟ ɩɪɨɝɪɚɦɦɧɨɝɨ ɤɨɞɚ 3-ɝɨ ɥɢɫɬɚ. ɋɨɛɵɬɢɟ ɭɫɬɚɧɚɜɥɢɜɚɟɬɫɹ ɜ ɩɪɚɜɨɦ ɫɩɢɫɤɟ. ȼ ɧɚɲɟɦ ɫɥɭɱɚɟ ɩɪɨɰɟɞɭɪɚ ɜɵɩɨɥɧɹɟɬɫɹ ɩɨɫɥɟ ɳɟɥɱɤɚ Click ɧɚ ɤɧɨɩɤɟ. ȼ ɩɪɨɰɟɞɭɪɟ ɩɪɟɞɫɬɚɜɥɟɧɵ ɞɜɚ ɜɢɞɚ ɜɵɡɨɜɚ ɪɚɧɟɟ ɫɨɡɞɚɧɧɵɯ ɨɛɳɢɯ ɩɪɨɰɟɞɭɪ. Ɋɟɡɭɥɶɬɚɬ ɩɪɢɦɟɧɟɧɢɹ ɩɪɨɰɟɞɭɪɵ ɩɪɟɞɫɬɚɜɥɟɧ ɧɚ ɪɢɫɭɧɤɟ. ɉɨɪɚ ɨɫɬɚɧɨɜɢɬɶɫɹ ɧɚ ɩɟɪɟɦɟɧɧɵɯ, ɤɨɬɨɪɵɟ ɞɨɥɠɧɵ ɢɦɟɬɶ ɢɦɟɧɚ ɢ 30

1.4. VBA ɢ Excel

ɬɢɩ. ɂɦɟɧɚ ɞɨɥɠɧɵ ɛɵɬɶ ɭɧɢɤɚɥɶɧɵɦɢ, ɤɨɬɨɪɵɟ ɫɨɫɬɨɹɬ ɢɡ ɪɚɡɥɢɱɧɵɯ ɫɢɦɜɨɥɨɜ. ȼ ɢɦɟɧɚɯ ɢɫɩɨɥɶɡɭɸɬɫɹ ɤɚɤ ɥɚɬɢɧɫɤɢɟ, ɬɚɤ ɢ ɪɭɫɫɤɢɟ ɛɭɤɜɵ. ɋɥɟɞɭɟɬ ɩɨɦɧɢɬɶ, ɱɬɨ ɜ ɢɦɟɧɚɯ ɩɪɨɮɟɫɫɢɨɧɚɥɵ ɩɪɢɦɟɧɹɸɬ ɩɪɢɫɬɚɜɤɭ, ɤɨɬɨɪɚɹ ɫɜɹɡɚɧɚ ɫ ɬɢɩɨɦ ɩɟɪɟɦɟɧɧɨɣ. ɉɟɪɟɦɟɧɧɵɟ ɢɦɟɸɬ ɪɚɡɥɢɱɧɵɟ ɬɢɩɵ. Ɉɬ ɬɢɩɚ ɩɟɪɟɦɟɧɧɨɣ ɡɚɜɢɫɢɬ, ɤɚɤɢɟ ɨɩɟɪɚɰɢɢ ɦɨɠɧɨ ɩɪɨɢɡɜɨɞɢɬɶ ɫ ɧɟɣ. ȼ ɬɚɛɥɢɰɟ ɩɪɟɞɫɬɚɜɥɟɧɵ ɧɚɢɛɨɥɟɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɧɵɟ ɬɢɩɵ ɩɟɪɟɦɟɧɧɵɯ. Ɍɢɩ ɩɟɪɟɦɟɧɧɨɣ Byte Integer Long Single

ȼɨɡɦɨɠɧɵɟ ɡɧɚɱɟɧɢɹ

String Date

ɐɟɥɵɟ ɱɢɫɥɚ ɨɬ 0 ɞɨ255 ɐɟɥɵɟ ɱɢɫɥɚ ɨɬ -32768 ɞɨ 32767 ɐɟɥɵɟ ɱɢɫɥɚ ɨɬ -2147483648 ɞɨ 2147483647 Ⱦɟɫɹɬɢɱɧɵɟ ɱɢɫɥɚ ɫ ɨɞɢɧɚɪɧɨɣ ɬɨɱɧɨɫɬɢ ɨɬ -1,4*10 -45 ɞɨ 3,4*1038 Ⱦɟɫɹɬɢɱɧɵɟ ɱɢɫɥɚ ɫ ɞɜɨɣɧɨɣ ɬɨɱɧɨɫɬɢ ɨɬ -5*10 -324 ɞɨ 1,7*10308 ɋɬɪɨɤɚ ɫɢɦɜɨɥɨɜ Ⱦɚɬɚ ɨɬ 1 ɹɧɜɚɪɹ 100 ɝɨɞɚ

Object

ɋɫɵɥɤɚ ɧɚ ɥɸɛɨɣ ɨɛɴɟɤɬ

Doudle

ɉɪɢɦɟɧɟɧɢɟ Ⱦɥɹ ɨɪɝɚɧɢɡɚɰɢɢ ɰɢɤɥɨɜ Ⱦɥɹ ɨɪɝɚɧɢɡɚɰɢɢ ɰɢɤɥɨɜ, ɪɚɫɱɟɬɵ Ɋɚɫɱɟɬɵ Ɋɚɫɱɟɬɵ Ɋɚɫɱɟɬɵ Ɉɛɪɚɛɨɬɤɚ ɬɟɤɫɬɨɜ Ɋɚɫɱɟɬɵ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɜɪɟɦɟɧɢ ɢ ɩɚɪɚɦɟɬɪɨɜ ɞɚɬ (ɝɨɞ, ɦɟɫɹɰ, ɧɟɞɟɥɹ, ɞɟɧɶ)

ɉɪɢ ɫɨɡɞɚɧɢɢ ɪɚɡɥɢɱɧɵɯ ɨɛɴɟɤɬɨɜ

ɋɬɪɭɤɬɭɪɚ ɨɛɴɹɜɥɟɧɢɹ ɩɟɪɟɦɟɧɧɵɯ Dim ɂɦɹɉɟɪɟɦɟɧɧɨɣ As Ɍɢɩɉɟɪɟɦɟɧɧɨɣ. ɉɟɪɟɦɟɧɧɵɟ, ɤɨɬɨɪɵɟ ɢɦɟɸɬ ɩɨɫɬɨɹɧɧɨɟ ɡɧɚɱɟɧɢɟ, ɹɜɥɹɸɬɫɹ ɤɨɧɫɬɚɧɬɚɦɢ. ɋɬɪɭɤɬɭɪɚ ɨɛɴɹɜɥɟɧɢɹ ɤɨɧɫɬɚɧɬ ɫɥɟɞɭɸɳɚɹ Const ɂɦɹɄɨɧɫɬɚɧɬɵ As ɌɢɩɄɨɧɫɬɚɧɬɵ =ɁɧɚɱɟɧɢɟɄɨɧɫɬɚɧɬɵ. Ɉɛɴɹɜɥɟɧɢɟ ɩɟɪɟɦɟɧɧɵɯ ɦɨɠɧɨ ɩɪɨɢɡɜɨɞɢɬɶ ɜ ɫɩɢɫɤɟ ɚɪɝɭɦɟɧɬɨɜ (ɩɚɪɚɦɟɬɪɨɜ) ɮɭɧɤɰɢɢ ɢ ɩɪɨɰɟɞɭɪɵ, ɜɧɭɬɪɢ ɮɭɧɤɰɢɢ (ɩɪɨɰɟɞɭɪɵ), ɚ ɬɚɤɠɟ ɜɧɟ ɮɭɧɤɰɢɢ ɜ ɩɪɨɝɪɚɦɦɧɨɦ ɦɨɞɭɥɟ ɢɥɢ ɜɧɟ ɩɪɨɰɟɞɭɪɵ ɜ ɩɪɨɝɪɚɦɦɧɨɦ ɨɤɧɟ ɭɩɪɚɜɥɹɸɳɟɝɨ ɷɥɟɦɟɧɬɚ (ɩɪɨɝɪɚɦɦɧɨɦ ɨɤɧɟ ɮɨɪɦɵ). ɉɟɪɟɦɟɧɧɭɸ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɜ ɥɸɛɨɦ ɦɟɫɬɟ, ɟɫɥɢ ɟɟ ɨɛɴɹɜɥɟɧɢɟ ɧɚɱɢɧɚɟɬɫɹ ɫ ɤɥɸɱɟɜɨɝɨ ɫɥɨɜɚ Public ɢ ɨɧɚ ɨɛɴɹɜɥɟɧɚ ɜ ɧɚɱɚɥɟ ɥɸɛɨɝɨ ɦɨɞɭɥɹ ɜɧɟ ɩɪɨɰɟɞɭɪɵ ɢɥɢ ɮɭɧɤɰɢɢ. ɗɬɨ ɧɚɢɛɨɥɟɟ ɩɪɟɞɩɨɱɬɢɬɟɥɶɧɵɣ ɜɚɪɢɚɧɬ. ȿɫɥɢ ɩɟɪɟɦɟɧɧɚɹ ɨɛɴɹɜɥɟɧɚ ɜ ɧɚɱɚɥɟ ɦɨɞɭɥɹ ɢ ɨɛɴɹɜɥɟɧɢɟ ɧɚɱɢɧɚɟɬɫɹ ɫ ɤɥɸɱɟɜɵɯ ɫɥɨɜ Dim ɢɥɢ Private, ɬɨ ɟɟ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɬɨɥɶɤɨ ɜ ɷɬɨɦ ɦɨɞɭɥɟ. ɉɪɢ ɨɛɴɹɜɥɟɧɢɢ ɩɟɪɟɦɟɧɨɣ ɜɧɭɬɪɢ ɩɪɨɰɟɞɭɪɵ ɢɥɢ ɮɭɧɤɰɢɢ ɟɟ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɬɨɥɶɤɨ ɜ ɧɢɯ. Ɋɚɫɫɦɨɬɪɢɦ ɫɨɡɞɚɧɢɟ ɮɨɪɦɵ ɫ ɭɩɪɚɜɥɹɸɳɢɦɢ ɷɥɟɦɟɧɬɚɦɢ. ɑɟɪɟɡ ɜɤɥɚɞɤɭ Ɋɚɡɪɚɛɨɬɱɢɤ ɢ ɤɧɨɩɤɭ Visual Basic ɨɬɤɪɵɜɚɟɦ ɨɤɧɨ ɪɟɞɚɤɬɨɪɚ VBA. ȼ ɦɟɧɸ View ɜɵɛɢɪɚɟɦ ɩɭɧɤɬ Insert ɢ ɳɟɥɤɚɟɦ ɧɚ ɩɭɧɤɬɟ UserForm. 31

1. Ɉ ɦɨɞɟɥɢɪɨɜɚɧɢɢ, ɪɟɲɟɧɢɢ ɡɚɞɚɱ, ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɢ ɢ MS Excel

ɉɨɥɭɱɚɟɦ ɡɚɝɨɬɨɜɤɭ ɮɨɪɦɵ ɫ ɨɤɧɨɦ Toolbox (ɉɚɧɟɥɶ ɷɥɟɦɟɧɬɨɜ ɭɩɪɚɜɥɟɧɢɹ), ɫɨɞɟɪɠɚɳɢɦ ɧɚɛɨɪ ɭɩɪɚɜɥɹɸɳɢɯ ɷɥɟɦɟɧɬɨɜ. ȼɵɡɵɜɚɟɦ ɫɜɨɣɫɬɜɚ ɮɨɪɦɵ ɞɥɹ ɮɨɪɦɢɪɨɜɚɧɢɹ ɧɚɡɜɚɧɢɹ ɮɨɪɦɵ ɱɟɪɟɡ ɦɟɧɸ View ɢ ɩɭɧɤɬ Properties Window. ȼ ɨɤɧɟ Properties UserForm ɜ ɩɭɧɤɬɟ Caption ɡɚɩɢɫɵɜɚɟɦ ɧɚɡɜɚɧɢɟ ɮɨɪɦɵ «Ƚɪɚɮɢɤ ɫɥɭɱɚɣɧɵɯ ɱɢɫɟɥ». Ⱦɚɥɟɟ ɫɨɡɞɚɟɦ ɧɚ ɮɨɪɦɟ ɭɩɪɚɜɥɹɸɳɢɟ ɷɥɟɦɟɧɬɵ. ȼɵɛɢɪɚɟɦ ɢɯ ɧɚ Toolbox, ɚ ɡɚɬɟɦ ɩɪɨɬɹɠɤɨɣ ɭɫɬɚɧɚɜɥɢɜɚɟɦ ɧɚ ɮɨɪɦɟ. ɇɚ ɮɨɪɦɟ ɭɫɬɚɧɚɜɥɢɜɚɟɦ Label,

TextBox ɢ CommandButton. ɓɟɥɤɚɹ ɧɚ ɤɚɠɞɨɦ ɷɥɟɦɟɧɬɟ ɩɪɚɜɨɣ ɤɥɚɜɢɲɟɣ ɢ ɱɟɪɟɡ ɤɨɧɬɟɤɫɬɧɨɟ ɦɟɧɸ ɜɵɯɨɞɢɦ ɧɚ ɢɯ ɫɜɨɣɫɬɜɚ. ȼ ɨɤɧɟ Properties-Label1 ɜ ɩɭɧɤɬɟ Caption ɫɨɡɞɚɟɦ ɡɚɩɢɫɶ, ɜ ɩɭɧɤɬɟ TextAlign ɢɡ ɫɩɢɫɤɚ ɜɵɛɢɪɚɟɦ ɰɟɧɬɪɢɪɨɜɚɧɢɟ ɬɟɤɫɬɚ, ɚ ɜ ɩɭɧɤɬɟ Font ɜɵɡɵɜɚɟɦ ɨɤɧɨ ɒɪɢɮɬ ɢ ɞɟɥɚɟɦ ɡɚɩɢɫɶ ɠɢɪɧɨɣ. ɉɪɢ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɦɨɠɧɨ ɭɫɬɚɧɨɜɢɬɶ ɧɭɠɧɵɟ ɩɚɪɚɦɟɬɪɵ ɜ ɞɪɭɝɢɯ ɫɜɨɣɫɬɜɚɯ.

32

1.4. VBA ɢ Excel

Ⱥɧɚɥɨɝɢɱɧɨ ɩɨɫɬɭɩɚɟɦ ɫ CommandButton1, CommandButton2 ɢ ɫɨɡɞɚɟɦ ɜ ɩɭɧɤɬɟ Caption ɧɚɡɜɚɧɢɟ ɤɧɨɩɤɢ ɢ ɭɫɬɚɧɚɜɥɢɜɚɟɦ ɩɚɪɚɦɟɬɪɵ ɮɨɪɦɚɬɚ ɲɪɢɮɬɚ. ȼ TextBox1 ɭɫɬɚɧɚɜɥɢɜɚɟɦ ɬɨɥɶɤɨ ɩɚɪɚɦɟɬɪɵ ɲɪɢɮɬɚ. Ɉɫɬɚɥɨɫɶ ɫɨɡɞɚɬɶ ɩɪɨɝɪɚɦɦɵ ɞɥɹ ɜɵɡɨɜɚ ɮɨɪɦɵ ɩɪɢ ɨɬɤɪɵɬɢɢ ɮɚɣɥɚ, ɩɪɨɜɟɪɤɢ ɩɪɚɜɢɥɶɧɨɫɬɢ ɡɚɞɚɧɢɹ ɤɨɥɢɱɟɫɬɜɚ ɱɢɫɟɥ ɢ ɩɨɫɬɪɨɟɧɢɹ ɝɪɚɮɢɤɚ. ɓɟɥɤɚɟɦ ɧɚ ɗɬɚɄɧɢɝɚ ɢ ɜ ɫɩɢɫɤɟ ɨɛɴɟɤɬɨɜ ɜɵɛɢɪɚɟɦ Workbook. ȼ ɩɪɚɜɨɦ ɫɩɢɫɤɟ – Open. ȼ ɡɚɝɨɬɨɜɤɭ ɫɨɛɵɬɢɣɧɨɣ ɩɪɨɰɟɞɭɪɵ ɤɧɢɝɢ ɜɫɬɚɜɥɹɟɦ ɤɨɞ ɩɨɤɚɡɚ ɮɨɪɦɵ ɩɪɢ ɨɬɤɪɵɬɢɢ ɮɚɣɥɚ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɨɬ33

1. Ɉ ɦɨɞɟɥɢɪɨɜɚɧɢɢ, ɪɟɲɟɧɢɢ ɡɚɞɚɱ, ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɢ ɢ MS Excel

ɤɪɵɬɢɹ ɜ ɰɟɧɬɪɟ ɥɢɫɬɚ ɛɭɞɟɬ ɩɨɹɜɥɹɬɶɫɹ ɫɨɡɞɚɧɧɚɹ ɮɨɪɦɚ. Ɉɞɧɚɤɨ ɧɭɠɧɨ ɩɪɟɞɭɫɦɨɬɪɟɬɶ ɭɞɚɥɟɧɢɟ ɫɨɡɞɚɜɚɟɦɵɯ ɞɢɚɝɪɚɦɦ. ɉɨɷɬɨɦɭ ɜɧɚɱɚɥɟ ɩɪɨɜɟɪɹɟɦ ɫɭɳɟɫɬɜɨɜɚɧɢɟ ɭɠɟ ɫɨɡɞɚɧɧɵɯ ɞɢɚɝɪɚɦɦ, ɤɨɬɨɪɵɟ ɡɚɬɟɦ ɭɞɚɥɹɟɦ. ɗɬɨ ɧɟɨɛɯɨɞɢɦɨ ɫɞɟɥɚɬɶ ɞɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɭɫɬɚɧɨɜɤɢ ɧɟɨɛɯɨɞɢɦɵɯ ɫɜɨɣɫɬɜ ɫɨɡɞɚɜɚɟɦɨɣ ɞɢɚɝɪɚɦɦɵ (ɨɧɚ ɢɦɟɟɬ 1-ɣ ɧɨɦɟɪ) ɩɪɢ ɨɬɨɛɪɚɠɟɧɢɢ ɝɪɚɮɢɤɚ ɫɥɭɱɚɣɧɵɯ ɱɢɫɟɥ. ɑɬɨɛɵ ɡɚɤɨɧɱɢɬɶ ɫ ɤɧɢɝɨɣ ɫɨɡɞɚɞɢɦ ɫɨɛɵɬɢɣɧɭɸ ɩɪɨɰɟɞɭɪɭ ɩɪɢ ɡɚɤɪɵɬɢɢ ɤɧɢɝɢ (ɮɚɣɥɚ). ɋɚɦɨɟ ɝɥɚɜɧɨɟ ɧɚɣɬɢ ɧɭɠɧɨɟ ɫɨɛɵɬɢɟ ɞɥɹ ɤɧɢɝɢ ɜ ɫɩɢɫɤɟ ɫɨɛɵɬɢɣ. ȼ ɩɪɨɰɟɞɭɪɟ ɛɭɞɟɦ ɨɛɧɭɥɹɬɶ ɦɚɫɫɢɜ ɫɥɭɱɚɣɧɵɯ ɱɢɫɟɥ ɢ ɫɨɯɪɚɧɹɬɶ ɮɚɣɥ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɦɟɬɨɞɚ Save. ɉɪɟɠɞɟ ɱɟɦ ɫɨɡɞɚɜɚɬɶ ɩɪɨɰɟɞɭɪɵ ɞɥɹ ɤɧɨɩɨɤ ɤɪɚɬɤɨ ɨɡɧɚɤɨɦɢɦɫɹ ɫ ɫɨɡɞɚɧɢɟɦ ɞɢɚɝɪɚɦɦ, ɤɨɬɨɪɵɟ ɩɨɡɜɨɥɹɸɬ ɨɛɟɫɩɟɱɢɬɶ ɝɪɚɮɢɤɭ ɩɪɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ ɡɚɞɚɱ. Ⱦɢɚɝɪɚɦɦɵ ɦɨɠɧɨ ɫɮɨɪɦɢɪɨɜɚɬɶ ɬɪɟɦɹ ɨɫɧɨɜɧɵɦɢ ɫɩɨɫɨɛɚɦɢ: x «ȼɪɭɱɧɭɸ» ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɦɚɫɬɟɪɚ ɞɢɚɝɪɚɦɦ. x ɉɪɢ ɩɨɦɨɳɢ ɨɛɴɟɤɬɚ Chart ɧɚ ɨɬɞɟɥɶɧɨɦ ɥɢɫɬɟ ɞɢɚɝɪɚɦɦɵ. x ɇɚ ɪɚɛɨɱɟɦ ɥɢɫɬɟ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɨɛɴɟɤɬɚ ChartObject. ɉɟɪɜɵɣ ɫɩɨɫɨɛ ɩɨɫɬɪɨɟɧɢɹ ɞɢɚɝɪɚɦɦɵ ɞɨɫɬɚɬɨɱɧɨ ɩɨɞɪɨɛɧɨ ɪɚɫɫɦɨɬɪɟɧ ɜ ɩɪɟɞɵɞɭɳɟɦ ɩɚɪɚɝɪɚɮɟ. ɉɪɨɫɬɨɣ ɢ ɷɮɮɟɤɬɢɜɧɵɣ ɫɩɨɫɨɛ, ɤɨɬɨɪɵɣ ɩɨɡɜɨɥɹɟɬ ɭɫɬɚɧɨɜɢɬɶ ɧɭɠɧɵɟ ɩɚɪɚɦɟɬɪɵ ɞɢɚɝɪɚɦɦɵ ɩɪɢ ɧɚɥɢɱɢɢ ɞɚɧɧɵɯ ɦɨɞɟɥɢ ɜ ɡɚɞɚɧɧɵɯ ɨɛɥɚɫɬɹɯ ɹɱɟɟɤ. ȼ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ «ɮɢɡɢɤɢ» ɡɚɞɚɱɢ ɧɭɠɧɨ ɜɵɛɢɪɚɬɶ ɬɨɱɟɱɧɵɣ ɝɪɚɮɢɤ ɫ ɝɥɚɞɤɢɦɢ ɤɪɢɜɵɦɢ ɢɥɢ ɫ ɩɪɹɦɵɦɢ ɨɬɪɟɡɤɚɦɢ. ɉɪɢ ɞɚɥɶɧɟɣɲɟɣ ɪɚɡɪɚɛɨɬɤɟ ɦɨɞɟɥɢ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɦɟɬɨɞɵ ɢ ɡɚɞɚɜɚɬɶ ɫɜɨɣɫɬɜɚ ɞɥɹ ɧɭɠɧɵɯ ɢɡɦɟɧɟɧɢɣ ɜ ɞɢɚɝɪɚɦɦɟ. ɉɪɢ ɫɨɡɞɚɧɢɢ ɞɢɚɝɪɚɦɦɵ ɜɬɨɪɵɦ ɫɩɨɫɨɛɨɦ ɫɥɟɞɭɟɬ ɩɨɦɧɢɬɶ, ɱɬɨ ɞɢɚɝɪɚɦɦɚ ɩɪɢɧɚɞɥɟɠɢɬ ɨɛɴɟɤɬɭ ɥɢɫɬɚ (Sheets). ɉɪɢɦɟɪɵ ɩɪɢɦɟɧɟɧɢɹ ɷɬɨɝɨ ɫɩɨɫɨɛɚ ɛɭɞɭɬ ɩɪɢɜɟɞɟɧɵ ɜ ɡɚɞɚɱɚɯ. Ɉɫɬɚɧɨɜɢɦɫɹ ɧɚ ɩɨɫɥɟɞɧɟɦ ɫɩɨɫɨɛɟ ɮɨɪɦɢɪɨɜɚɧɢɹ ɞɢɚɝɪɚɦɦɵ. Ɂɞɟɫɶ ɞɢɚɝɪɚɦɦɚ ɩɪɢɧɚɞɥɟɠɢɬ ɨɛɴɟɤɬɭ ɚɤɬɢɜɧɵɣ ɥɢɫɬ ActiveSheet. Ɉɬɤɪɵɜɚɟɦ ɩɪɨɟɤɬ, ɳɟɥɤɚɟɦ ɧɚ ɨɛɴɟɤɬɟ UserForm1. ɇɚ ɩɨɹɜɢɜɲɟɣɫɹ ɮɨɪɦɟ ɞɜɚɠɞɵ ɳɟɥɤɧɟɦ ɧɚ ɤɧɨɩɤɟ «ɋɬɪɨɢɦ ɝɪɚɮɢɤ» ɢ ɜ ɨɤɧɟ ɤɨɞɚ ɫɨɡɞɚɟɦ ɫɨɛɵɬɢɣɧɭɸ ɩɪɨɰɟɞɭɪɭ ɤɧɨɩɤɢ. Private Sub CommandButton1_Click() 'ɋɬɪɨɢɦ ɝɪɚɮɢɤ If ActiveSheet.ChartObjects.Count > 0 Then ActiveSheet.ChartObjects.Delete 'ɍɞɚɥɟɧɢɟ ɫɨɡɞɚɧɧɵɯ ɞɢɚɝɪɚɦɦ 34

1.4. VBA ɢ Excel

End If Cells(1, 2).Value = "ɑɢɫɥɨ" 'Ɂɚɝɨɥɨɜɨɤ ɫɬɨɥɛɰɚ k = Int(TextBox1) 'Ɂɚɩɢɫɶ ɢɡ ɬɟɤɫɬɨɜɨɝɨ ɩɨɥɹ Range(Cells(2, 1), Cells(31, 2)) = Null 'ɍɞɚɥɟɧɢɟ ɱɢɫɟɥ ɢɡ ɦɚɫɫɢɜɚ If (k < 10 Or k > 30) Then MsgBox "ɑɢɫɥɨ ɜɵɲɥɨ ɡɚ ɡɚɞɚɧɧɵɣ ɞɢɚɩɚɡɨɧ! ɂɫɩɪɚɜɶɬɟ!" 'ȼɵɞɚɱɚ ɫɨɨɛɳɟɧɢɹ Else ɇɚɞɩɢɫɶ 2, 1, k 'ȼɵɡɨɜ ɩɪɨɰɟɞɭɪɵ ɉɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ 2, 1, k 'ȼɵɡɨɜ ɩɪɨɰɟɞɭɪɵ Randomize 'Ɂɚɩɭɫɤ ɞɚɬɱɢɤɚ ɫɥɭɱɚɣɧɵɯ ɱɢɫɟɥ For i = 1 To k 'ɐɢɤɥ ɡɚɩɨɥɧɟɧɢɹ ɹɱɟɟɤ y = Int(70 * Rnd) 'ɰɟɥɨɟ ɫɥɭɱɚɣɧɨɟ ɱɢɫɥɨ ɨɬ 0 ɞɨ 69 Cells((1 + i), 2) = y 'Ɂɚɩɢɫɶ ɜ ɦɚɫɫɢɜ Next Ƚɪɚɮɢɤ 'ȼɵɡɨɜ ɩɪɨɰɟɞɭɪɵ ɩɨɫɬɪɨɟɧɢɹ ɝɪɚɮɢɤɚ End If End Sub. Ʉɚɤ ɜɢɞɧɨ, ɜɧɚɱɚɥɟ ɭɞɚɥɹɟɦ ɫɨɡɞɚɧɧɵɟ ɞɢɚɝɪɚɦɦɵ. Ɏɨɪɦɢɪɭɟɦ ɡɚɝɨɥɨɜɨɤ ɫɬɨɥɛɰɚ ɫɥɭɱɚɣɧɵɯ ɱɢɫɟɥ. ɉɪɨɜɟɪɹɟɦ ɱɢɫɥɨ ɜ ɬɟɤɫɬɨɜɨɦ ɩɨɥɟ ɧɚ ɭɫɬɚɧɨɜɥɟɧɧɵɣ ɞɢɚɩɚɡɨɧ ɫɥɭɱɚɣɧɵɯ ɱɢɫɟɥ. ȼɵɞɚɟɦ ɫɨɨɛɳɟɧɢɟ ɨ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɩɪɨɜɟɫɬɢ ɤɨɪɪɟɤɬɢɪɨɜɤɭ ɱɢɫɥɚ. ȼɵɡɵɜɚɟɦ ɩɪɨɰɟɞɭɪɵ ɞɥɹ ɮɨɪɦɢɪɨɜɚɧɢɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɧɨɦɟɪɨɜ ɱɢɫɟɥ. Ɂɚɩɭɫɤɚɟɦ ɞɚɬɱɢɤ ɫɥɭɱɚɣɧɵɯ ɱɢɫɟɥ ɢ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɡɚɩɢɫɵɜɚɟɦ ɱɢɫɥɚ ɜ ɡɚɞɚɧɧɵɣ ɞɢɚɩɚɡɨɧ. ȼ ɤɨɧɰɟ ɜɵɡɵɜɚɟɦ ɩɪɨɰɟɞɭɪɭ ɩɨɫɬɪɨɟɧɢɹ ɝɪɚɮɢɤɚ ɫɥɭɱɚɣɧɵɯ ɱɢɫɟɥ, ɤɨɬɨɪɚɹ ɧɚɯɨɞɢɬɫɹ ɜ ɦɨɞɭɥɟ. Public Sub Ƚɪɚɮɢɤ() ActiveSheet.ChartObjects.Add(100, 30, 250, 200).Select 'Ⱦɨɛɚɜɥɹɟɦ ɞɢɚɝɪɚɦɦɭ ɧɚ ɚɤɬɢɜɧɵɣ ɥɢɫɬ ActiveSheet.ChartObjects(1).Chart.Axes(xlValue).MaximumScale = 70 'Ɂɚɞɚɧɢɟ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ ɨɫɢ Y ActiveSheet.ChartObjects(1).Chart.Axes(xlCategory).MaximumScale = 30 'Ɂɚɞɚɧɢɟ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ ɨɫɢ ɏ ActiveChart.ChartWizard Source:=Range("A2:B31") 'Ɇɚɫɫɢɜ ɞɚɧɧɵɯ ɞɢɚɝɪɚɦɦɵ ActiveChart.ChartWizard Gallery:=xlXYScatterLines 'Ɍɨɱɟɱɧɚɹ ɞɢɚɝɪɚɦɦɚ ɫ ɥɢɧɢɹɦɢ ActiveChart.ChartWizard Format:=1 'Ɍɢɩ ɮɨɪɦɚɬɚ ɞɢɚɝɪɚɦɦɵ ActiveChart.ChartWizard PlotBy:=xlColumns 'Ⱦɥɹ ɩɨɫɬɪɨɟɧɢɹ ɞɢɚɝɪɚɦɦɵ ɢɫɩɨɥɶɡɭɸɬɫɹ ɫɬɨɥɛɰɵ 35

1. Ɉ ɦɨɞɟɥɢɪɨɜɚɧɢɢ, ɪɟɲɟɧɢɢ ɡɚɞɚɱ, ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɢ ɢ MS Excel

ActiveChart.ChartWizard CategoryLabels:=1 'ɉɟɪɜɵɣ ɫɬɨɥɛɟɰ ɞɥɹ ɞɚɧɧɵɯ ɨɫɢ ɏ ActiveChart.ChartWizard SeriesLabels:=0 ' ActiveChart.ChartWizard HasLegend:=False 'ɇɟɬ ɥɟɝɟɧɞɵ ActiveChart.ChartWizard Title:="Ƚɪɚɮɢɤ ɫɥɭɱɚɣɧɵɯ ɱɢɫɟɥ" 'Ɂɚɝɨɥɨɜɨɤ ɞɢɚɝɪɚɦɦɵ ActiveChart.ChartWizard CategoryTitle:="ɇɨɦɟɪ ɱɢɫɥɚ" 'ɇɚɡɜɚɧɢɟ ɨɫɢ ɏ ActiveChart.ChartWizard ValueTitle:="Ɂɧɚɱɟɧɢɟ ɱɢɫɥɚ" 'ɇɚɡɜɚɧɢɟ ɨɫɢ Y End Sub. ȼɧɚɱɚɥɟ ɫ ɩɨɦɨɳɶɸ ɦɟɬɨɞɚ Add ɫɨɡɞɚɟɦ ɞɢɚɝɪɚɦɦɭ ɧɚ ɚɤɬɢɜɧɨɦ ɥɢɫɬɟ. ȼ ɩɚɪɚɦɟɬɪɚɯ ɦɟɬɨɞɚ ɭɤɚɡɵɜɚɟɦ ɪɚɫɩɨɥɨɠɟɧɢɟ ɧɚ ɪɚɛɨɱɟɦ ɥɢɫɬɟ ɢ ɪɚɡɦɟɪɵ ɞɢɚɝɪɚɦɦɵ. Ⱦɚɥɟɟ ɢɫɩɨɥɶɡɭɟɦ ɦɟɬɨɞ ChartWizard ɞɥɹ ɮɨɪɦɢɪɨɜɚɧɢɹ ɷɥɟɦɟɧɬɨɜ ɞɢɚɝɪɚɦɦɵ ɢ ɡɚɞɚɧɢɹ ɢɯ ɩɚɪɚɦɟɬɪɨɜ. Ɇɟɬɨɞ ɩɨɡɜɨɥɹɟɬ ɫɨɡɞɚɜɚɬɶ ɢ ɩɪɨɢɡɜɨɞɢɬɶ ɢɡɦɟɧɟɧɢɹ ɜ ɭɠɟ ɫɭɳɟɫɬɜɭɸɳɢɯ ɞɢɚɝɪɚɦɦɚɯ. Ɉɧ ɢɦɟɟɬ 11 ɚɪɝɭɦɟɧɬɨɜ. ɇɨ ɩɟɪɟɞ ɷɬɢɦ ɡɚɞɚɟɦ ɫɜɨɣɫɬɜɚ ɨɫɟɣ ɝɪɚɮɢɤɚ. ɂɯ ɦɚɤɫɢɦɚɥɶɧɵɟ ɡɧɚɱɟɧɢɹ, ɤɨɬɨɪɵɟ ɜ ɧɚɲɟɦ ɫɥɭɱɚɟ ɮɢɤɫɢɪɨɜɚɧɧɵɟ. Ɉɫɬɚɟɬɫɹ ɫɨɡɞɚɬɶ ɩɪɨɰɟɞɭɪɭ ɞɥɹ ɤɧɨɩɤɢ «ɍɞɚɥɟɧɢɟ ɱɢɫɟɥ». Ⱦɜɚɠɞɵ ɳɟɥɤɚɟɦ ɧɚ ɤɧɨɩɤɟ ɢ ɜ ɨɤɧɟ ɤɨɞɨɜ ɫɨɡɞɚɟɦ ɩɪɨɰɟɞɭɪɭ. Private Sub CommandButton2_Click() 'ɍɞɚɥɟɧɢɟ ɱɢɫɟɥ If ActiveSheet.ChartObjects.Count > 0 Then ActiveSheet.ChartObjects.Delete 'ɍɞɚɥɟɧɢɟ ɫɨɡɞɚɧɧɵɯ ɞɢɚɝɪɚɦɦ End If Range(Cells(2, 1), Cells(31, 2)) = Null 'ɍɞɚɥɟɧɢɟ ɱɢɫɟɥ ɢɡ ɦɚɫɫɢɜɚ End Sub. ȼ ɩɪɨɰɟɞɭɪɟ ɭɞɚɥɹɟɦ ɞɢɚɝɪɚɦɦɵ ɢ ɬɨɥɶɤɨ ɨɱɢɳɚɟɦ ɦɚɫɫɢɜ ɱɢɫɟɥ. Ɂɚɝɨɥɨɜɤɢ ɫɬɨɥɛɰɨɜ ɧɟ ɬɪɨɝɚɟɦ. ȼɟɫɶ ɦɚɫɫɢɜ ɱɢɫɬɢɦ ɩɪɢ ɡɚɤɪɵɬɢɢ ɮɚɣɥɚ. ɍɞɚɥɹɟɦ ɞɢɚɝɪɚɦɦɵ ɫ ɰɟɥɶɸ ɨɛɟɫɩɟɱɟɧɢɹ ɮɨɪɦɢɪɨɜɚɧɢɹ ɦɚɤɫɢɦɚɥɶɧɵɯ ɡɧɚɱɟɧɢɣ ɨɫɟɣ ɝɪɚɮɢɤɚ, ɤɨɬɨɪɵɟ ɩɪɢɧɚɞɥɟɠɚɬ ɞɢɚɝɪɚɦɦɟ ɫ ɩɨɪɹɞɤɨɜɵɦ ɧɨɦɟɪɨɦ 1. ȿɫɥɢ ɧɟ ɭɞɚɥɹɬɶ ɞɢɚɝɪɚɦɦɵ, ɬɨ ɧɨɦɟɪɚ ɝɪɚɮɢɤɨɜ ɛɭɞɭɬ ɪɚɫɬɢ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɫɜɨɣɫɬɜɚ ɨɫɟɣ ɞɥɹ ɞɪɭɝɢɯ ɝɪɚɮɢɤɨɜ (ɫ ɧɨɦɟɪɚɦɢ ɨɬɥɢɱɧɵɦɢ ɨɬ 1) ɧɟ ɛɭɞɭɬ ɡɚɞɚɜɚɬɶɫɹ. Ɇɨɞɟɥɶ ɝɨɬɨɜɚ ɤ ɢɫɩɨɥɶɡɨɜɚɧɢɸ. ɇɭɠɧɨ ɡɚɧɟɫɬɢ ɤɨɥɢɱɟɫɬɜɨ ɝɟɧɟɪɢɪɭɟɦɵɯ ɫɥɭɱɚɣɧɵɯ ɱɢɫɟɥ. ɓɟɥɤɧɭɬɶ ɧɚ ɤɧɨɩɤɟ «ɋɬɪɨɢɦ ɝɪɚɮɢɤ». ɉɨɥɭɱɢɦ ɝɪɚɮɢɤ. Ɇɨɠɧɨ ɟɳɟ ɧɟɫɤɨɥɶɤɨ ɪɚɡ ɳɟɥɤɧɭɬɶ ɩɨ ɷɬɨɣ ɤɧɨɩɤɟ. Ȼɭɞɟɦ ɧɚɛɥɸɞɚɬɶ ɢɡɦɟɧɟɧɢɹ ɧɚ ɝɪɚɮɢɤɟ. ɉɪɢ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɭɞɚɥɹɟɦ ɫɥɭɱɚɣɧɵɟ ɱɢɫɥɚ ɢ ɫɬɪɨɢɦ ɧɨɜɵɣ ɝɪɚɮɢɤ. Ɍɚɤɠɟ ɦɨɠɧɨ ɢɡɦɟɧɹɬɶ ɤɨɥɢɱɟɫɬɜɨ ɱɢɫɟɥ. ɉɪɢ ɡɚɤɪɵɬɢɢ ɮɚɣɥɚ ɧɭɠɧɨ ɡɚɤɪɵɬɶ ɮɨɪɦɭ.

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1.4. VBA ɢ Excel

ɇɚɞɟɟɦɫɹ, ɱɬɨ ɩɪɟɞɫɬɚɜɥɟɧɧɚɹ ɢɧɮɨɪɦɚɰɢɹ ɜ ɩɚɪɚɝɪɚɮɟ ɩɨɡɜɨɥɢɬ ɪɚɡɨɛɪɚɬɶɫɹ ɜ ɤɨɞɚɯ, ɪɚɫɫɦɨɬɪɟɧɧɵɯ ɦɨɞɟɥɟɣ ɜ ɤɧɢɝɟ. Ɂɞɟɫɶ ɧɟ ɪɚɫɫɦɚɬɪɢɜɚɥɢ ɨɫɧɨɜɵ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ, ɫɢɧɬɚɤɫɢɫ ɨɫɧɨɜɧɵɯ ɚɥɝɨɪɢɬɦɢɱɟɫɤɢɯ ɫɬɪɭɤɬɭɪ ɜ VBA. ȼɫɟ ɷɬɨ ɦɨɠɧɨ ɧɚɣɬɢ ɜ ɥɸɛɨɦ ɭɱɟɛɧɢɤɟ. ȿɫɥɢ ɜɨɡɧɢɤɚɸɬ ɤɚɤɢɟ-ɬɨ ɬɪɭɞɧɨɫɬɢ ɩɪɢ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɢ, ɡɚɩɢɲɢɬɟ ɦɚɤɪɨɫ ɫ ɞɟɣɫɬɜɢɹɦɢ, ɤɨɬɨɪɵɟ ɜɚɫ ɢɧɬɟɪɟɫɭɸɬ, ɢ ɩɨɫɦɨɬɪɢɬɟ ɤɨɞ ɦɚɤɪɨɫɚ. ȼ ɨɩɪɟɞɟɥɟɧɧɵɯ ɫɥɭɱɚɹɯ ɬɚɦ ɧɚɣɞɟɬɟ ɩɭɬɢ ɪɟɲɟɧɢɹ ɜɨɡɧɢɤɲɢɯ ɩɪɨɛɥɟɦ. Ɇɨɠɧɨ ɫɤɪɵɬɶ ɤɨɞɵ ɦɨɞɟɥɢ. Ⱦɥɹ ɷɬɨɝɨ ɱɟɪɟɡ ɦɟɧɸ Tools ɪɟɞɚɤɬɨɪɚ VBA ɜɵɣɬɢ ɧɚ ɩɭɧɤɬ VBAProjectProperties ɢ ɜ ɩɨɹɜɢɜɲɟɦɫɹ ɨɤɧɟ ɧɚ ɜɤɥɚɞɤɟ Protection ɜɤɥɸɱɢɬɶ Lock project for viewing, ɜɧɟɫɬɢ ɩɚɪɨɥɶ ɢ ɳɟɥɤɧɭɬɶ OK. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɤɨɞɵ ɧɟ ɛɭɞɭɬ ɩɪɨɫɦɚɬɪɢɜɚɬɶɫɹ ɩɪɢ ɨɬɤɪɵɬɢɢ ɮɚɣɥɚ ɦɨɞɟɥɢ.

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1. Ɉ ɦɨɞɟɥɢɪɨɜɚɧɢɢ, ɪɟɲɟɧɢɢ ɡɚɞɚɱ, ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɢ ɢ MS Excel

1.5. ɋɨɡɞɚɧɢɟ ɫɱɟɬɱɢɤɨɜ ɞɥɹ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɩɪɨɰɟɫɫɚ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɋɱɟɬɱɢɤɢ ɧɟɨɛɯɨɞɢɦɵ ɞɥɹ ɨɫɭɳɟɫɬɜɥɟɧɢɹ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɢ ɩɪɢ ɪɟɲɟɧɢɢ ɞɢɧɚɦɢɱɟɫɤɢɯ ɡɚɞɚɱ. ɋɱɟɬɱɢɤɢ ɦɨɝɭɬ ɛɵɬɶ ɞɟɬɟɪɦɢɧɢɪɨɜɚɧɧɵɦɢ ɢ ɫɥɭɱɚɣɧɵɦɢ, ɩɟɪɢɨɞɢɱɟɫɤɢɦɢ ɢ ɧɟɩɟɪɢɨɞɢɱɟɫɤɢɦɢ, ɚ ɬɚɤɠɟ ɝɟɧɟɪɢɪɨɜɚɬɶ ɱɢɫɥɚ, ɜɪɟɦɹ ɢɥɢ ɞɚɬɵ. Ɏɭɧɤɰɢɨɧɢɪɨɜɚɬɶ ɫɱɟɬɱɢɤɢ ɦɨɝɭɬ ɚɜɬɨɦɚɬɢɱɟɫɤɢ ɢɥɢ ɚɜɬɨɦɚɬɢɡɢɪɨɜɚɧɨ, ɡɚɩɭɫɤɚɬɶɫɹ (ɨɫɬɚɧɚɜɥɢɜɚɬɶɫɹ) – ɜɪɭɱɧɭɸ ɢɥɢ ɩɪɢ ɜɵɩɨɥɧɟɧɢɢ ɡɚɞɚɧɧɵɯ ɭɫɥɨɜɢɣ. Ɋɚɫɫɦɨɬɪɢɦ ɫɨɡɞɚɧɢɟ ɫɱɟɬɱɢɤɨɜ, ɤɨɬɨɪɵɟ ɛɭɞɭɬ ɜ ɞɚɥɶɧɟɣɲɟɦ ɩɪɢɦɟɧɹɬɶɫɹ ɩɪɢ ɪɟɲɟɧɢɢ ɡɚɞɚɱ. ɋɚɦɵɦ ɩɪɨɫɬɵɦ ɫɱɟɬɱɢɤɨɦ ɹɜɥɹɟɬɫɹ ɜɵɛɪɚɧɧɚɹ ɹɱɟɣɤɚ, ɜ ɤɨɬɨɪɭɸ ɩɟɪɢɨɞɢɱɟɫɤɢ ɡɚɧɨɫɹɬɫɹ ɧɭɠɧɵɟ ɡɧɚɱɟɧɢɹ ɫ ɤɥɚɜɢɚɬɭɪɵ ɉɄ. Ɉɱɟɧɶ ɭɞɨɛɧɨ ɟɟ ɢɫɩɨɥɶɡɨɜɚɬɶ ɧɚ ɷɬɚɩɟ ɨɬɥɚɞɤɢ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ. Ɂɧɚɱɟɧɢɹ ɫɱɟɬɱɢɤɚ ɦɨɠɧɨ ɡɚɞɚɬɶ ɜ ɜɢɞɟ ɬɚɛɥɢɰɵ (ɫɬɨɥɛɰɚ) ɜɯɨɞɧɵɯ ɞɚɧɧɵɯ, ɤɨɝɞɚ ɬɨɱɧɨ ɢɡɜɟɫɬɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɡɧɚɱɟɧɢɹ ɩɪɢ ɪɟɲɟɧɢɢ ɡɚɞɚɱɢ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɦɨɠɧɨ ɫɪɚɡɭ ɭɜɢɞɟɬɶ ɜɨɡɧɢɤɚɸɳɢɟ ɨɲɢɛɤɢ ɜ ɪɚɫɱɟɬɚɯ ɩɪɢ ɨɩɪɟɞɟɥɟɧɧɵɯ ɡɧɚɱɟɧɢɹɯ ɫɱɟɬɱɢɤɚ. ɇɨ ɬɚɤɢɟ ɫɱɟɬɱɢɤɢ ɧɟ ɨɱɟɧɶ ɭɞɨɛɧɵ ɩɪɢ ɞɟɦɨɧɫɬɪɚɰɢɢ ɦɨɞɟɥɟɣ ɢɥɢ ɜ ɞɢɧɚɦɢɱɟɫɤɢɯ ɡɚɞɚɱɚɯ. ȼɨɫɩɨɥɶɡɭɟɦɫɹ ɜɨɡɦɨɠɧɨɫɬɹɦɢ MS Excel ɞɥɹ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɫɱɟɬɱɢɤɨɜ. ɋɱɟɬɱɢɤ ɞɨɥɠɟɧ ɭɫɬɚɧɚɜɥɢɜɚɬɶɫɹ ɜ ɧɚɱɚɥɶɧɨɟ ɩɨɥɨɠɟɧɢɟ, ɚɜɬɨɦɚɬɢɱɟɫɤɢ ɧɚɱɢɫɥɹɬɶɫɹ ɩɪɢ ɳɟɥɱɤɚɯ ɧɚ ɤɧɨɩɤɟ ɢ ɢɦɟɬɶ ɜɨɡɦɨɠɧɨɫɬɶ ɤɨɪɪɟɤɰɢɢ ɢɧɬɟɪɜɚɥɚ ɢɡɦɟɧɟɧɢɹ ɡɧɚɱɟɧɢɣ. ɋɨɡɞɚɞɢɦ ɫɱɟɬɱɢɤ ɰɟɥɵɯ ɱɢɫɟɥ ɫ ɡɚɞɚɧɧɵɦ ɢɧɬɟɪɜɚɥɨɦ ɢɡɦɟɧɟɧɢɣ. ɋɮɨɪɦɢɪɭɟɦ ɹɱɟɣɤɢ ɫ ɧɚɱɚɥɶɧɵɦ ɡɧɚɱɟɧɢɟɦ, ɢɧɬɟɪɜɚɥɨɦ ɢɡɦɟɧɟɧɢɣ ɢ ɫɚɦɭ ɹɱɟɣɤɭ ɫɱɟɬɱɢɤɚ. Ɍɟɩɟɪɶ ɦɨɠɧɨ ɩɪɢɫɬɭɩɢɬɶ ɤ ɮɨɪɦɢɪɨɜɚɧɢɸ ɤɧɨɩɨɤ ɢɡɦɟɧɟɧɢɹ ɡɧɚɱɟɧɢɣ ɫɱɟɬɱɢɤɚ ɢ ɟɝɨ «ɨɛɧɭɥɟɧɢɹ» ɢɥɢ ɡɚɞɚɧɢɹ ɧɚɱɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ. Ɉɛɪɚɳɚɟɦɫɹ ɤ ɡɚɤɥɚɞɤɟ Ɋɚɡɪɚɛɨɬɱɢɤ ɢ ɜ ɝɪɭɩɩɟ ɗɥɟɦɟɧɬɵ ɭɩɪɚɜɥɟɧɢɹ ɢɡ ɫɩɢɫɤɚ ȼɫɬɚɜɢɬɶ ɜɵɛɢɪɚɟɦ ɤɧɨɩɤɭ ɢɡ ɗɥɟɦɟɧɬɵ ActiveX. ɉɪɨɬɹɠɤɨɣ ɨɩɪɟɞɟɥɹɟɦ ɪɚɡɦɟɪɵ ɤɧɨɩɨɤ, ɜ ɤɨɧɬɟɤɫɬɧɨɦ ɦɟɧɸ ɤɧɨɩɤɢ ɱɟɪɟɡ ɩɭɧɤɬ ɋɜɨɣɫɬɜɚ ɜɵ38

1.5. ɋɨɡɞɚɧɢɟ ɫɱɟɬɱɢɤɨɜ ɞɥɹ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɩɪɨɰɟɫɫɚ ɦɨɞɟɥɢɪɨɜɚɧɢɹ

ɡɵɜɚɟɦ ɨɤɧɨ Properties (ɋɜɨɣɫɬɜɚ) ɢ ɜ Caption (Ɂɚɝɨɥɨɜɨɤ) ɜɧɨɫɢɦ ɧɚɡɜɚɧɢɟ «Ɉɛɧɭɥɟɧɢɟ ɫɱɟɬɱɢɤɚ». ȼ ɪɟɠɢɦɟ Ʉɨɧɫɬɪɭɤɬɨɪɚ ɞɜɚɠɞɵ ɳɟɥɤɚɟɦ ɧɚ ɤɧɨɩɤɟ ɢ ɜɧɨɫɢɦ ɫɥɟɞɭɸɳɢɣ ɬɟɤɫɬ ɩɪɨɝɪɚɦɦɵ: Private Sub CommandButton1_Click() Cells(3, 2) = Cells(1, 2) End Sub. ȼ ɮɭɧɤɰɢɢ Cells ɭɤɚɡɵɜɚɟɦ ɧɨɦɟɪ ɫɬɪɨɤɢ ɢ ɧɨɦɟɪ ɫɬɨɥɛɰɚ ɧɭɠɧɨɣ ɹɱɟɣɤɢ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɫɱɟɬɱɢɤɭ ɩɪɢɫɜɚɢɜɚɟɬɫɹ ɧɚɱɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ. ɉɨɫɥɟ ɫɨɡɞɚɧɢɹ ɩɪɨɝɪɚɦɦɵ ɤɧɨɩɤɢ ɡɚɤɪɵɜɚɟɦ ɤɧɢɝɭ ɫ ɫɨɯɪɚɧɟɧɢɟɦ ɢɡɦɟɧɟɧɢɣ ɢ ɨɬɤɪɵɜɚɟɦ ɫ ɭɫɬɚɧɨɜɤɨɣ ɪɚɡɪɟɲɟɧɢɹ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɦɚɤɪɨɫɨɜ. ɓɟɥɤɧɭɜ ɧɚ ɤɧɨɩɤɟ «Ɉɛɧɭɥɟɧɢɟ ɫɱɟɬɱɢɤɚ» ɩɪɢɫɜɚɢɜɚɟɦ ɫɱɟɬɱɢɤɭ ɧɚɱɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ. Ⱥɧɚɥɨɝɢɱɧɨ ɫɨɡɞɚɟɦ ɤɧɨɩɤɭ ɞɥɹ ɧɚɱɢɫɥɟɧɢɹ ɫɱɟɬɱɢɤɚ ɩɨɞ ɧɚɡɜɚɧɢɟɦ «ɋɱɟɬɱɢɤ». ɉɪɨɝɪɚɦɦɚ ɤɧɨɩɤɢ ɢɦɟɟɬ ɫɥɟɞɭɸɳɢɣ ɜɢɞ: Private Sub CommandButton2_Click() Cells(3, 2) = Cells(3, 2) + Cells(2, 2) End Sub. Ɍɟɩɟɪɶ ɩɪɢ ɳɟɥɱɤɟ ɧɚ ɫɨɡɞɚɧɧɨɣ ɤɧɨɩɤɟ ɛɭɞɭɬ ɭɜɟɥɢɱɢɜɚɬɶɫɹ ɡɧɚɱɟɧɢɹ ɫɱɟɬɱɢɤɚ. Ɇɨɠɧɨ ɫɞɟɥɚɬɶ ɞɨɩɨɥɧɢɬɟɥɶɧɭɸ ɤɧɨɩɤɭ ɞɥɹ ɭɦɟɧɶɲɟɧɢɹ ɡɧɚɱɟɧɢɣ ɫɱɟɬɱɢɤɚ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɜ ɩɪɨɝɪɚɦɦɟ ɜɦɟɫɬɨ ɩɥɸɫɚ ɧɭɠɧɨ ɩɨɫɬɚɜɢɬɶ ɦɢɧɭɫ. ɂɧɨɝɞɚ ɰɟɥɟɫɨɨɛɪɚɡɧɨ ɫɨɡɞɚɬɶ ɞɢɚɥɨɝɨɜɨɟ ɨɤɧɨ ɫ ɩɨɦɨɳɶɸ ɮɨɪɦ ɞɥɹ ɭɩɪɚɜɥɟɧɢɹ ɫɱɟɬɱɢɤɨɦ. ɉɨɩɪɨɛɭɟɦ ɫɨɡɞɚɬɶ ɞɢɚɥɨɝɨɜɨɟ ɨɤɧɨ ɧɚ ɛɚɡɟ ɩɪɢɜɟɞɟɧɧɨɝɨ ɜɵɲɟ ɩɪɢɦɟɪɚ. ɑɟɪɟɡ ɡɚɤɥɚɞɤɭ Ɋɚɡɪɚɛɨɬɱɢɤ ɜ ɝɪɭɩɩɟ Ʉɨɞ ɳɟɥɤɚɟɦ ɧɚ ɤɧɨɩɤɟ Visual Basic. ɉɨɹɜɥɹɟɬɫɹ ɨɤɧɨ ɢɧɬɟɝɪɢɪɨɜɚɧɧɨɣ ɫɪɟɞɵ ɪɚɡɪɚɛɨɬɤɢ ɹɡɵɤɚ VBA. ȼ ɦɟɧɸ Insert ɜɵɛɢɪɚɟɦ UserForm. ȼ ɨɤɧɟ ɫɜɨɣɫɬɜ Alphabetic ɜɵɛɢɪɚɟɦ ɩɭɧɤɬ ɧɚɡɜɚɧɢɟ Caption ɢ ɜɧɨɫɢɦ ɫɥɨɜɨ ɍɩɪɚɜɥɟɧɢɟ ɫɱɟɬɱɢɤɨɦ, ɜ ɩɭɧɤɬɟ Name ɜɧɨɫɢɦ ɢɦɹ ɮɨɪɦɵ Chet. ɇɚ ɩɚɧɟɥɢ ɢɧɫɬɪɭɦɟɧɬɨɜ Toolbox ɜɵɛɢɪɚɟɦ ɤɨɦɚɧɞɧɭɸ ɤɧɨɩɤɭ CommandButton ɢ ɩɪɨɬɹɠɤɨɣ ɪɚɡɦɟɳɚɟɦ ɟɟ ɧɚ ɨɤɧɟ ɮɨɪɦɵ. ɑɟɪɟɡ ɤɨɧɬɟɤɫɬɧɨɟ ɦɟɧɸ ɤɧɨɩɤɢ ɜɵɯɨɞɢɦ ɧɚ ɟɟ ɫɜɨɣɫɬɜɚ 39

1. Ɉ ɦɨɞɟɥɢɪɨɜɚɧɢɢ, ɪɟɲɟɧɢɢ ɡɚɞɚɱ, ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɢ ɢ MS Excel

Properties, ɝɞɟ ɜ ɩɭɧɤɬɟ ɧɚɡɜɚɧɢɟ ɡɚɩɢɫɵɜɚɟɦ Ɉɛɧɭɥɟɧɢɟ ɫɱɟɬɱɢɤɚ. Ⱥɧɚɥɨɝɢɱɧɨ ɫɨɡɞɚɟɦ ɜɬɨɪɭɸ ɤɧɨɩɤɭ ɫ ɧɚɡɜɚɧɢɟɦ ɋɱɟɬɱɢɤ. ɋɪɚɡɭ ɦɨɠɧɨ ɧɚɩɨɦɧɢɬɶ ɨ ɬɨɦ, ɱɬɨ ɢɫɩɨɥɶɡɭɹ ɩɭɧɤɬɵ ɫɜɨɣɫɬɜ ɮɨɪɦɵ ɢ ɤɧɨɩɨɤ ɦɨɠɧɨ ɛɟɡ ɡɚɬɪɭɞɧɟɧɢɣ ɢɡɦɟɧɢɬɶ ɢɯ ɰɜɟɬ, ɲɪɢɮɬ ɧɚɞɩɢɫɟɣ ɧɚ ɤɧɨɩɤɚɯ. Ɇɨɠɧɨ ɬɚɤɠɟ ɭɦɟɧɶɲɢɬɶ ɪɚɡɦɟɪ ɮɨɪɦɵ ɫ ɤɧɨɩɤɚɦɢ. Ɍɟɩɟɪɶ ɦɨɠɧɨ ɩɟɪɟɣɬɢ ɤ ɩɪɨɝɪɚɦɦɧɨɦɭ ɤɨɞɭ ɤɧɨɩɨɤ ɢ ɜɧɟɫɬɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɢɦ ɩɪɨɝɪɚɦɦɵ. ɉɪɨɝɪɚɦɦɵ ɨɛɴɟɤɬɨɜ ɛɭɞɭɬ ɡɚɩɭɫɤɚɬɶɫɹ ɩɨ ɳɟɥɱɤɭ ɧɚ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɤɧɨɩɤɚɯ. ɓɟɥɤɧɟɦ ɞɜɚɠɞɵ ɩɨ ɩɟɪɜɨɣ, ɡɚɬɟɦ ɩɨ ɜɬɨɪɨɣ ɤɧɨɩɤɟ ɢ ɨɤɧɚɯ ɤɨɞɨɜ ɭɜɢɞɢɦ ɡɚɝɨɬɨɜɤɢ ɩɪɨɝɪɚɦɦ ɞɥɹ ɤɧɨɩɨɤ ɢ ɮɨɪɦɵ. ɉɪɨɰɟɞɭɪɵ ɨɛɴɟɤɬɨɜ ɧɚɱɢɧɚɸɬ ɮɭɧɤɰɢɨɧɢɪɨɜɚɬɶ ɩɨ ɳɟɥɱɤɭ (ɫɨɛɵɬɢɸ Click). ȼɧɟɫɟɦ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɤɨɞɵ ɩɪɨɝɪɚɦɦ ɞɥɹ ɤɧɨɩɨɤ ɢ ɤɨɦɦɟɧɬɚɪɢɢ. ɉɟɪɜɚɹ ɤɧɨɩɤɚ ɨɛɟɫɩɟɱɢɜɚɟɬ ɭɫɬɚɧɨɜɤɭ ɧɚɱɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ (ɨɛɧɭɥɟɧɢɟ) ɫɱɟɬɱɢɤɚ, ɚ ɜɬɨɪɚɹ ɩɨ ɳɟɥɱɤɭ ɢɡɦɟɧɹɟɬ ɡɧɚɱɟɧɢɟ ɫɱɟɬɱɢɤɚ ɧɚ ɡɚɞɚɧɧɵɣ ɲɚɝ. Ɍɟɩɟɪɶ ɦɨɠɧɨ ɡɚɧɹɬɶɫɹ ɩɪɨɝɪɚɦɦɨɣ ɮɨɪɦɵ. Ɂɞɟɫɶ ɧɭɠɧɨ ɨɬɦɟɬɢɬɶ ɜɚɪɢɚɧɬɵ ɜɵɡɨɜɚ ɮɨɪɦɵ ɧɚ ɥɢɫɬ. ɋɭɳɟɫɬɜɭɸɬ ɞɜɚ ɧɚɢɛɨɥɟɟ ɭɞɚɱɧɵɯ ɫɩɨɫɨɛɚ ɜɵɡɨɜɚ ɮɨɪɦɵ: x ȼɵɡɨɜ ɱɟɪɟɡ ɤɨɦɚɧɞɧɭɸ ɤɧɨɩɤɭ, ɫɨɡɞɚɧɧɭɸ ɧɚ ɥɢɫɬɟ. x ȼɵɡɨɜ ɩɪɢ ɨɬɤɪɵɬɢɢ ɤɧɢɝɢ. Ɋɚɫɫɦɨɬɪɢɦ ɜɵɡɨɜ ɮɨɪɦɵ ɱɟɪɟɡ ɤɧɨɩɤɭ. Ⱦɥɹ ɷɬɨɝɨ ɫɨɡɞɚɟɦ ɤɧɨɩɤɭ ɧɚ ɥɢɫɬɟ ɱɟɪɟɡ ɡɚɤɥɚɞɤɭ Ɋɚɡɪɚɛɨɬɱɢɤ, ɝɪɭɩɩɭ ɗɥɟɦɟɧɬɵ ɭɩɪɚɜɥɟɧɢɹ. ȼ ɫɩɢɫɤɟ ȼɫɬɚɜɢɬɶ ɜɵɛɢɪɚɟɦ ɤɧɨɩɤɭ ɢɡ ɗɥɟɦɟɧɬɵ ActiveX. ɉɪɨɬɹɠɤɨɣ ɨɩɪɟɞɟɥɹɟɦ ɪɚɡɦɟɪɵ ɤɧɨɩɤɢ ɧɚ ɥɢɫɬɟ, ɜ ɤɨɧɬɟɤɫɬɧɨɦ ɦɟɧɸ ɤɧɨɩɤɢ ɱɟɪɟɡ ɩɭɧɤɬ ɋɜɨɣɫɬɜɚ ɜɵɡɵɜɚɟɦ ɨɤɧɨ Properties (ɋɜɨɣɫɬɜɚ) ɢ ɜ Caption (Ɂɚɝɨɥɨɜɨɤ) ɜɧɨɫɢɦ ɧɚɡɜɚɧɢɟ Ɂɚɝɪɭɡɤɚ ɮɨɪɦɵ. ȼ ɪɟɠɢɦɟ Ʉɨɧɫɬɪɭɤɬɨɪɚ ɞɜɚɠɞɵ ɳɟɥɤɚɟɦ ɧɚ ɤɧɨɩɤɟ ɢ ɜɧɨɫɢɦ ɫɥɟɞɭɸɳɢɣ ɬɟɤɫɬ ɩɪɨɝɪɚɦɦɵ: Private Sub CommandButton3_Click() Chet.Show ‘ɉɨɤɚɡ ɨɛɴɟɤɬɚ ɮɨɪɦɵ ɫ ɢɦɟɧɟɦ Chet End Sub. Ⱦɚɥɟɟ ɨɛɪɚɳɚɟɦɫɹ ɤ ɩɪɨɝɪɚɦɦɟ ɮɨɪɦɚ ɢ ɜ ɫɩɢɫɤɟ ɫɨɛɵɬɢɣ ɜɵɛɢɪɚɟɦ Initialize. ȼɧɨɫɢɦ ɜɦɟɫɬɨ UserForm Chet. ȼɫɟ ɫɨɯɪɚɧɹɟɦ. ɉɪɢ ɳɟɥɱɤɟ ɩɨ ɤɧɨɩɤɟ Ɂɚɝɪɭɡɤɚ ɮɨɪɦɵ ɜɵɡɵɜɚɟɬɫɹ ɮɨɪɦɚ, ɚ ɩɪɢ ɳɟɥɱɤɟ ɧɚ ɭɩɪɚɜɥɹɸɳɟɦ ɷɥɟɦɟɧɬɟ Ɂɚɤɪɵɬɶ ɮɨɪɦɵ ɨɧɚ ɡɚɤɪɵɜɚɟɬɫɹ. 40

1.5. ɋɨɡɞɚɧɢɟ ɫɱɟɬɱɢɤɨɜ ɞɥɹ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɩɪɨɰɟɫɫɚ ɦɨɞɟɥɢɪɨɜɚɧɢɹ

Ɉɫɬɚɥɨɫɶ ɫɮɨɪɦɢɪɨɜɚɬɶ ɜɵɡɨɜ ɮɨɪɦɵ ɩɪɢ ɨɬɤɪɵɬɢɢ ɤɧɢɝɢ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɧɭɠɧɨ ɜ ɫɩɢɫɤɟ Microsoft Excel Object ɞɜɚɠɞɵ ɳɟɥɤɧɭɬɶ ɧɚ ɨɛɴɟɤɬɟ ɤɧɢɝɢ ɗɬɚɄɧɢɝɚ ɞɥɹ ɜɵɡɨɜɚ ɨɤɧɚ ɤɨɞɨɜ. Ⱦɚɥɟɟ ɧɭɠɧɨ ɜɧɟɫɬɢ ɩɪɨɝɪɚɦɦɭ ɩɪɨɰɟɞɭɪɵ ɫɥɟɞɭɸɳɟɝɨ ɜɢɞɚ: Private Sub Workbook_Open() Chet.Show End Sub. Ɏɭɧɤɰɢɹ Workbook_Open() ɚɜɬɨɦɚɬɢɱɟɫɤɢ ɡɚɩɭɫɤɚɟɬɫɹ ɩɪɢ ɨɬɤɪɵɬɢɢ ɤɧɢɝɢ ɢ ɜɵɩɨɥɧɹɟɬɫɹ ɡɚɩɢɫɚɧɧɚɹ ɩɪɨɝɪɚɦɦɚ. ɋɨɯɪɚɧɹɟɦ ɢ ɡɚɤɪɵɜɚɟɦ ɤɧɢɝɭ. ɉɪɢ ɜɵɡɨɜɟ ɤɧɢɝɢ ɧɭɠɧɨ ɪɚɡɪɟɲɢɬɶ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɟ ɦɚɤɪɨɫɨɜ ɢ ɷɥɟɦɟɧɬɨɜ ActiveX. Ⱦɚɥɟɟ ɩɨɹɜɢɬɶɫɹ ɫɨɡɞɚɧɧɚɹ ɮɨɪɦɚ ɭɩɪɚɜɥɟɧɢɹ ɫɱɟɬɱɢɤɨɦ. ȼɵɛɨɪ ɜɵɡɨɜɚ ɮɨɪɦɵ ɡɚɜɢɫɢɬ ɜ ɨɫɧɨɜɧɨɦ ɨɬ ɢɧɞɢɜɢɞɭɚɥɶɧɵɯ ɩɪɢɫɬɪɚɫɬɢɣ ɩɨɥɶɡɨɜɚɬɟɥɹ ɉɄ. ɇɸɚɧɫɵ ɪɚɛɨɬɵ ɜ ɢɧɬɟɝɪɢɪɨɜɚɧɧɨɣ ɫɪɟɞɟ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ VBA ɜɫɟɝɞɚ ɦɨɠɧɨ ɜɵɹɫɧɢɬɶ ɜ ɦɚɬɟɪɢɚɥɚɯ, ɪɚɡɦɟɳɟɧɧɵɯ ɜ ɂɧɬɟɪɧɟɬɟ. Ɋɚɛɨɬɚ ɫɨ ɫɱɟɬɱɢɤɚɦɢ ɜɪɟɦɟɧɢ ɫɜɹɡɚɧɚ ɫ ɧɟɛɨɥɶɲɢɦɢ ɨɫɨɛɟɧɧɨɫɬɹɦɢ. Ɉɛɵɱɧɨ ɜ ɫɱɟɬɱɢɤɚɯ ɜɪɟɦɟɧɢ ɢɫɩɨɥɶɡɭɟɬɫɹ ɜɪɟɦɹ ɜ ɫɟɤɭɧɞɚɯ ɨɬ ɩɨɥɭɧɨɱɢ ɢɥɢ ɨɬ ɧɚɱɚɥɚ ɫɭɬɨɤ. ɉɨɷɬɨɦɭ ɜɨɡɧɢɤɚɸɬ ɡɚɞɚɱɢ ɩɟɪɟɫɱɟɬɚ ɜɪɟɦɟɧɢ ɢɡ ɫɟɤɭɧɞ ɜ ɱɚɫɵ, ɦɢɧɭɬɵ, ɚ ɡɚɬɟɦ ɨɛɪɚɬɧɨɝɨ ɩɟɪɟɫɱɟɬɚ ɜ ɫɟɤɭɧɞɵ ɢɡ ɡɚɞɚɧɧɨɝɨ ɜɪɟɦɟɧɢ ɜ ɱɚɫɚɯ, ɦɢɧɭɬɚɯ. Ⱦɥɹ ɪɟɲɟɧɢɹ ɷɬɢɯ ɡɚɞɚɱ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɭɠɟ ɢɦɟɸɳɢɟɫɹ ɮɭɧɤɰɢɢ ɢɥɢ ɫɨɡɞɚɬɶ ɩɨɥɶɡɨɜɚɬɟɥɶɫɤɢɟ. ɋɨɡɞɚɞɢɦ ɮɭɧɤɰɢɸ ɩɟɪɟɜɨɞɚ ɫɟɤɭɧɞ ɜ ɱɚɫɵ, ɦɢɧɭɬɵ, ɫɟɤɭɧɞɵ. ɂɫɯɨɞɢɦ ɢɡ ɬɨɝɨ, ɱɬɨ ɜ 1 ɦɢɧɭɬɟ 60 ɫɟɤɭɧɞ, ɚ ɜ 1 ɱɚɫɟ 60 ɦɢɧɭɬ. Ɉɩɹɬɶ ɨɛɪɚɬɢɦɫɹ ɱɟɪɟɡ ɡɚɤɥɚɞɤɭ Ɋɚɡɪɚɛɨɬɱɢɤ ɤ ɤɧɨɩɤɟ Visual Basic ɢ ɜɵɡɨɜɟɦ ɪɟɞɚɤɬɨɪ VBA. ȼɵɛɢɪɚɟɦ ɩɭɧɤɬ ɫɨɡɞɚɧɢɹ ɧɨɜɨɝɨ ɦɨɞɭɥɹ Module ɜ ɦɟɧɸ Insert. ȼɧɨɫɢɦ ɫɥɨɜɨ Function, ɞɚɥɟɟ ɢɦɹ ɧɚɲɟɣ ɮɭɧɤɰɢɢ Hmc ɢ ɨɛɨɡɧɚɱɟɧɢɟ ɜɯɨɞɧɨɣ ɩɟɪɟɦɟɧɧɨɣ Second, ɫ ɩɨɦɨɳɶɸ ɤɨɬɨɪɨɣ ɛɭɞɟɬ ɩɟɪɟɞɚɜɚɬɶɫɹ ɡɧɚɱɟɧɢɟ ɫɱɟɬɱɢɤɚ ɫɟɤɭɧɞ ɨɬ ɧɚɱɚɥɚ ɫɭɬɨɤ. ȼ ɪɚɫɱɟɬɚɯ ɛɭɞɟɦ ɢɫɩɨɥɶɡɨɜɚɬɶ ɮɭɧɤɰɢɸ ɨɩɪɟɞɟɥɟɧɢɹ ɧɚɢɦɟɧɶɲɟɣ ɰɟɥɨɣ ɱɚɫɬɢ ɱɢɫɥɚ Int(). Ɍɚɤ ɤɚɤ ɜɪɟɦɹ ɰɟɥɟɫɨɨɛɪɚɡɧɨ ɩɨɤɚɡɵɜɚɬɶ ɫ ɪɚɡɦɟɪɧɨɫɬɹɦɢ, ɬɨ ɤɨɥɢɱɟɫɬɜɨ ɱɚɫɨɜ, ɦɢɧɭɬ ɢ ɫɟɤɭɧɞ ɩɨɫɥɟ ɪɚɫɱɟɬɚ ɩɪɟɨɛɪɚɡɨɜɵɜɚɟɦ ɜ ɫɬɪɨɤɢ ɫ ɩɨɦɨɳɶɸ ɮɭɧɤɰɢɢ Str(). ȼ ɤɨɧɰɟ ɫɮɨɪɦɢɪɭɟɦ ɫɬɪɨɤɭ

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1. Ɉ ɦɨɞɟɥɢɪɨɜɚɧɢɢ, ɪɟɲɟɧɢɢ ɡɚɞɚɱ, ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɢ ɢ MS Excel

ɜɪɟɦɟɧɢ ɫ ɭɤɚɡɚɧɢɟɦ ɪɚɡɦɟɪɧɨɫɬɟɣ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɱɚɫɬɟɣ.

ɉɨɫɥɟ ɜɧɟɫɟɧɢɹ ɬɟɤɫɬɚ ɩɪɨɝɪɚɦɦɵ ɮɭɧɤɰɢɢ ɡɚɤɪɵɜɚɟɦ ɨɤɧɚ ɪɟɞɚɤɬɨɪɚ, ɫɨɯɪɚɧɹɟɦ ɮɚɣɥ ɫ ɩɨɞɞɟɪɠɤɨɣ ɦɚɤɪɨɫɨɜ. Ɍɟɩɟɪɶ ɫɨɡɞɚɧɧɚɹ ɮɭɧɤɰɢɹ ɧɚɯɨɞɢɬɫɹ ɜ Ɇɚɫɬɟɪɟ ɮɭɧɤɰɢɣ ɜ ɤɚɬɟɝɨɪɢɢ Ɉɩɪɟɞɟɥɟɧɧɵɟ ɩɨɥɶɡɨɜɚɬɟɥɟɦ. ɉɪɢɦɟɪ ɩɪɢɦɟɧɟɧɢɟ ɩɨɥɶɡɨɜɚɬɟɥɶɫɤɨɣ ɮɭɧɤɰɢɢ Hmc() ɩɟɪɟɫɱɟɬɚ ɫɱɟɬɱɢɤɚ ɫɟɤɭɧɞ ɜ ɱɚɫɵ, ɦɢɧɭɬɵ, ɫɟɤɭɧɞɵ ɩɪɟɞɫɬɚɜɥɟɧ ɧɚ ɪɢɫɭɧɤɟ. ɉɪɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ ɞɥɹ ɪɹɞɚ ɡɚɞɚɱ ɧɟɨɛɯɨɞɢɦɵ ɫɱɟɬɱɢɤɢ ɧɚ ɛɚɡɟ ɞɚɬɱɢɤɨɜ ɫɥɭɱɚɣɧɵɯ ɱɢɫɟɥ. ɇɚɢɛɨɥɟɟ ɪɚɫɩɪɨɫɬɪɚɧɟɧɧɵɦ ɞɚɬɱɢɤɨɦ ɹɜɥɹɟɬɫɹ ɞɚɬɱɢɤ ɫ ɪɚɜɧɨɦɟɪɧɵɦ ɡɚɤɨɧɨɦ, ɤɨɬɨɪɵɣ ɨɛɥɚɞɚɟɬ ɧɚɢɛɨɥɶɲɟɣ ɷɧɬɪɨɩɢɟɣ. ɑɚɫɬɨ ɢɫɩɨɥɶɡɭɸɬɫɹ ɞɚɬɱɢɤɢ ɫ ɧɨɪɦɚɥɶɧɵɦ ɡɚɤɨɧɨɦ ɪɚɫɩɪɟɞɟɥɟɧɢɹ. ɋɨɡɞɚɞɢɦ ɫɱɟɬɱɢɤ ɧɚ ɨɫɧɨɜɟ ɞɚɬɱɢɤɚ ɫ ɪɚɜɧɨɦɟɪɧɵɦ ɪɚɫɩɪɟɞɟɥɟɧɢɟɦ ɱɢɫɟɥ. ɉɪɢ ɫɨɡɞɚɧɢɢ ɬɚɤɨɝɨ ɫɱɟɬɱɢɤɚ ɨɛɵɱɧɨ ɢɫɩɨɥɶɡɭɟɬɫɹ ɮɭɧɤɰɢɹ ɝɟɧɟɪɚɬɨɪɚ ɫɥɭɱɚɣɧɵɯ ɱɢɫɟɥ Rnd() ɢ ɩɪɨɰɟɞɭɪɚ Randomize. Ɏɭɧɤɰɢɹ Rnd (ɩɚɪɚɦɟɬɪ) ɜɨɡɜɪɚɳɚɟɬ ɫɥɭɱɚɣɧɵɟ ɱɢɫɥɚ ɢɡ ɢɧɬɟɪɜɚɥɚ [0,1), ɩɨɞɱɢɧɹɸɳɢɟɫɹ ɪɚɜɧɨɦɟɪɧɨɦɭ ɡɚɤɨɧɭ ɪɚɫɩɪɟɞɟɥɟɧɢɹ. Ɉɬ ɡɧɚɱɟɧɢɹ ɩɚɪɚɦɟɬɪɚ ɡɚɜɢɫɢɬ ɝɟɧɟɪɚɰɢɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɫɥɭɱɚɣɧɵɯ ɱɢɫɟɥ. Ɂɧɚɱɟɧɢɟ ɩɚɪɚɦɟɬɪɚ ɑɬɨ ɝɟɧɟɪɢɪɭɟɬɫɹ? Ɇɟɧɶɲɟ ɧɭɥɹ

Ʉɚɠɞɵɣ ɪɚɡ ɨɞɧɨ ɢ ɬɨɠɟ ɱɢɫɥɨ. ɉɚɪɚɦɟɬɪ ɢɫɩɨɥɶɡɭɟɬɫɹ ɤɚɤ ɧɚɱɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ.

Ɋɚɜɧɨ ɧɭɥɸ

ɉɨɫɥɟɞɧɟɟ ɫɝɟɧɟɪɢɪɨɜɚɧɧɨɟ ɱɢɫɥɨ.

Ȼɨɥɶɲɟ ɧɭɥɹ ɢɥɢ ɩɚɪɚɦɟɬɪ ɨɬɫɭɬɫɬɜɭɟɬ

ɋɥɟɞɭɸɳɢɟ ɫɥɭɱɚɣɧɨɟ ɱɢɫɥɨ ɜ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ.

ɉɟɪɟɞ ɜɵɡɨɜɨɦ ɮɭɧɤɰɢɢ Rnd() ɧɟɨɛɯɨɞɢɦɨ ɜɵɩɨɥɧɢɬɶ ɤɨɦɚɧɞɭ Randomize ɞɥɹ ɢɧɢɰɢɚɥɢɡɚɰɢɢ (ɡɚɩɭɫɤɚ) ɝɟɧɟɪɚɬɨɪɚ ɫɥɭɱɚɣɧɵɯ ɱɢɫɟɥ. ɉɪɢ ɷɬɨɦ ɭɫɬɚɧɚɜɥɢɜɚɟɬɫɹ ɧɚɱɚɥɶɧɨɟ ɱɢɫɥɨ ɞɥɹ ɝɟɧɟɪɚɬɨɪɚ, ɤɨɬɨɪɨɟ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɨɞɧɨɦɭ ɢɡ ɱɢɫɟɥ ɜ ɟɝɨ ɩɫɟɜɞɨɫɥɭɱɚɣɧɨɣ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɢɡ 232 ɱɢɫɟɥ. Randomize ɥɭɱɲɟ ɢɫɩɨɥɶɡɨɜɚɬɶ ɛɟɡ ɩɚɪɚɦɟɬɪɚ, ɱɬɨɛɵ ɡɚɩɭɫɤɚɬɶ ɝɟɧɟɪɚɬɨɪ ɫɥɭɱɚɣɧɨɝɨ ɱɢɫɥɚ ɫ ɧɚɱɚɥɶɧɵɦ ɱɢɫɥɨɦ, ɨɫɧɨɜɚɧɧɵɦ ɧɚ ɫɢɫɬɟɦɧɨɦ ɬɚɣɦɟɪɟ. ɉɭɫɬɶ ɡɚɞɚɧɨ ɫɪɟɞɧɟɟ ɡɧɚɱɟɧɢɟ ɞɢɚɩɚɡɨɧɚ ɱɢɫɟɥ ɱɢɫɥɨɦ a ɢ ɪɚɡɛɪɨɫ ɱɢɫɟɥ ɨɬɧɨɫɢɬɟɥɶɧɨ ɫɪɟɞɧɟɝɨ ɡɧɚɱɟɧɢɹ – b. Ɍɨɝɞɚ ɞɥɹ ɝɟɧɟɪɚɰɢɢ ɰɟɥɵɯ ɱɢɫɟɥ ɜ ɞɢɚɩɚɡɨɧɟ ɨɬ (ɚ-b) ɞɨ (ɚ+b) ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɫɥɟɞɭɸɳɢɟ ɜɵɪɚɠɟɧɢɟ: 42

1.5. ɋɨɡɞɚɧɢɟ ɫɱɟɬɱɢɤɨɜ ɞɥɹ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɩɪɨɰɟɫɫɚ ɦɨɞɟɥɢɪɨɜɚɧɢɹ

Int((a-b)+(2*b+1)*Rnd). ɉɪɢɛɚɜɥɟɧɢɟ 1 ɜ ɤɨɷɮɮɢɰɢɟɧɬɟ ɩɪɢ Rnd ɫɜɹɡɚɧɨ ɫ ɨɛɟɫɩɟɱɟɧɢɟɦ ɩɨɥɭɱɟɧɢɹ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɜɨɡɦɨɠɧɨɝɨ ɱɢɫɥɚ (ɚ+ b). Ɍɚɤ ɤɚɤ ɝɟɧɟɪɢɪɭɸɬɫɹ ɱɢɫɥɚ ɨɬ 0 (ɜɤɥɸɱɢɬɟɥɶɧɨ) ɞɨ 1, ɤɨɬɨɪɚɹ ɧɟ ɜɯɨɞɢɬ ɜ ɞɢɚɩɚɡɨɧ ɝɟɧɟɪɚɰɢɢ ɱɢɫɟɥ. Ɏɨɪɦɢɪɭɟɦ ɧɚ ɥɢɫɬɟ ɹɱɟɣɤɢ ɋɪɟɞɧɟɟ ɡɧɚɱɟɧɢɟ (ȼ7), Ɋɚɡɛɪɨɫ (ȼ8) , Ⱦɋɑ-ɪɚɜɧɨɦɟɪɧɵɣ (ȼ9) ɢ ɫɨɡɞɚɟɦ ɤɨɦɚɧɞɧɭɸ ɤɧɨɩɤɭ ɫɨ ɫɥɟɞɭɸɳɟɣ ɩɪɨɝɪɚɦɦɨɣ: Private Sub CommandButton5_Click() Randomize Cells(9, 2) = Int((Cells(7, 2) - Cells(8, 2)) + (2 * Cells(8, 2) + 1) * Rnd) End Sub. ɉɪɢ ɳɟɥɱɤɟ ɧɚ ɤɧɨɩɤɟ Ⱦɋɑ-ɪɚɜɧɨɦɟɪɧɵɣ ɩɨɥɭɱɚɟɦ ɫɥɭɱɚɣɧɨɟ ɱɢɫɥɨ ɜ ɞɢɚɩɚɡɨɧɟ ɨɬ -7 ɞɨ +7. ɂɧɬɟɪɟɫɟɧ ɜɨɩɪɨɫ ɝɟɧɟɪɚɰɢɢ ɫɥɭɱɚɣɧɵɯ ɱɢɫɟɥ ɫ ɧɨɪɦɚɥɶɧɵɦ ɪɚɫɩɪɟɞɟɥɟɧɢɟɦ. ɋɭɳɟɫɬɜɭɟɬ ɪɹɞ ɦɟɬɨɞɨɜ ɫɨɡɞɚɧɢɹ ɞɚɬɱɢɤɨɜ ɫɥɭɱɚɣɧɵɯ ɱɢɫɟɥ ɫ ɧɨɪɦɚɥɶɧɵɦ ɡɚɤɨɧɨɦ ɪɚɫɩɪɟɞɟɥɟɧɢɹ. Ɉɫɬɚɧɨɜɢɦɫɹ ɧɚ ɦɟɬɨɞɟ, ɨɫɧɨɜɚɧɧɨɦ ɧɚ ɰɟɧɬɪɚɥɶɧɨɣ ɩɪɟɞɟɥɶɧɨɣ ɬɟɨɪɟɦɟ, ɤɨɬɨɪɚɹ ɩɨɡɜɨɥɹɟɬ ɜɵɱɢɫɥɢɬɶ ɦɚɬɟɦɚɬɢɱɟɫɤɨɟ ɨɠɢɞɚɧɢɟ ɢ ɞɢɫɩɟɪɫɢɸ ɫɭɦɦɚɪɧɨɝɨ ɡɚɤɨɧɚ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɩɨ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦ ɫɭɦɦɢɪɭɟɦɵɯ ɫɥɭɱɚɣɧɵɯ ɜɟɥɢɱɢɧ. ɉɪɢ ɨɬɫɭɬɫɬɜɢɢ ɞɨɦɢɧɢɪɭɸɳɢɯ ɮɚɤɬɨɪɨɜ ɜ ɫɭɦɦɢɪɭɟɦɵɯ ɫɥɭɱɚɣɧɵɯ ɜɟɥɢɱɢɧɚɯ ɩɨɥɭɱɚɟɬɫɹ ɫɥɭɱɚɣɧɚɹ ɜɟɥɢɱɢɧɚ, ɪɚɫɩɪɟɞɟɥɟɧɧɚɹ ɩɨ ɧɨɪɦɚɥɶɧɨɦɭ ɡɚɤɨɧɭ. ȼɵɱɢɫɥɟɧɢɟ ɫɥɭɱɚɣɧɨɣ ɜɟɥɢɱɢɧɵ ɩɪɨɢɡɜɨɞɢɬɫɹ ɩɨ ɮɨɪɦɭɥɟ ‫ ݔ‬ൌ ݉ ൅ ߪሺσଵଶ ௜ୀଵ ‫ݕ‬௜ െ ͸ሻ, ɝɞɟ ݉ - ɦɚɬɟɦɚɬɢɱɟɫɤɨɟ ɨɠɢɞɚɧɢɟ ɧɨɪɦɚɥɶɧɨɝɨ ɡɚɤɨɧɚ, ߪ - ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɟɫɤɨɟ ɨɬɤɥɨɧɟɧɢɟ ɧɨɪɦɚɥɶɧɨɝɨ ɡɚɤɨɧɚ, ‫ݕ‬௜ – ɫɥɭɱɚɣɧɨɟ ɱɢɫɥɨ ɫ ɪɚɜɧɨɦɟɪɧɵɦ ɪɚɫɩɪɟɞɟɥɟɧɢɟɦ ɜ ɢɧɬɟɪɜɚɥɟ ɨɬ 0 ɞɨ 1. ɋɭɦɦɚ ɢɡ 12 ɫɥɭɱɚɣɧɵɯ ɜɟɥɢɱɢɧ ‫ݕ‬௜ ɩɨɡɜɨɥɹɟɬ ɢɫɩɨɥɶɡɨɜɚɬɶ ɞɚɬɱɢɤ ɞɥɹ ɪɟɲɟɧɢɹ ɩɪɨɫɬɵɯ ɡɚɞɚɱ. ɉɪɢ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɩɨɜɵɲɟɧɢɹ ɞɨɫɬɨɜɟɪɧɨɫɬɢ ɝɟɧɟɪɚɰɢɢ ɫɥɭɱɚɣɧɵɯ ɱɢɫɟɥ, ɪɚɫɩɪɟɞɟɥɟɧɧɵɯ ɩɨ ɧɨɪɦɚɥɶɧɨɦɭ ɡɚɤɨɧɭ, ɤɨɥɢɱɟɫɬɜɨ ɫɭɦɦɢɪɭɟɦɵɯ ɫɥɭɱɚɣɧɵɯ ɜɟɥɢɱɢɧ ɭɜɟɥɢɱɢɜɚɸɬ. Ɏɨɪɦɭɥɵ ɪɚɫɱɟɬɚ ɦɨɠɧɨ ɧɚɣɬɢ ɜ ɂɧɬɟɪɧɟɬɟ. Ɍɚɤ ɤɚɤ ɨɛɵɱɧɨ ɩɪɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ ɢɫɩɨɥɶɡɭɸɬ ɧɟɫɤɨɥɶɤɨ ɞɚɬɱɢɤɨɜ, ɬɨ ɞɨɩɨɥɧɢɦ ɜ ɧɚɡɜɚɧɢɹ ɩɚɪɚɦɟɬɪɨɜ ɪɚɜɧɨɦɟɪɧɨɝɨ ɡɚɤɨɧɚ ɧɚɡɜɚɧɢɹ ɩɚɪɚɦɟɬɪɨɜ ɧɨɪɦɚɥɶɧɨɝɨ ɡɚɤɨɧɚ (ɆɈ – ɦɚɬɟɦɚɬɢɱɟɫɤɨɟ ɨɠɢɞɚɧɢɟ, ɋɄɈ – ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɟɫɤɨɟ ɨɬɤɥɨɧɟɧɢɟ) ɢ ɫɨɡɞɚɞɢɦ ɤɨɦɚɧɞɧɭɸ ɤɧɨɩɤɭ ɞɥɹ ɝɟɧɟɪɚɰɢɢ ɱɢɫɟɥ ɩɨ ɧɨɪɦɚɥɶɧɨɦɭ ɡɚɤɨɧɭ (ɇɁ). ɉɪɨɝɪɚɦɦɚ ɤɨɦɚɧɞɧɨɣ ɤɧɨɩɤɢ ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɢɠɟ: Private Sub CommandButton9_Click() 'Ⱦɋɑ-ɇɁ 43

1. Ɉ ɦɨɞɟɥɢɪɨɜɚɧɢɢ, ɪɟɲɟɧɢɢ ɡɚɞɚɱ, ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɢ ɢ MS Excel

Randomize 'ɮɨɪɦɢɪɨɜɚɧɢɟ ɧɚɱɚɥɶɧɨɝɨ ɫɥɭɱɚɣɧɨɝɨ ɡɧɚɱɧɢɹ ɞɥɹ ɝɟɧɟɪɚɬɨɪɚ ɫɥɭɱɚɣɧɵɯ ɱɢɫɟɥ Y1 = Rnd: Y2 = Rnd: Y3 = Rnd: Y4 = Rnd: Y5 = Rnd: Y6 = Rnd: Y7 = Rnd Y8 = Rnd: Y9 = Rnd: Y10 = Rnd: Y11 = Rnd: Y12 = Rnd '12 ɫɥɭɱɚɣɧɵɯ ɱɢɫɟɥ ɫ ɪɚɜɧɨɦɟɪɧɵɦ ɡɚɤɨɧɨɦ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɨɬ 0 ɞɨ 1 y = Y1 + Y2 + Y3 + Y4 + Y5 + Y6 + Y7 + Y8 + Y9 + Y10 + Y11 + Y12 Cells(9, 2) = Int(Cells(7, 2) + Cells(8, 2) * (y - 6)) 'ɋɥɭɱɚɣɧɚɹ ɜɟɥɢɱɢɧɚ ɩɨ ɇɁ End Sub. Ɉɬɦɟɱɚɟɦ, ɱɬɨ ɬɨɱɤɢ ɜ ɤɨɧɰɟ ɬɟɤɫɬɚ ɩɪɨɝɪɚɦɦɵ ɧɟ ɫɬɚɜɹɬɫɹ. ɋɥɟɞɭɟɬ ɩɨɞɦɟɬɢɬɶ, ɱɬɨ ɫɥɭɱɚɣɧɵɟ ɱɢɫɥɚ ɝɟɧɟɪɢɪɭɸɬɫɹ ɜ ɞɢɚɩɚɡɨɧɟ ±3ߪ ɫ ɜɟɪɨɹɬɧɨɫɬɶɸ 0,993. ɗɬɨ ɧɭɠɧɨ ɭɱɢɬɵɜɚɬɶ ɩɪɢ ɡɚɞɚɧɢɢ ɩɚɪɚɦɟɬɪɨɜ ɧɨɪɦɚɥɶɧɨɝɨ ɡɚɤɨɧɚ. ɉɪɢɦɟɪ ɨɮɨɪɦɥɟɧɢɹ ɫɱɟɬɱɢɤɚ ɩɪɟɞɫɬɚɜɥɟɧ ɧɚ ɪɢɫɭɧɤɟ. Ɂɞɟɫɶ ɭɦɟɫɬɧɨ ɨɛɫɭɞɢɬɶ ɜɨɩɪɨɫ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɹ ɫɱɟɬɱɢɤɨɜ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɧɭɠɧɨ ɛɭɞɟɬ ɬɨɥɶɤɨ ɨɛɟɫɩɟɱɢɬɶ ɡɚɩɭɫɤ ɢ ɨɫɬɚɧɨɜ ɧɚɱɢɫɥɟɧɢɹ ɫɱɟɬɱɢɤɚ. ȼɨɩɪɨɫ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɬɟɫɧɨ ɫɜɹɡɚɧ ɫ ɩɪɢɜɹɡɤɨɣ ɧɚɱɢɫɥɟɧɢɹ ɫɱɟɬɱɢɤɚ ɤ ɪɟɚɥɶɧɨɦɭ ɜɪɟɦɟɧɢ. ɗɬɨ ɜɚɠɧɨ, ɬɚɤ ɤɚɤ ɱɚɫɬɨ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɜ ɪɟɚɥɶɧɨɦ ɦɚɫɲɬɚɛɟ ɜɪɟɦɟɧɢ (ɊɆȼ). ɇɚɱɧɟɦ ɫɨɡɞɚɧɢɟ ɫɱɟɬɱɢɤɚ ɊɆȼ ɫ ɮɨɪɦɢɪɨɜɚɧɢɹ ɤɨɦɚɧɞɧɵɯ ɤɧɨɩɨɤ ɩɨɞ ɧɚɡɜɚɧɢɹɦɢ Ɉɛɧɭɥɟɧɢɟ ɫɱɟɬɱɢɤɚ, Ɂɚɩɭɫɤ ɫɱɟɬɱɢɤɚ ɊɆȼ ɢ Ɉɫɬɚɧɨɜ, ɤɨɬɨɪɵɟ ɪɟɚɝɢɪɭɸɬ ɧɚ ɳɟɥɱɨɤ. Ⱦɥɹ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɢɫɩɨɥɶɡɭɟɦ ɩɪɨɰɟɞɭɪɭ ɩɪɢɥɨɠɟɧɢɹ OnTime (EarliestTime, Procedure, LatestTime, Schedule). Ⱥɪɝɭɦɟɧɬ ɩɪɨɰɟɞɭɪɵ EarliestTime ɨɩɪɟɞɟɥɹɟɬ ɦɨɦɟɧɬ ɡɚɩɭɫɤɚ ɧɭɠɧɨɣ ɩɪɨɰɟɞɭɪɵ, ɚɪɝɭɦɟɧɬ Procedure - ɢɦɹ ɡɚɩɭɫɤɚɟɦɨɣ ɩɪɨɰɟɞɭɪɵ. Ⱥɪɝɭɦɟɧɬ LatestTime - ɟɫɥɢ ɧɚ ɦɨɦɟɧɬ ɡɚɩɭɫɤɚ ɩɪɨɰɟɞɭɪɵ, Excel ɧɟ ɦɨɠɟɬ ɟɟ ɡɚɩɭɫɬɢɬɶ ɜ ɫɢɥɭ ɬɨɝɨ, ɱɬɨ ɜɵɩɨɥɧɹɟɬɫɹ ɞɪɭɝɨɟ ɞɟɣɫɬɜɢɟ. Ⱥɪɝɭɦɟɧɬ LatestTime ɨɩɪɟɞɟɥɹɟɬ ɩɨɫɥɟɞɧɟɟ ɜɪɟɦɹ ɡɚɩɭɫɤɚ ɩɪɨɰɟɞɭɪɵ. ȿɫɥɢ ɷɬɨɬ ɚɪɝɭɦɟɧɬ ɨɩɭɳɟɧ, ɬɨ Excel ɛɭɞɟɬ ɠɞɚɬɶ ɞɨ ɬɟɯ ɩɨɪ, ɩɨɤɚ ɧɟ ɫɦɨɠɟɬ ɜɵɩɨɥɧɢɬɶ ɷɬɭ ɩɪɨɰɟɞɭɪɭ. Ⱥɪɝɭɦɟɧɬ Schedule ɦɨɠɟɬ ɢɦɟɬɶ ɡɧɚɱɟɧɢɹ True ɢɥɢ False. ɉɪɢ True ɜɵɩɨɥɧɟɧɢɟ ɩɪɨɰɟɞɭɪɵ ɨɬɤɥɚɞɵɜɚɟɬɫɹ ɧɚ ɫɭɬɤɢ, ɚ ɩɪɢ False ɩɪɨɰɟɞɭɪɚ ɧɟ ɜɵɩɨɥɧɹɟɬɫɹ. Ɍɨ ɟɫɬɶ ɧɭɠɧɚɹ ɩɪɨɰɟɞɭɪɚ ɩɨɞ ɢɦɟɧɟɦ Procedure ɧɚɱɢɧɚɟɬ ɜɵɩɨɥɧɹɬɶɫɹ ɜ ɡɚɞɚɧɧɵɣ ɦɨɦɟɧɬ ɪɟɚɥɶɧɨɝɨ ɜɪɟɦɟɧɢ EarliestTime. Ɉɩɪɟɞɟɥɢɦ ɹɱɟɣɤɢ: ɋɱɟɬɱɢɤ ɊɆȼ (ȿ1), ȼɪɟɦɟɧɧɨɣ ɢɧɬɟɪɜɚɥ ɫɱɟɬɱɢɤɚ (ȿ4), Ʉɨɥɢɱɟɫɬɜɨ ɬɚɤɬɨɜ (ȿ2), ȼɟɥɢɱɢɧɚ ɬɚɤɬɨɜ (ȿ3). ȼɪɟɦɟɧɧɨɣ ɢɧɬɟɪɜɚɥ ɜ ɩɪɨɫɬɟɣɲɟɦ ɫɥɭɱɚɟ ɪɚɜɟɧ 1 ɫɟɤɭɧɞɟ. ɉɪɢ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɡɚɦɟɞɥɟɧɢɢ ɬɟɦɩɚ ɧɚɱɢɫɥɟɧɢɹ ɫɱɟɬɱɢɤɚ ɧɭɠɧɨ ɭɜɟɥɢɱɢɬɶ ɜɪɟɦɟɧɧɨɣ ɢɧɬɟɪɜɚɥ. ɐɟɥɟɫɨɨɛɪɚɡɧɨ ɩɪɟɞɭɫɦɨɬɪɟɬɶ ɩɨɞɫɱɟɬ ɤɨɥɢɱɟɫɬɜɚ ɬɚɤɬɨɜ ɧɚɱɢɫɥɟɧɢɹ ɫɱɟɬɱɢɤɚ, ɤɨɬɨɪɨɟ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɞɥɹ ɭɫɤɨɪɟɧɢɹ ɢɥɢ ɡɚɦɟɞɥɟɧɢɹ ɜɪɟɦɟɧɢ ɦɨɞɟɥɢɪɨɜɚɧɢɹ. ȼ ɩɪɨɝɪɚɦɦɟ ɤɨɦɚɧɞɧɨɣ ɤɧɨɩɤɢ Ɉɛɧɭɥɟɧɢɟ ɫɱɟɬɱɢɤɚ ɩɪɟɞɭɫɦɨɬɪɟɧɨ ɨɛɧɭɥɟɧɢɟ ɬɨɥɶɤɨ ɹɱɟɟɤ ɋɱɟɬɱɢɤ ɊɆȼ ɢ Ʉɨɥɢɱɟɫɬɜɨ ɬɚɤɬɨɜ: Sub CommandButton6_Click() 'Ɉɛɧɭɥɟɧɢɟ ɹɱɟɟɤ ɫɱɟɬɱɢɤɚ ɩɨ ɳɟɥɱɤɭ 44

1.5. ɋɨɡɞɚɧɢɟ ɫɱɟɬɱɢɤɨɜ ɞɥɹ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɩɪɨɰɟɫɫɚ ɦɨɞɟɥɢɪɨɜɚɧɢɹ

Cells(1, 5) = Null 'Ɉɛɧɭɥɟɧɢɟ ɹɱɟɣɤɢ ɫɱɟɬɱɢɤɚ ɜɪɟɦɟɧɢ Cells(2, 5) = Null 'Ɉɛɧɭɥɟɧɢɟ ɹɱɟɣɤɢ ɬɚɤɬɨɜ ɫɱɟɬɱɢɤɚ ɜɪɟɦɟɧɢ End Sub. ȼ ɩɪɨɝɪɚɦɦɚɯ ɞɪɭɝɢɯ ɤɧɨɩɨɤ ɜɵɡɵɜɚɟɦ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɩɪɨɰɟɞɭɪɵ Sub CommandButton4_Click() 'Ɂɚɩɭɫɤ ɫɱɟɬɱɢɤɚ ɩɨ ɳɟɥɱɤɭ Call Bklshetchika 'ȼɵɡɨɜ ɩɪɨɰɟɞɭɪɵ ɜɤɥɸɱɟɧɢɹ ɫɱɟɬɱɢɤɚ End Sub Sub CommandButton5_Click() 'Ɉɫɬɚɧɨɜ ɫɱɟɬɱɢɤɚ ɩɨ ɳɟɥɱɤɭ Call Stopchet 'ȼɵɡɨɜ ɩɪɨɰɟɞɭɪɵ ɨɫɬɚɧɨɜɤɢ ɫɱɟɬɱɢɤɚ End Sub. ɉɪɨɰɟɞɭɪɚ ɜɤɥɸɱɟɧɢɹ ɫɱɟɬɱɢɤɚ ɜɵɝɥɹɞɢɬ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ: Dim Zadaniecledtime As Date Sub Bklshetchika() 'Ɂɚɩɭɫɤ ɫɱɟɬɱɢɤɚ ɫ ɡɚɞɚɧɧɵɦ ɢɧɬɟɪɜɚɥɨɦ Zadaniecledtime = Now + Cells(4, 5) 'Ɂɚɩɢɫɶ ɡɧɚɱɟɧɢɹ ɜɪɟɦɟɧɢ ɞɥɹ ɡɚɩɭɫɤɚ ɫɱɟɬɱɢɤɚ ɫ ɭɱɟɬɨɦ ɢɧɬɟɪɜɚɥɚ Application.OnTime Zadaniecledtime, "Zapistime" 'ȼɵɡɨɜ ɩɪɨɰɟɞɭɪɵ ɡɚɩɢɫɢ ɫɱɟɬɱɢɤɚ ɜɪɟɦɟɧɢ ɜ ɡɚɞɚɧɧɨɟ ɜɪɟɦɹ End Sub. Ⱦɥɹ ɮɨɪɦɢɪɨɜɚɧɢɹ ɜɪɟɦɟɧɢ ɡɚɩɭɫɤɚ ɩɪɨɰɟɞɭɪɵ zapistime ɢɫɩɨɥɶɡɭɟɦ ɩɟɪɟɦɟɧɧɭɸ Zadaniecledtime, ɜ ɤɨɬɨɪɭɸ ɡɚɩɢɫɵɜɚɟɦ ɬɟɤɭɳɟɟ ɜɪɟɦɹ ɢ ɩɪɢɛɚɜɥɹɟɦ ɡɚɞɚɧɧɵɣ ɢɧɬɟɪɜɚɥ ɜ ɹɱɟɣɤɟ ȿ4. ɉɪɟɞɜɚɪɢɬɟɥɶɧɨ ɹɱɟɣɤɟ ȿ4 ɡɚɞɚɟɦ ɜɪɟɦɟɧɧɨɣ ɮɨɪɦɚɬ ɱ:ɦ:ɫ. ɉɪɢ ɧɚɫɬɭɩɥɟɧɢɢ ɡɚɞɚɧɧɨɝɨ ɜɪɟɦɟɧɢ Zadaniecledtime ɩɪɨɢɡɜɨɞɢɬɫɹ ɡɚɩɢɫɶ ɬɟɤɭɳɟɝɨ ɡɧɚɱɟɧɢɹ ɜɪɟɦɟɧɢ ɢ ɤɨɥɢɱɟɫɬɜɨ ɬɚɤɬɨɜ: Sub Zapistime() 'ɉɪɨɰɟɞɭɪɚ ɡɚɩɢɫɢ ɬɟɤɭɳɟɝɨ ɡɧɚɱɟɧɢɹ ɫɱɟɬɱɢɤɚ ɢ ɬɚɤɬɨɜ Cells(1, 5) = Now 'Ɂɚɩɢɫɶ ɬɟɤɭɳɟɝɨ ɡɧɚɱɟɧɢɹ ɜɪɟɦɟɧɢ Cells(2, 5) = Cells(2, 5) + Cells(3, 5) 'ɇɚɱɢɫɥɟɧɢɟ ɬɚɤɬɨɜ ɫɱɟɬɱɢɤɚ ɜɪɟɦɟɧɢ Call Bklshetchika End Sub. ɉɨɫɥɟ ɡɚɩɢɫɢ ɬɟɤɭɳɟɝɨ ɡɧɚɱɟɧɢɹ ɜɪɟɦɟɧɢ ɨɩɹɬɶ ɨɛɪɚɳɚɟɦɫɹ ɤ Bklshetchika ɞɥɹ ɮɨɪɦɢɪɨɜɚɧɢɹ ɫɥɟɞɭɸɳɟɝɨ ɦɨɦɟɧɬɚ ɜɪɟɦɟɧɢ ɧɚɱɢɫɥɟɧɢɹ ɫɱɟɬɱɢɤɚ. Ⱦɥɹ ɨɬɨɛɪɚɠɟɧɢɹ ɜ ɹɱɟɣɤɢ ɫɱɟɬɱɢɤɚ ɬɨɥɶɤɨ ɜɪɟɦɟɧɢ (ɛɟɡ ɞɚɬɵ) ɡɚɞɚɟɦ ɮɨɪɦɚɬ ɜɪɟɦɟɧɢ. Ⱦɥɹ ɩɪɟɤɪɚɳɟɧɢɹ ɧɚɱɢɫɥɟɧɢɹ ɫɱɟɬɱɢɤɚ ɩɪɢɫɜɚɢɜɚɟɦ ɩɚɪɚɦɟɬɪɭ Schedule:=False ɞɥɹ ɨɫɬɚɧɨɜɤɢ ɡɚɩɭɫɤɚ ɩɪɨɰɟɞɭɪɵ Zapistime: Sub Stopchet() 'ɉɪɨɰɟɞɭɪɚ ɨɫɬɚɧɨɜɤɢ ɫɱɟɬɱɢɤɚ Application.OnTime EarliestTime:=Zadaniecledtime, Procedure:="Zapistime", Schedule:=False 'Ɏɨɪɦɢɪɨɜɚɧɢɟ ɡɚɩɪɟɬɚ ɜɵɡɨɜɚ ɩɪɨɰɟɞɭɪɵ ɡɚɩɢɫɢ ɡɧɚɱɟɧɢɹ ɜɪɟɦɟɧɢ ɫɱɟɬɱɢɤɚ End Sub. 45

1. Ɉ ɦɨɞɟɥɢɪɨɜɚɧɢɢ, ɪɟɲɟɧɢɢ ɡɚɞɚɱ, ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɢ ɢ MS Excel

ȼ ɧɚɱɚɥɟ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɧɭɠɧɨ ɡɚɞɚɬɶ ɢɧɬɟɪɜɚɥɵ ɜɪɟɦɟɧɢ ɢ ɬɚɤɬɨɜ, ɡɚɬɟɦ ɨɛɧɭɥɢɬɶ ɹɱɟɣɤɢ ɢ ɳɟɥɤɧɭɬɶ ɧɚ ɤɧɨɩɤɟ Ɂɚɩɭɫɤ ɫɱɟɬɱɢɤɚ ɊɆȼ. ɉɪɢ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɜ ɩɪɨɰɟɫɫɟ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɦɨɠɧɨ ɢɡɦɟɧɹɬɶ ɡɧɚɱɟɧɢɹ ɢɧɬɟɪɜɚɥɨɜ. ɂɧɨɝɞɚ ɜɨɡɧɢɤɚɟɬ ɧɟɨɛɯɨɞɢɦɨɫɬɶ ɮɢɤɫɚɰɢɢ ɜɪɟɦɟɧɢ ɧɚɱɚɥɚ ɦɨɞɟɥɢɪɨɜɚɧɢɹ. ɗɬɨ ɦɨɠɧɨ ɫɞɟɥɚɬɶ ɛɟɡ ɨɫɨɛɵɯ ɡɚɬɪɭɞɧɟɧɢɣ. Ɉɫɬɚɥɨɫɶ ɪɚɫɫɦɨɬɪɟɬɶ ɩɪɢɦɟɧɟɧɢɟ ɞɚɬ ɢ ɜɪɟɦɟɧɢ ɩɪɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ. ɋɚɦɨɟ ɝɥɚɜɧɨɟ ɡɞɟɫɶ ɧɭɠɧɨ ɡɧɚɬɶ ɬɨɱɤɢ ɨɬɫɱɟɬɚ ɞɚɬ, ɤɨɬɨɪɵɟ ɢɫɩɨɥɶɡɭɸɬɫɹ ɜ ɮɨɪɦɭɥɚɯ ɡɚɞɚɱɢ ɢ ɩɪɢ ɝɟɧɟɪɚɰɢɢ ɜ ɉɄ. ɗɬɨ ɨɛɭɫɥɨɜɥɟɧɨ ɬɟɦ, ɱɬɨ ɩɪɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ ɨɛɵɱɧɨ ɢɫɩɨɥɶɡɭɸɬ ɧɟ ɞɚɬɵ, ɚ ɤɨɥɢɱɟɫɬɜɨ ɫɭɬɨɤ ɢɥɢ ɜɪɟɦɹ ɨɬ ɬɨɱɤɢ ɨɬɫɱɟɬɚ. ɉɨɷɬɨɦɭ ɩɟɪɜɨɟ ɞɟɣɫɬɜɢɟ, ɤɨɬɨɪɨɟ ɧɭɠɧɨ ɨɫɭɳɟɫɬɜɢɬɶ ɷɬɨ ɢɡ ɡɚɞɚɧɧɨɣ ɞɚɬɵ ɜɵɱɟɫɬɶ ɞɚɬɭ ɧɭɠɧɭɸ ɞɚɬɭ ɨɬɫɱɟɬɚ, ɚ ɡɚɬɟɦ ɨɩɪɟɞɟɥɢɬɶ ɤɨɥɢɱɟɫɬɜɨ ɫɭɬɨɤ, ɱɚɫɨɜ ɢɥɢ ɦɢɧɭɬ ɢ ɬ.ɞ. ɋɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɫɬɚɧɞɚɪɬɧɵɟ ɮɭɧɤɰɢɢ ɞɚɬɵ ɜ Excel ɧɟ ɨɱɟɧɶ ɭɞɨɛɧɵ. Ʌɭɱɲɟ ɜɨɫɩɨɥɶɡɨɜɚɬɶɫɹ ɮɭɧɤɰɢɹɦɢ VBA. ȼ VBA ɬɢɩ ɞɚɬɵ ɮɨɪɦɢɪɭɟɬɫɹ ɨɬ 1 ɹɧɜɚɪɹ 100 ɝ. ɞɨ 31 ɞɟɤɚɛɪɹ 9999 ɝɨɞɚ. Ɏɭɧɤɰɢɢ ɜɵɱɢɫɥɟɧɢɣ ɫ ɞɚɬɚɦɢ ɩɨɡɜɨɥɹɸɬ ɩɨɥɭɱɚɬɶ ɪɟɡɭɥɶɬɚɬ ɜ ɝɨɞɚɯ (ɥɟɬ) ɞɨ ɫɟɤɭɧɞ. ɉɪɢ ɷɬɨɦ ɜ ɮɭɧɤɰɢɢ ɭɤɚɡɵɜɚɟɬɫɹ ɚɪɝɭɦɟɧɬ, ɤɨɬɨɪɵɣ ɦɨɠɟɬ ɢɦɟɬɶ ɫɥɟɞɭɸɳɢɟ ɡɧɚɱɟɧɢɹ: "yyyy" ɝɨɞ, "q" ɤɜɚɪɬɚɥ, "m" ɦɟɫɹɰ, "y" ɞɟɧɶ ɝɨɞɚ, "d" ɞɟɧɶ, "w" ɞɟɧɶ ɧɟɞɟɥɢ, "ww" ɧɟɞɟɥɹ, "h" ɱɚɫ, "n" ɦɢɧɭɬɚ, "s" ɫɟɤɭɧɞɚ. ȿɫɥɢ ɩɪɨɢɡɜɨɞɢɦ ɮɨɪɦɚɬɢɪɨɜɚɧɢɟ, ɬɨ ɤɨɥɢɱɟɫɬɜɨ ɫɢɦɜɨɥɨɜ ɜ ɫɨɫɬɚɜɥɹɸɳɢɯ ɚɪɝɭɦɟɧɬɚ ɫɜɹɡɚɧɨ ɫ ɤɨɥɢɱɟɫɬɜɨɦ ɨɬɨɛɪɚɠɚɟɦɵɯ ɱɢɫɟɥ ɩɚɪɚɦɟɬɪɚ ɞɚɬɵ (ɜɪɟɦɟɧɢ). ɋɚɦɨɟ ɝɥɚɜɧɨɟ, ɱɬɨ ɹɜɥɹɟɬɫɹ ɨɫɧɨɜɨɣ ɫɱɟɬɱɢɤɚ: ɝɨɞ, ɤɨɥɢɱɟɫɬɜɨ ɞɧɟɣ, ɱɚɫɵ, ɦɢɧɭɬɵ ɢɥɢ ɫɟɤɭɧɞɵ. ɉɪɢ ɷɬɨɦ ɧɭɠɧɨ ɨɛɟɫɩɟɱɢɬɶ ɜɵɱɢɫɥɟɧɢɟ ɬɟɤɭɳɟɣ ɞɚɬɵ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɩɨ ɢɡɦɟɧɹɟɦɨɦɭ ɡɧɚɱɟɧɢɸ ɫɱɟɬɱɢɤɚ, ɤɨɬɨɪɨɟ ɩɨ ɢɟɪɚɪɯɢɢ ɦɨɠɟɬ ɛɵɬɶ ɜ ɫɚɦɨɦ ɫɥɨɠɧɨɦ ɫɥɭɱɚɟ ɫɱɟɬɱɢɤɨɦ ɫɟɤɭɧɞ. ɉɪɢ ɷɬɨɦ ɦɨɠɟɬ ɩɨɧɚɞɨɛɢɬɶɫɹ ɧɟ ɬɨɥɶɤɨ ɬɟɤɭɳɟɟ ɡɧɚɱɟɧɢɟ ɞɚɬɵ ɦɨɞɟɥɢɪɨɜɚɧɢɹ, ɧɨ ɢ ɢɧɬɟɪɜɚɥ (ɩɪɨɦɟɠɭɬɨɤ) ɞɚɬɵ (ɜɪɟɦɟɧɢ) ɨɬ ɧɚɱɚɥɶɧɨɣ ɞɚɬɵ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɜ ɧɚɱɚɥɟ ɫɨɡɞɚɞɢɦ ɹɱɟɣɤɢ ɞɥɹ ɡɚɩɢɫɢ ɨɬɞɟɥɶɧɵɯ ɩɚɪɚɦɟɬɪɨɜ ɧɚɱɚɥɶɧɨɣ ɞɚɬɵ ɢ ɡɚɬɟɦ ɫɨɛɟɪɟɦ ɢɯ ɜ ɨɞɧɭ ɹɱɟɣɤɭ ɫ ɮɨɪɦɚɬɨɦ ɞɚɬɵ. ȼ ɹɱɟɣɤɢ ɩɚɪɚɦɟɬɪɨɜ ɡɚɧɨɫɢɦ ɞɚɧɧɵɟ ɨɬ ɡɧɚɱɟɧɢɹ ɝɨɞɚ ɞɨ ɫɟɤɭɧɞ. Ⱦɚɥɟɟ ɢɫɩɨɥɶɡɭɹ ɫɬɚɧɞɚɪɬɧɵɟ ɮɭɧɤɰɢɢ (ɫɦ. ɩɪɢɦɟɱɚɧɢɹ) ɢ ɮɨɪɦɢɪɭɟɦ ɹɱɟɣɤɢ ɫɨ ɫɬɚɧɞɚɪɬɧɵɦ ɮɨɪɦɚɬɢɪɨɜɚɧɢ46

1.5. ɋɨɡɞɚɧɢɟ ɫɱɟɬɱɢɤɨɜ ɞɥɹ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɩɪɨɰɟɫɫɚ ɦɨɞɟɥɢɪɨɜɚɧɢɹ

ɟɦ ɞɥɹ ɜɪɟɦɟɧɢ ɢ ɞɚɬɵ. ɉɪɢ ɫɨɡɞɚɧɢɢ ɹɱɟɣɤɢ ɞɥɹ ɨɬɨɛɪɚɠɟɧɢɹ ɞɚɬɵ ɢ ɜɪɟɦɟɧɢ ɩɪɢɦɟɧɹɟɦ ɮɭɧɤɰɢɸ ɫɰɟɩɤɢ ɋɐȿɉɂɌɖ(). Ⱦɥɹ ɪɚɡɞɟɥɟɧɢɹ ɞɚɧɧɵɯ ɢɫɩɨɥɶɡɭɟɦ ɮɭɧɤɰɢɸ ɫɢɦɜɨɥ ɋɂɆȼɈɅ () ɫ ɤɨɞɚɦɢ: 46 – ɬɨɱɤɚ; 32 – ɩɪɨɛɟɥ; 58 – ɞɜɨɟɬɨɱɢɟ. Ʉɨɞɵ ɫɢɦɜɨɥɨɜ ɥɟɝɤɨ ɨɩɪɟɞɟɥɢɬɶ ɫ ɩɨɦɨɳɶɸ ɮɭɧɤɰɢɢ ɄɈȾɋɂɆȼ(), ɝɞɟ ɜ ɤɚɱɟɫɬɜɟ ɚɪɝɭɦɟɧɬɚ ɡɚɩɢɫɵɜɚɟɬɫɹ ɧɭɠɧɵɣ ɫɢɦɜɨɥ. ɉɟɪɟɣɞɟɦ ɤ ɫɨɡɞɚɧɢɸ ɫɱɟɬɱɢɤɚ ɞɥɹ ɮɨɪɦɢɪɨɜɚɧɢɹ ɬɟɤɭɳɟɣ ɞɚɬɵ (ɜɪɟɦɟɧɢ) ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɢ ɢɧɬɟɪɜɚɥɨɜ ɩɚɪɚɦɟɬɪɨɜ, ɤɨɬɨɪɵɟ ɦɨɝɭɬ ɩɨɧɚɞɨɛɢɬɶɫɹ ɩɪɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ. ɇɟɨɛɯɨɞɢɦɨ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɧɟ ɜɫɟ ɩɚɪɚɦɟɬɪɵ ɦɨɝɭɬ ɩɨɧɚɞɨɛɢɬɶɫɹ ɩɪɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ ɤɨɧɤɪɟɬɧɨɣ ɡɚɞɚɱɢ. ɉɨɷɬɨɦɭ ɨɬɞɟɥɶɧɵɟ ɩɚɪɚɦɟɬɪɵ ɧɚɲɟɝɨ ɫɱɟɬɱɢɤɚ ɦɨɝɭɬ ɛɵɬɶ ɢɫɤɥɸɱɟɧɵ ɢɡ ɦɨɞɟɥɢ. ɋɧɚɱɚɥɚ ɨɡɚɝɥɚɜɢɦ ɢ ɨɬɮɨɪɦɚɬɢɪɭɟɦ ɹɱɟɣɤɢ ɞɥɹ ɩɚɪɚɦɟɬɪɨɜ, ɢɧɬɟɪɜɚɥɨɜ ɢ ɫɱɟɬɱɢɤɚ. Ⱦɚɥɟɟ ɜ ɪɟɠɢɦɟ Ʉɨɧɫɬɪɭɤɬɨɪ ɫɨɡɞɚɞɢɦ ɤɨɦɚɧɞɧɵɟ ɤɧɨɩɤɢ ɫɨ ɫɥɟɞɭɸɳɢɦɢ ɧɚɡɜɚɧɢɹɦɢ: Ɉɛɧɭɥɟɧɢɟ ɫɱɟɬɱɢɤɚ, ɩɚɪɚɦɟɬɪɨɜ ɢ ɢɧɬɟɪɜɚɥɨɜ; ɋɱɟɬɱɢɤ ɞɚɬɚ-ɜɪɟɦɹ, ɫɟɤ; ɋɱɟɬɱɢɤ ɞɚɬɚ-ɜɪɟɦɹ, ɞɟɧɶ. ɉɪɨɝɪɚɦɦɚ ɞɥɹ ɨɛɧɭɥɟɧɢɹ ɫɨɞɟɪɠɢɬ ɨɩɟɪɚɬɨɪɵ ɞɥɹ ɡɚɩɢɫɢ ɡɚɝɨɥɨɜɤɨɜ ɫɱɟɬɱɢɤɚ ɢ ɢɧɬɟɪɜɚɥɨɜ ɫɱɟɬɱɢɤɚ ɛɟɡ ɪɚɡɦɟɪɧɨɫɬɟɣ. Private Sub CommandButton2_Click() Range("c2:d10", "e2") = Null 'Ɉɛɧɭɥɟɧɢɟ ɨɛɥɚɫɬɢ ɩɚɪɚɦɟɬɪɨɜ, ɢɧɬɟɪɜɚɥɨɜ ɢ ɫɱɟɬɱɢɤɚ Cells(1, 5) = "ɋɱɟɬɱɢɤ" 'Ɂɚɩɢɫɶ ɧɚɞɩɢɫɢ ɛɟɡ ɪɚɡɦɟɪɧɨɫɬɢ Cells(1, 6) = "ɂɧɬɟɪɜɚɥ ɫɱɟɬɱɢɤɚ" 'Ɂɚɩɢɫɶ ɧɚɞɩɢɫɢ ɛɟɡ ɪɚɡɦɟɪɧɨɫɬɢ End Sub. ɗɬɨ ɫɞɟɥɚɧɨ ɞɥɹ ɬɨɝɨ, ɱɬɨɛɵ ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɫɱɟɬɱɢɤɚ ɫɟɤɭɧɞ ɢɥɢ ɞɧɟɣ, ɚ ɜɟɪɧɟɟ ɫɭɬɨɤ, ɫɮɨɪɦɢɪɨɜɚɬɶ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɧɚɡɜɚɧɢɹ. ɉɪɨɝɪɚɦɦɚ ɞɥɹ ɫɱɟɬɱɢɤɚ ɞɧɟɣ (ɫɭɬɨɤ) ɢɦɟɟɬ ɫɥɟɞɭɸɳɢɣ ɜɢɞ: Private Sub CommandButton3_Click() Dim Tymdhms As Date 'Ɉɛɴɹɜɥɟɧɢɟ ɩɟɪɟɦɟɧɧɨɣ ɞɥɹ ɧɚɱɢɫɥɟɧɢɹ ɫɱɟɬɱɢɤɚ Cells(2, 5) = Cells(2, 5) + Cells(2, 6) 'ɇɚɱɢɫɥɟɧɢɹ ɫɱɟɬɱɢɤɚ ɞɧɟɣ Tymdhms = DateAdd("d", Cells(2, 5), Cells(10, 2)) 'ɍɜɟɥɢɱɟɧɢɟ ɧɚɱɚɥɶɧɨɣ ɞɚɬɵ ɧɚ ɜɟɥɢɱɢɧɭ ɫɱɟɬɱɢɤɚ ɞɧɟɣ Cells(2, 3) = Year(Tymdhms) 'Ɉɩɪɟɞɟɥɟɧɢɟ ɬɟɤɭɳɟɝɨ ɝɨɞɚ Cells(3, 3) = Month(Tymdhms) 'Ɉɩɪɟɞɟɥɟɧɢɟ ɬɟɤɭɳɟɝɨ ɦɟɫɹɰɚ Cells(4, 3) = Day(Tymdhms) 'Ɉɩɪɟɞɟɥɟɧɢɟ ɬɟɤɭɳɟɝɨ ɞɧɹ ɦɟɫɹɰɚ Cells(5, 3) = Hour(Tymdhms) 'Ɉɩɪɟɞɟɥɟɧɢɟ ɬɟɤɭɳɟɝɨ ɱɚɫɚ Cells(6, 3) = Minute(Tymdhms) 'Ɉɩɪɟɞɟɥɟɧɢɟ ɬɟɤɭɳɟɣ ɦɢɧɭɬɵ Cells(7, 3) = Second(Tymdhms) 'Ɉɩɪɟɞɟɥɟɧɢɟ ɬɟɤɭɳɟɣ ɫɟɤɭɧɞɵ Cells(8, 3) = Format(Tymdhms, "h:m:s") 'Ɏɨɪɦɚɬɢɪɨɜɚɧɢɟ ɬɟɤɭɳɟɝɨ ɜɪɟɦɟɧɢ Cells(9, 3) = Format(Tymdhms, "d/m/yyyy") 'Ɏɨɪɦɚɬɢɪɨɜɚɧɢɟ ɬɟɤɭɳɟɣ ɞɚɬɵ 47

1. Ɉ ɦɨɞɟɥɢɪɨɜɚɧɢɢ, ɪɟɲɟɧɢɢ ɡɚɞɚɱ, ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɢ ɢ MS Excel

Cells(10, 3) = Format(Tymdhms, "d/m/yyyy h:m:s") 'Ɏɨɪɦɚɬɢɪɨɜɚɧɢɟ ɬɟɤɭɳɟɝɨ ɞɚɬɵ ɢ ɜɪɟɦɟɧɢ Cells(1, 5) = "ɋɱɟɬɱɢɤ, ɞɟɧɶ" 'Ɂɚɩɢɫɶ ɧɚɞɩɢɫɢ ɫ ɪɚɡɦɟɪɧɨɫɬɶɸ ɞɟɧɶ Cells(1, 6) = "ɂɧɬɟɪɜɚɥ ɫɱɟɬɱɢɤɚ, ɞɟɧɶ" 'Ɂɚɩɢɫɶ ɧɚɞɩɢɫɢ ɫ ɪɚɡɦɟɪɧɨɫɬɶɸ ɞɟɧɶ Cells(2, 4) = DateDiff("yyyy", Cells(10, 2), Cells(10, 3)) 'Ɏɨɪɦɢɪɨɜɚɧɢɟ ɢɧɬɟɪɜɚɥɚ ɜ ɝɨɞɚɯ Cells(3, 4) = DateDiff("m", Cells(10, 2), Cells(10, 3)) 'Ɏɨɪɦɢɪɨɜɚɧɢɟ ɢɧɬɟɪɜɚɥɚ ɜ ɦɟɫɹɰɚɯ Cells(4, 4) = DateDiff("d", Cells(10, 2), Cells(10, 3)) 'Ɏɨɪɦɢɪɨɜɚɧɢɟ ɢɧɬɟɪɜɚɥɚ ɜ ɞɧɹɯ Cells(5, 4) = DateDiff("h", Cells(10, 2), Cells(10, 3)) 'Ɏɨɪɦɢɪɨɜɚɧɢɟ ɢɧɬɟɪɜɚɥɚ ɜ ɱɚɫɚɯ Cells(6, 4) = DateDiff("n", Cells(10, 2), Cells(10, 3)) 'Ɏɨɪɦɢɪɨɜɚɧɢɟ ɢɧɬɟɪɜɚɥɚ ɜ ɦɢɧɭɬɚɯ Cells(7, 4) = DateDiff("s", Cells(10, 2), Cells(10, 3)) 'Ɏɨɪɦɢɪɨɜɚɧɢɟ ɢɧɬɟɪɜɚɥɚ ɜ ɫɟɤɭɧɞɚɯ End Sub. ȼ ɩɪɨɝɪɚɦɦɭ ɜɤɥɸɱɟɧɚ ɩɪɨɰɟɞɭɪɚ DateAdd("d", Cells(2, 5), Cells(10, 2)) ɫɥɨɠɟɧɢɹ ɹɱɟɟɤ ɫɱɟɬɱɢɤɚ ɞɧɟɣ ɢ ɧɚɱɚɥɶɧɨɣ ɞɚɬɵ. ɉɚɪɚɦɟɬɪ "d" ɭɤɚɡɵɜɚɟɬ ɧɚ ɫɥɨɠɟɧɢɟ ɜ ɞɧɹɯ. ɉɟɪɟɦɟɧɧɚɹ Tymdhms ɢɦɟɟɬ ɫɬɚɧɞɚɪɬɧɵɣ ɮɨɪɦɚɬ ɞɚɬɵ. Ⱦɚɥɟɟ ɜɵɞɟɥɹɸɬɫɹ ɩɚɪɚɦɟɬɪɵ ɞɚɬɵ ɢ ɡɚɩɢɫɵɜɚɸɬɫɹ ɜ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɹɱɟɣɤɢ. Ɍɚɤ ɤɚɤ ɜ ɫɬɚɧɞɚɪɬɧɨɦ ɮɨɪɦɚɬɟ ɩɟɪɟɦɟɧɧɨɣ Tymdhms ɧɟ ɨɬɪɚɠɚɸɬɫɹ ɫɟɤɭɧɞɵ, ɬɨ ɫ ɩɨɦɨɳɶɸ ɩɪɨɰɟɞɭɪɵ Format() ɩɪɨɢɡɜɨɞɢɦ ɮɨɪɦɚɬɢɪɨɜɚɧɢɟ. ɋɥɟɞɭɟɬ ɧɚɩɨɦɧɢɬɶ, ɱɬɨ ɟɫɥɢ ɭɤɚɠɟɦ ɚɪɝɭɦɟɧɬ ɞɧɹ ɫ ɞɜɭɦɹ ɫɢɦɜɨɥɚɦɢ dd, ɬɨ ɞɧɢ ɛɭɞɭɬ ɢɡɨɛɪɚɠɚɬɶɫɹ ɞɜɭɦɹ ɰɢɮɪɚɦɢ ɢ ɜ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɫɥɭɱɚɹɯ ɨɬɨɛɪɚɠɚɬɶɫɹ ɫ ɧɭɥɟɦ. ɗɬɨ ɩɨɥɨɠɟɧɢɟ ɪɚɫɩɪɨɫɬɪɚɧɹɟɬɫɹ ɧɚ ɞɪɭɝɢɟ ɩɚɪɚɦɟɬɪɵ ɞɚɬɵ. Ⱦɥɹ ɜɵɱɢɫɥɟɧɢɹ ɢɧɬɟɪɜɚɥɨɜ ɩɚɪɚɦɟɬɪɨɜ ɢɫɩɨɥɶɡɭɟɬɫɹ ɩɪɨɰɟɞɭɪɚ DateDiff(), ɝɞɟ ɨɬ ɧɚɱɚɥɶɧɨɣ ɞɚɬɵ ɜɵɱɢɬɚɟɬɫɹ ɬɟɤɭɳɚɹ ɞɚɬɚ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɫ ɭɤɚɡɚɧɢɟɦ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɝɨ ɩɪɢɡɧɚɤɚ ɩɚɪɚɦɟɬɪɚ (ɝɨɞ, ɦɟɫɹɰ ɢ ɬ.ɞ.). ȼ ɩɪɨɝɪɚɦɦɟ ɡɚɩɢɫɵɜɚɸɬɫɹ ɧɚɡɜɚɧɢɟ ɫɱɟɬɱɢɤɚ ɢ ɢɧɬɟɪɜɚɥɚ ɫ ɭɤɚɡɚɧɢɟɦ ɪɚɡɦɟɪɧɨɫɬɢ ɞɟɧɶ. Ⱦɥɹ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɫɱɟɬɱɢɤɚ ɫɟɤɭɧɞ ɢɫɩɨɥɶɡɭɟɬɫɹ ɚɧɚɥɨɝɢɱɧɚɹ ɩɪɨɝɪɚɦɦɚ ɤɨɦɚɧɞɧɨɣ ɤɧɨɩɤɢ: Private Sub CommandButton1_Click() Dim Tymdhms As Date 'Ɉɛɴɹɜɥɟɧɢɟ ɩɟɪɟɦɟɧɧɨɣ ɞɥɹ ɧɚɱɢɫɥɟɧɢɹ ɫɱɟɬɱɢɤɚ Cells(2, 5) = Cells(2, 5) + Cells(2, 6) 'ɇɚɱɢɫɥɟɧɢɹ ɫɱɟɬɱɢɤɚ ɫɟɤɭɧɞ Tymdhms = DateAdd("s", Cells(2, 5), Cells(10, 2)) 'ɍɜɟɥɢɱɟɧɢɟ ɧɚɱɚɥɶɧɨɣ ɞɚɬɵ ɧɚ ɜɟɥɢɱɢɧɭ ɫɱɟɬɱɢɤɚ ɫɟɤɭɧɞ Cells(2, 3) = Year(Tymdhms) 48

1.5. ɋɨɡɞɚɧɢɟ ɫɱɟɬɱɢɤɨɜ ɞɥɹ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɩɪɨɰɟɫɫɚ ɦɨɞɟɥɢɪɨɜɚɧɢɹ

Cells(3, 3) = Month(Tymdhms) Cells(4, 3) = Day(Tymdhms) Cells(5, 3) = Hour(Tymdhms) Cells(6, 3) = Minute(Tymdhms) Cells(7, 3) = Second(Tymdhms) Cells(8, 3) = Format(Tymdhms, "h:m:s") Cells(9, 3) = Format(Tymdhms, "d/m/yyyy") Cells(10, 3) = Format(Tymdhms, "d/m/yyyy h:m:s") Cells(1, 5) = "ɋɱɟɬɱɢɤ, ɫɟɤ" Cells(1, 6) = "ɂɧɬɟɪɜɚɥ ɫɱɟɬɱɢɤɚ, ɫɟɤ" Cells(2, 4) = DateDiff("yyyy", Cells(10, 2), Cells(10, 3)) Cells(3, 4) = DateDiff("m", Cells(10, 2), Cells(10, 3)) Cells(4, 4) = DateDiff("d", Cells(10, 2), Cells(10, 3)) Cells(5, 4) = DateDiff("h", Cells(10, 2), Cells(10, 3)) Cells(6, 4) = DateDiff("n", Cells(10, 2), Cells(10, 3)) Cells(7, 4) = DateDiff("s", Cells(10, 2), Cells(10, 3)) End Sub.

ȼ ɧɚɱɚɥɟ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɳɟɥɤɚɟɦ ɧɚ ɤɧɨɩɤɟ ɨɛɧɭɥɟɧɢɹ, ɡɚɧɨɫɢɦ ɡɧɚɱɟɧɢɟ ɢɧɬɟɪɜɚɥɚ ɦɨɞɟɥɢɪɨɜɚɧɢɹ, ɚ ɡɚɬɟɦ ɳɟɥɤɚɟɦ ɩɨ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɤɧɨɩɤɟ ɫɱɟɬɱɢɤɚ. ɋɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɜ ɧɚɲɟɦ ɜɚɪɢɚɧɬɟ ɫɱɟɬɱɢɤɚ ɨɬɫɭɬɫɬɜɭɟɬ ɧɚɱɚɥɶɧɨɟ ɧɭɥɟɜɨɟ ɡɧɚɱɟɧɢɟ. ɗɬɨ ɧɭɠɧɨ ɭɱɢɬɵɜɚɬɶ ɩɪɢ ɪɚɡɪɚɛɨɬɤɟ ɦɨɞɟɥɢ. ɇɚ ɪɢɫɭɧɤɟ ɩɨɤɚɡɚɧɨ ɩɪɢɦɟɧɟɧɢɟ ɫɱɟɬɱɢɤɚ ɞɧɟɣ. ɋɥɟɞɭɟɬ ɧɚɩɨɦɧɢɬɶ, ɱɬɨ ɩɪɢ ɪɚɫɱɟɬɚɯ ɤɨɨɪɞɢɧɚɬ ɩɥɚɧɟɬ ɢɫɩɨɥɶɡɭɟɬɫɹ ɢɧɬɟɪɜɚɥ ɜɪɟɦɟɧɢ ɜ ɸɥɢɚɧɫɤɢɯ ɫɬɨɥɟɬɢɹɯ ɨɬ ɤɨɧɤɪɟɬɧɨɣ ɞɚɬɵ Ɍ. Ⱦɥɹ ɪɚɫɱɟɬɚ ɢɧɬɟɪɜɚɥɚ ɧɟɨɛɯɨɞɢɦɨ ɜɵɱɢɫɥɢɬɶ ɬɟɤɭɳɭɸ ɸɥɢɚɧɫɤɭɸ ɞɚɬɭ JD ɨɬ Ƚɪɢɧɜɢɱɫɤɨɝɨ ɩɨɥɭɞɧɹ ɜɫɟɦɢɪɧɨɝɨ ɜɪɟɦɟɧɢ, ɤɨɬɨɪɵɣ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɩɨɥɞɧɸ 1 ɹɧɜɚɪɹ 4713 ɝ. ɞɨ ɧ.ɷ ɸɥɢɚɧɫɤɨɝɨ ɤɚɥɟɧɞɚɪɹ, ɢ ɡɧɚɬɶ ɸɥɢɚɧɫɤɭɸ ɞɚɬɭ ɧɚɱɚɥɶɧɨɣ ɷɩɨɯɢ JD0, ɤɨɬɨɪɚɹ ɢɫɩɨɥɶɡɭɸɬɫɹ ɜ ɮɨɪɦɭɥɚɯ ɜɵɱɢɫɥɟɧɢɹ ɩɨɥɨɠɟɧɢɹ ɩɥɚɧɟɬ. ɑɚɳɟ ɜɫɟɝɨ ɧɚɱɚɥɶɧɚɹ ɞɚɬɚ JD0 ɩɪɢɜɹɡɵɜɚɟɬɫɹ ɤ ɩɨɥɭɧɨɱɢ 1-ɝɨ ɹɧɜɚɪɹ 1900 49

1. Ɉ ɦɨɞɟɥɢɪɨɜɚɧɢɢ, ɪɟɲɟɧɢɢ ɡɚɞɚɱ, ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɢ ɢ MS Excel

ɝɨɞɚ ɢ ɪɚɜɧɹɟɬɫɹ 2415020,0. ɘɥɢɚɧɫɤɢɟ ɫɭɬɤɢ ɧɚɱɢɧɚɸɬɫɹ ɜ ɩɨɥɞɟɧɶ, ɚ ɧɟ ɜ ɩɨɥɧɨɱɶ ɤɚɤ ɤɚɥɟɧɞɚɪɧɵɟ ɫɭɬɤɢ. ȼɵɱɢɫɥɟɧɢɟ ɢɧɬɟɪɜɚɥɚ ɜɪɟɦɟɧɢ ɜ ɸɥɢɚɧɫɤɢɯ ɫɬɨɥɟɬɢɹɯ ɩɪɨɢɡɜɨɞɢɬɫɹ ɩɨ ɜɵɪɚɠɟɧɢɸ  ൌ ሺJD-JD0)»36525,0, ɝɞɟ 36525,0 – ɜɟɥɢɱɢɧɚ ɸɥɢɚɧɫɤɨɝɨ ɫɬɨɥɟɬɢɹ ɜ ɫɨɥɧɟɱɧɵɯ ɫɭɬɤɚɯ. Ɍɟɤɭɳɟɟ ɡɧɚɱɟɧɢɟ ɸɥɢɚɧɫɤɨɣ ɞɚɬɵ ɜɵɱɢɫɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ

 ൌ ሺ͵͸ͷǡʹͷ ‫› כ‬ሻ ൅ ൫͵Ͳǡ͸ͲͲͳ ‫ כ‬ሺ ൅ ͳሻ൯ ൅ † ൅ – ൅ ͳ͹ʹͲͻͻͶǡͷ, ɝɞɟ › - ɡɧɚɱɟɧɢɟ ɝɨɞɚ ɩɪɢ ɧɨɦɟɪɟ ɦɟɫɹɰɚ ɛɨɥɶɲɟ 2 ɢ ɡɧɚɱɟɧɢɟ ɝɨɞɚ ɧɚ 1 ɦɟɧɶɲɟ ɞɥɹ ɹɧɜɚɪɹ ɢ ɮɟɜɪɚɥɹ,  – ɩɚɪɚɦɟɬɪ, ɤɨɬɨɪɵɣ ɪɚɜɟɧ ɧɨɦɟɪɭ ɦɟɫɹɰɚ ɩɪɢ ɭɫɥɨɜɢɢ, ɱɬɨ ɡɧɚɱɟɧɢɟ ɦɟɫɹɰɚ ɛɨɥɶɲɟ 2, ɢ ɪɚɜɟɧ ɫɭɦɦɟ 12 ɢ ɧɨɦɟɪɚ ɦɟɫɹɰɚ ɞɥɹ ɹɧɜɚɪɹ ɢ ɮɟɜɪɚɥɹ. † - ɧɨɦɟɪ ɞɧɹ ɜ ɦɟɫɹɰɟ, ‫ ݐ‬- ɜɪɟɦɹ ɜ ɞɨɥɹɯ ɫɭɬɨɤ ɨɬ ɩɨɥɭɧɨɱɢ, ͳ͹ʹͲͻͻͶǡͷ - ɸɥɢɚɧɫɤɚɹ ɞɚɬɚ. Ɍɚɤ ɤɚɤ ɜɪɟɦɹ ɞɨɥɠɧɨ ɛɵɬɶ ɩɪɢɜɹɡɚɧɨ ɤ Ƚɪɢɧɜɢɱɫɤɨɦɭ ɦɟɪɢɞɢɚɧɭ, ɬɨ ɩɪɢ ɜɜɨɞɟ Ɇɨɫɤɨɜɫɤɨɝɨ ɜɪɟɦɟɧɢ ɧɭɠɧɨ ɜɵɱɢɬɚɬɶ 3 ɱɚɫɚ. ȿɫɥɢ ɞɚɬɚ ɛɨɥɶɲɟ 15 ɨɤɬɹɛɪɹ 1582 ɝɨɞɚ, ɤɨɬɨɪɚɹ ɹɜɥɹɟɬɫɹ ɧɚɱɚɥɨɦ ɝɪɢɝɨɪɢɚɧɫɤɨɝɨ ɤɚɥɟɧɞɚɪɹ, ɬɨ ɤ ɬɟɤɭɳɟɣ ɸɥɢɚɧɫɤɨɣ ɞɚɬɟ ɧɭɠɧɨ ɜɵɱɢɫɥɢɬɶ ɞɨɛɚɜɤɭ ܾ ɩɨ ɮɨɪɦɭɥɟ ܾ ൌ ʹ െ ܽ ൅ ‫ܶܰܫ‬ሺܽΤͶሻ, ɝɞɟ ܽ ൌ ‫ܶܰܫ‬ሺ‫ݕ‬ΤͳͲͲሻ . ȿɫɥɢ ɜɪɟɦɹ ɡɚɞɚɟɦ ɫ ɭɱɟɬɨɦ ɫɟɤɭɧɞ, ɬɨ ɧɟɨɛɯɨɞɢɦɨ ɩɪɢ ɩɪɢɜɟɞɟɧɢɢ ɤ ɞɨɥɹɦ ɫɭɬɨɤ ɩɨɦɧɢɬɶ ɱɬɨ ɜ ɫɭɬɤɚɯ 86400 ɫɟɤɭɧɞ. ɋɨɡɞɚɞɢɦ ɩɨɥɶɡɨɜɚɬɟɥɶɫɤɭɸ ɮɭɧɤɰɢɸ ɞɥɹ ɜɵɱɢɫɥɟɧɢɹ ɸɥɢɚɧɫɤɨɣ ɞɚɬɵ ɫ ɚɪɝɭɦɟɧɬɚɦɢ, ɤɨɬɨɪɵɟ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɩɚɪɚɦɟɬɪɚɦ ɞɚɬ ɜ ɧɚɲɟɣ ɬɚɛɥɢɰɟ. ɉɪɨɝɪɚɦɦɚ ɜɵɱɢɫɥɟɧɢɹ ɸɥɢɚɧɫɤɨɣ ɞɚɬɵ ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɢɠɟ: Function JD(yk, nk, dk, hk, mk, sk) 'ɜɵɱɢɫɥɟɧɢɟ ɸɥɢɚɧɫɤɨɣ ɞɚɬɵ ɩɨ ɤɚɥɟɧɞɚɪɧɵɦ ɞɚɬɚɦ ɛɨɥɶɲɟ 15 ɨɤɬɹɛɪɹ 1582 ɝɨɞɚ If nk > 2 Then y = yk: m = nk Else y = yk - 1: m = nk + 12 End If a = Int(y / 100): b = 2 - a + Int(a / 4) t = (hk * 3600 + mk * 60 + sk) / 86400 'ɪɚɫɱɟɬ ɞɨɥɢ ɫɭɬɨɤ JD = Int(365.25 * y) + Int(30.6001 * (m + 1)) + dk + t + 1720994.5 + b End Function. ɋɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɩɪɢ ɡɚɞɚɧɢɢ ɢɫɯɨɞɧɨɣ ɞɚɬɵ ɞɧɢ ɩɪɟɞɫɬɚɜɥɟɧɵ ɫ ɞɪɨɛɧɨɣ ɱɚɫɬɶɸ ɫɭɬɨɤ, ɬɨ ɩɚɪɚɦɟɬɪɵ ɜɪɟɦɟɧɢ ɧɭɠɧɨ ɡɚɞɚɬɶ ɧɭɥɟɜɵɟ (ɫɦ. ɋ2:ɋ4). 50 Powered by TCPDF (www.tcpdf.org)

1.5. ɋɨɡɞɚɧɢɟ ɫɱɟɬɱɢɤɨɜ ɞɥɹ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɩɪɨɰɟɫɫɚ ɦɨɞɟɥɢɪɨɜɚɧɢɹ

Ⱦɥɹ ɪɚɫɱɟɬɚ ɸɥɢɚɧɫɤɨɣ ɞɚɬɵ ɜ ɹɱɟɣɤɢ ȼ11 ɢ ɋ11 ɜɫɬɚɜɢɥɢ ɩɨɥɶɡɨɜɚɬɟɥɶɫɤɭɸ ɮɭɧɤɰɢɸ JD() ɫ ɩɚɪɚɦɟɬɪɚɦɢ ɤɚɥɟɧɞɚɪɧɵɯ ɞɚɬ. Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɢɧɬɟɪɜɚɥɚ ɜ ɸɥɢɚɧɫɤɢɯ ɫɬɨɥɟɬɢɹɯ Ɍ ɜɧɟɫɥɢ ɪɚɫɱɟɬɧɨɟ ɜɵɪɚɠɟɧɢɟ ɜ ɹɱɟɣɤɭ ɋ12 (ɫɦ. ɩɪɢɦɟɱɚɧɢɟ).

Ⱦɥɹ ɛɨɥɟɟ ɩɥɚɜɧɨɝɨ ɩɟɪɟɯɨɞɚ ɤ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɸ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ VBA ɪɚɫɫɦɨɬɪɢɦ ɜ ɨɬɞɟɥɶɧɵɯ ɦɨɞɟɥɹɯ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɮɨɪɦ ɫ ɪɹɞɨɦ ɭɩɪɚɜɥɹɸɳɢɯ ɷɥɟɦɟɧɬɨɜ. ɇɚ ɷɬɨɦ ɡɚɤɨɧɱɢɦ ɪɚɫɫɦɨɬɪɟɧɢɟ ɜɨɩɪɨɫɚ ɫɨɡɞɚɧɢɹ ɫɱɟɬɱɢɤɨɜ ɞɥɹ ɦɨɞɟɥɢɪɨɜɚɧɢɹ. ɉɪɢ ɪɟɲɟɧɢɢ ɡɚɞɚɱ ɢɥɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ ɪɚɫɫɦɨɬɪɟɧɧɵɟ ɜɨɩɪɨɫɵ ɫɨɡɞɚɧɢɹ ɫɱɟɬɱɢɤɨɜ ɛɭɞɟɦ ɨɩɭɫɤɚɬɶ ɫ ɧɚɞɟɠɞɨɣ, ɱɬɨ ɱɢɬɚɬɟɥɶ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨ ɫɦɨɠɟɬ ɫɨɡɞɚɬɶ ɧɟɨɛɯɨɞɢɦɵɣ ɫɱɟɬɱɢɤ ɞɥɹ ɤɨɧɤɪɟɬɧɨɣ ɦɨɞɟɥɢ.

51

2. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ MS Excel 2.1. Ɇɚɬɟɦɚɬɢɤɚ 2.1.1. ȼɪɚɳɟɧɢɟ ɝɪɚɮɢɤɨɜ Ɂɚɞɚɧ ɨɬɪɟɡɨɤ ɩɪɹɦɨɣ ɢ ɫɩɢɪɚɥɶ Ⱥɪɯɢɦɟɞɚ. ɇɭɠɧɨ ɩɨɫɬɪɨɢɬɶ ɢɯ ɝɪɚɮɢɤɢ ɢ ɨɛɟɫɩɟɱɢɬɶ ɜɪɚɳɟɧɢɟ ɨɬɧɨɫɢɬɟɥɶɧɨ ɰɟɧɬɪɚ ɩɪɹɦɨɭɝɨɥɶɧɵɯ ɤɨɨɪɞɢɧɚɬ. ɇɚɱɧɟɦ ɫ ɦɚɫɫɢɜɚ ɤɨɨɪɞɢɧɚɬ ɩɪɹɦɨɣ ɢ ɫɩɢɪɚɥɢ ɫ ɧɚɱɚɥɶɧɵɦɢ ɭɫɥɨɜɢɹɦɢ. Ɂɚɬɟɦ ɜɨ ɜɫɩɨɦɨɝɚɬɟɥɶɧɨɦ ɦɚɫɫɢɜɟ ɛɭɞɟɦ ɨɫɭɳɟɫɬɜɥɹɬɶ ɩɟɪɟɫɱɟɬ ɤɨɨɪɞɢɧɚɬ ɫ ɭɱɟɬɨɦ ɬɟɤɭɳɟɝɨ ɭɝɥɚ ɩɨɜɨɪɨɬɚ, ɤɨɬɨɪɵɣ ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɤɨɪɨɫɬɶɸ ɢɡɦɟɧɟɧɢɹ ɢ ɫɱɟɬɱɢɤɨɦ ɜɪɟɦɟɧɢ. ɗɬɨɬ ɦɚɫɫɢɜ ɤɨɨɪɞɢɧɚɬ ɛɭɞɟɬ ɫɥɭɠɢɬɶ ɞɥɹ ɩɨɫɬɪɨɟɧɢɹ ɝɪɚɮɢɤɨɜ ɩɪɹɦɨɣ ɢ ɫɩɢɪɚɥɢ. Ɉɬɪɟɡɨɤ ɩɪɹɦɨɣ ɡɚɞɚɞɢɦ ɤɨɨɪɞɢɧɚɬɚɦɢ ɟɟ ɤɨɧɰɨɜ, ɚ ɫɩɢɪɚɥɶ Ⱥɪɯɢɦɟɞɚ ɭɪɚɜɧɟɧɢɟɦ ɜ ɩɨɥɹɪɧɨɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ ɤɚɤ ܴ ൌ ܽ ‫߮ כ‬ǡ ɝɞɟ ܴ – ɪɚɞɢɭɫ, ܽ - ɩɚɪɚɦɟɬɪ, ɤɨɬɨɪɵɣ ɨɩɪɟɞɟɥɹɟɬ ɫɤɨɪɨɫɬɶ ɢɡɦɟɧɟɧɢɹ ɪɚɞɢɭɫɚ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɭɝɥɚ, ߮ - ɭɝɨɥ. Ɂɚɞɚɟɦ ɤɨɨɪɞɢɧɚɬɵ ɩɪɹɦɨɣ ɜ ɹɱɟɣɤɚɯ G3:H4 ɢ ɩɚɪɚɦɟɬɪ ɫɩɢɪɚɥɢ ɜ ɹɱɟɣɤɟ Ɇ3. Ɋɚɡɦɟɪɧɨɫɬɶ ɤɨɨɪɞɢɧɚɬ ɡɚɞɚɟɦ ɜ ɭɫɥɨɜɧɵɯ ɟɞɢɧɢɰɚɯ, ɚ ɭɝɨɥɨɜ – ɜ ɪɚɞɢɚɧɚɯ. Ⱦɥɹ ɪɟɚɥɢɡɚɰɢɢ ɦɨɞɟɥɢ ɜɪɚɳɟɧɢɹ ɩɟɪɟɫɱɢɬɵɜɚɟɦ ɩɪɹɦɨɭɝɨɥɶɧɵɟ ɤɨɨɪɞɢɧɚɬɵ ɤɨɧɰɨɜ ɩɪɹɦɨɣ ɜ ɩɨɥɹɪɧɵɟ ɩɨ ɮɨɪɦɭɥɚɦ ܴ௜ ൌ ሺ‫ݔ‬௜ ଶ ൅ ‫ݕ‬௜ ଶ ሻ଴ǡହ , ߮௜ ൌ ܽ‫ݕ ݃ݐܿݎ‬௜ Τ‫ݔ‬௜ , ɝɞɟ i=1,2 – ɧɨɦɟɪɚ ɤɨɨɪɞɢɧɚɬ ɤɨɧɰɨɜ ɩɪɹɦɨɣ ɥɢɧɢɢ. ɉɨɥɹɪɧɵɟ ɤɨɨɪɞɢɧɚɬɵ ɩɪɹɦɨɣ ɡɚɩɢɲɟɦ ɜ Y ɹɱɟɣɤɢ I3:J4. Ɏɨɪɦɢɪɭɟɦ ɦɚɫɫɢɜ ɤɨɨɪɞɢɧɚɬ ɝɪɚɮɢɤɨɜ ܴ௜ ɞɥɹ ɢɡɨɛɪɚɠɟɧɢɹ ɱɟɪɟɡ ɞɢɚߙ ɝɪɚɦɦɵ (Ⱥ7:ɋ20). ȼ ɹɱɟɣ߮௜ X ɤɚɯ ȼ7:ɋ8 ɜɵɱɢɫɥɹɟɦ ɩɪɹɦɨɭɝɨɥɶɧɵɟ ɤɨɨɪɞɢɧɚɬɵ ɤɨɧɰɨɜ ɩɪɹɦɨɣ ɫ ɭɱɟɬɨɦ ɭɝɥɚ ɩɨɜɨɪɨɬɚ ɩɨ ɮɨɪɦɭɥɚɦ (ɫɦ. ɪɢɫɭɧɨɤ) ‫ݔ‬௜ ൌ ܴ௜ ‫•‘… כ‬ሺ߮௜ ൅ ߙሻ, ‫ݕ‬௜ ൌ ܴ௜ ‫‹• כ‬ሺ߮௜ ൅ ߙሻ, ɝɞɟ ߙ െ ˖ˆˑˎ˒ˑ˅ˑ˓ˑ˕˃ˆ˓˃˗ˋˍ˃. 52

2.1. Ɇɚɬɟɦɚɬɢɤɚ

ɍɝɨɥ ɩɨɜɨɪɨɬɚ ɜɵɱɢɫɥɹɟɬɫɹ (ȿ3) ɫ ɭɱɟɬɨɦ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɢ (Ⱥ3) ɢ ɡɧɚɱɟɧɢɹ ɫɱɟɬɱɢɤɚ (ɋ3). Ɂɧɚɱɟɧɢɟ ɫɱɟɬɱɢɤɚ ɦɨɠɧɨ ɢɡɦɟɧɹɬɶ ɩɭɬɟɦ ɡɚɩɢɫɢ ɫ ɤɥɚɜɢɚɬɭɪɵ. Ⱦɥɹ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɩɪɨɰɟɫɫɚ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɩɨɜɨɪɨɬɚ ɝɪɚɮɢɤɨɜ ɫɨɡɞɚɞɢɦ ɹɱɟɣɤɭ, ɤɨɬɨɪɚɹ ɨɩɪɟɞɟɥɹɟɬ ɲɚɝ ɢɡɦɟɧɟɧɢɹ ɡɧɚɱɟɧɢɹ ɫɱɟɬɱɢɤɚ (D3). ɋɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɩɨɜɨɪɨɬ ɩɪɹɦɨɣ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɩɪɨɬɢɜ ɱɚɫɨɜɨɣ ɫɬɪɟɥɤɢ ɩɪɢ ɩɨɥɨɠɢɬɟɥɶɧɨɦ ɡɧɚɱɟɧɢɢ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɢ (Ⱥ3). ȼ ɦɚɫɫɢɜɟ Ⱥ10:ɋ20 ɮɨɪɦɢɪɭɟɦ 11 ɬɨɱɟɤ ɞɥɹ ɢɡɨɛɪɚɠɟɧɢɹ ɫɩɢɪɚɥɢ Ⱥɪɯɢɦɟɞɚ, ɝɞɟ ɩɟɪɟɫɱɢɬɵɜɚɟɦ ɩɨɥɹɪɧɵɟ ɤɨɨɪɞɢɧɚɬɵ ɜ ɩɪɹɦɨɭɝɨɥɶɧɵɟ (ɫɦ. ɩɪɢɦɟɱɚɧɢɹ). Ɇɨɠɧɨ ɢɡɦɟɧɢɬɶ ɤɨɥɢɱɟɫɬɜɨ ɬɨɱɟɤ. ɉɪɢ ɩɟɪɟɫɱɟɬɟ ɢɫɩɨɥɶɡɭɟɦ ɦɚɫɫɢɜ ɩɨɥɹɪɧɵɯ ɤɨɨɪɞɢɧɚɬ ɫɩɢɪɚɥɢ ɛɟɡ ɭɱɟɬɚ ɭɝɥɚ ɩɨɜɨɪɨɬɚ (I8:J17). Ʉɨɨɪɞɢɧɚɬɵ ɬɨɱɟɤ ɜɵɱɢɫɥɹɟɦ ɫ ɭɱɟɬɨɦ ɧɨɦɟɪɚ ɬɨɱɤɢ, ɤɨɬɨɪɵɣ ɨɩɪɟɞɟɥɹɟɬ ɩɨɥɹɪɧɵɣ ɭɝɨɥ ɬɨɱɤɢ ɫɩɢɪɚɥɢ (ɫɦ.ɩɪɢɦɟɱɚɧɢɹ). Ɍɚɤ ɤɚɤ ɩɪɢ ɩɟɪɟɫɱɟɬɟ ɤɨɨɪɞɢɧɚɬ ɜ ɦɚɫɫɢɜɟ Ⱥ10:ɋ20 ɜɵɱɢɬɚɟɦ ɡɧɚɱɟɧɢɟ ɭɝɥɚ ɩɨɜɨɪɨɬɚ, ɬɨ ɫɩɢɪɚɥɶ ɜɪɚɳɚɟɬɫɹ ɩɨ ɱɚɫɨɜɨɣ ɫɬɪɟɥɤɟ. ɂɬɚɤ, ɩɪɹɦɚɹ ɜɪɚɳɚɟɬɫɹ ɩɨ ɱɚɫɨɜɨɣ ɫɬɪɟɥɤɟ, ɚ ɫɩɢɪɚɥɶ – ɩɪɨɬɢɜ. Ɇɨɠɧɨ ɢɡɦɟɧɢɬɶ ɜɪɚɳɟɧɢɟ ɝɪɚɮɢɤɨɜ ɧɚ ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɣ ɩɭɬɟɦ ɡɚɞɚɧɢɹ ɨɬɪɢɰɚɬɟɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɢ. ȼɵɞɟɥɹɟɦ ɦɚɫɫɢɜ Ⱥ7:ɋ20 ɢ ɱɟɪɟɡ ɡɚɤɥɚɞɤɭ ȼɫɬɚɜɤɚ, ɜ ɝɪɭɩɩɟ Ⱦɢɚɝɪɚɦɦɚ ɜɵɛɢɪɚɟɦ ɝɪɚɮɢɤ Ɍɨɱɟɱɧɚɹ ɫ ɝɥɚɞɤɢɦɢ ɤɪɢɜɵɦɢ ɢ ɦɚɪɤɟɪɚɦɢ. ɐɟɥɟɫɨɨɛɪɚɡɧɨ ɡɚɮɢɤɫɢɪɨɜɚɬɶ ɜ ɩɭɧɤɬɟ Ɏɨɪɦɚɬ ɨɫɢ ɤɨɧɬɟɤɫɬɧɨɝɨ ɦɟɧɸ ɨɫɢ ɦɚɤɫɢɦɚɥɶɧɵɟ ɢ ɦɢɧɢɦɚɥɶɧɵɟ ɡɧɚɱɟɧɢɹ ɨɫɟɣ. ɉɨɥɭɱɢɦ ɢɡɨɛɪɚɠɟɧɢɟ ɝɪɚɮɢɤɨɜ, ɤɨɬɨɪɵɟ ɜɪɚɳɚɸɬɫɹ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɡɧɚɱɟɧɢɹ ɫɱɟɬɱɢɤɚ. Ⱥɜɬɨɦɚɬɢɡɢɪɭɟɦ ɢɡɦɟɧɟɧɢɟ ɡɧɚɱɟɧɢɟ ɫɱɟɬɱɢɤɚ. Ⱦɥɹ ɷɬɨɝɨ ɫɨɡɞɚɞɢɦ ɤɧɨɩɤɢ Ɉɛɧɭɥɟɧɢɟ ɫɱɟɬɱɢɤɚ ɢ ɇɚɱɢɫɥɟɧɢɟ ɫɱɟɬɱɢɤɚ. ɇɚ ɡɚɤɥɚɞɤɟ Ɋɚɡɪɚɛɨɬɱɢɤ, ɜ ɝɪɭɩɩɟ ɗɥɟɦɟɧɬɵ ɭɩɪɚɜɥɟɧɢɹ, ɜ ɫɩɢɫɤɟ ȼɫɬɚɜɢɬɶ ɜɵɛɢɪɚɟɦ ɜ ɗɥɟɦɟɧɬɵ ActiveX ɷɥɟɦɟɧɬ Ʉɧɨɩɤɚ. ɉɪɨɬɹɠɤɨɣ ɨɩɪɟɞɟɥɹɟɦ ɦɟɫɬɨ ɢ ɪɚɡɦɟɪ ɢɡɨɛɪɚɠɟɧɢɹ ɤɧɨɩɤɢ ɧɚ ɥɢɫɬɟ. ɇɟ ɡɚɤɪɵɜɚɹ ɨɛɴɟɤɬ Ʉɧɨɩɤɚ, ɱɟɪɟɡ ɤɨɧɬɟɤɫɬɧɨɟ ɦɟɧɸ ɜɵɯɨɞɢɦ ɧɚ ɋɜɨɣɫɬɜɚ ɢ ɜ ɩɭɧɤɬɟ Caption ɡɚɧɨɫɢɦ ɧɚɡɜɚɧɢɟ ɤɧɨɩɤɢ. Ⱦɚɥɟɟ ɳɟɥɤɧɭɜ ɞɜɚɠɞɵ ɧɚ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɤɧɨɩɤɟ, ɡɚɧɨɫɢɦ ɫɥɟɞɭɸɳɢɟ ɬɟɤɫɬɵ ɩɪɨɝɪɚɦɦ: Private Sub CommandButton1_Click() Cells(3, 3) = 0 'Ɉɛɧɭɥɟɧɢɟ ɫɱɟɬɱɢɤɚ' End Sub Private Sub CommandButton2_Click() Cells(3, 3) = Cells(3, 3) + Cells(3, 4) 'ɇɚɱɢɫɥɟɧɢɟ ɫɱɟɬɱɢɤɚ' 53

2. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ MS Excel

End Sub. Ɍɨɱɤɭ ɧɟ ɧɚɞɨ ɫɬɚɜɢɬɶ ɜ ɬɟɤɫɬɟ ɩɪɨɝɪɚɦɦɵ ɤɧɨɩɨɤ. ɋɬɢɥɶ ɫɫɵɥɨɤ ɜ ɩɪɨɝɪɚɦɦɚɯ ɤɧɨɩɨɤ ɫɨɨɬɜɟɬɫɬɜɭɟɬ R1C1. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɫɧɚɱɚɥɚ ɭɤɚɡɵɜɚɟɬɫɹ ɧɨɦɟɪ ɫɬɪɨɤɢ, ɚ ɡɚɬɟɦ ɧɨɦɟɪ ɫɬɨɥɛɰɚ ɜ ɮɭɧɤɰɢɢ Cells. Ɉɛɧɭɥɟɧɢɟ ɢ ɧɚɱɢɫɥɟɧɢɟ ɫɱɟɬɱɢɤɚ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɩɭɬɟɦ ɳɟɥɱɤɨɜ ɧɚ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɤɧɨɩɤɚɯ. ɉɪɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ ɦɨɠɧɨ ɢɡɦɟɧɢɬɶ ɲɚɝ ɧɚɱɢɫɥɟɧɢɹ ɫɱɟɬɱɢɤɚ (D3 ɢɥɢ Cells(3, 4)). Ɉɛɹɡɚɬɟɥɶɧɨ ɫɨɯɪɚɧɢɬɟ ɮɚɣɥ ɫ ɪɚɫɲɢɪɟɧɢɟɦ Ʉɧɢɝɚ Excel ɫ ɩɨɞɞɟɪɠɤɨɣ ɦɚɤɪɨɫɨɜ, ɚ ɩɪɢ ɨɬɤɪɵɬɢɢ ɮɚɣɥɚ ɜɤɥɸɱɢɬɶ ɪɚɡɪɟɲɟɧɢɟ ɧɚ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɟ ɦɚɤɪɨɫɨɜ. ɇɚ ɪɢɫɭɧɤɚɯ ɩɪɟɞɫɬɚɜɥɟɧɵ ɝɪɚɮɢɤɢ ɜ ɧɚɱɚɥɶɧɨɦ ɩɨɥɨɠɟɧɢɢ ɢ ɩɨɫɥɟ ɧɚɱɢɫɥɟɧɢɹ ɫɱɟɬɱɢɤɚ.

ȼ ɧɢɠɧɟɣ ɬɚɛɥɢɰɵ ɩɪɟɞɫɬɚɜɥɟɧɵ ɭɪɚɜɧɟɧɢɹ ɤɪɢɜɵɯ ɜ ɩɨɥɹɪɧɨɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ, ɤɨɬɨɪɵɟ ɦɨɝɭɬ ɛɵɬɶ ɢɫɩɨɥɶɡɨɜɚɧɵ ɞɥɹ ɦɨɞɟɥɢɪɨɜɚɧɢɹ. ɍɪɚɜɧɟɧɢɟ ܴ ൌ ܽ ‫•‘… כ‬ሺܾ ‫ ߮ כ‬൅ ߮଴ ሻ ܴ ൌܽ൅ܾ‫߮כ‬ ܴ ൌ ܽ ‫‹• כ‬ሺʹ ‫߮ כ‬ሻ ܴ ൌ ܽ ‫݊݅ݏ כ‬ሺͶ ‫߮ כ‬ሻ ܴଶ ൌ ܽଶ ‫•‘… כ‬ሺʹ ‫߮ כ‬ሻ ܴ ൌ ܽ ‫ כ‬ሺͳ ൅ …‘•ሺ߮ሻሻ ܴ ൌ ሺ͵ ‫•‘… כ ܽ כ‬ሺ߮ሻ ‫‹• כ‬ሺ߮ሻሻȀሺܿ‫ ݏ݋‬ଷ ሺ߮ሻ ൅ ‫݊݅ݏ‬ଷ ሺ߮ሻሻ ܴ ൌ ʹ ‫•‘… כ ܽ כ‬ሺ߮ሻ ൅ ܾ ܴ ൌ ͳ ൅ …‘•ሺ͵ ‫߮ כ‬ሻ ൅ ‫݊݅ݏ‬ଶ ሺ͵ ‫߮ כ‬ሻ ܴ ൌ ܽ ‫’š‡ כ‬ሺܾ ‫߮ כ‬ሻ ܴ ൌ ܽ ‫ ݏ݋ܿ כ‬଴ǡହ ሺʹ ‫߮ כ‬ሻ 54

ɇɚɡɜɚɧɢɟ ɩɨɥɹɪɧɚɹ ɪɨɡɚ ɫɩɢɪɚɥɶ Ⱥɪɯɢɦɟɞɚ ɞɜɭɥɢɫɬɧɢɤ ɱɟɬɵɪɟɯɥɢɫɬɧɢɤ ɥɟɦɧɢɫɤɚɬɚ Ȼɟɪɧɭɥɥɢ ɤɚɪɞɢɨɢɞɚ, ܽ >0 ɥɢɫɬ Ⱦɟɤɚɪɬɚ, ܽ >0 ɭɥɢɬɤɚ ɉɚɫɤɚɥɹ ɥɢɫɬ ɳɚɜɟɥɹ ɥɨɝɚɪɢɮɦɢɱɟɫɤɚɹ ɫɩɢɪɚɥɶ ɥɟɦɧɢɫɤɚɬɚ Ȼɟɪɧɭɥɥɢ

2.1. Ɇɚɬɟɦɚɬɢɤɚ

2.1.2. Ʉɨɦɩɥɟɤɫɧɨɟ ɧɚɯɨɠɞɟɧɢɟ ɤɨɪɧɟɣ ɭɪɚɜɧɟɧɢɣ Ɂɚɞɚɧɨ ɭɪɚɜɧɟɧɢɟ. ɇɭɠɧɨ ɧɚɣɬɢ ɬɨɱɧɨɟ ɡɧɚɱɟɧɢɟ ɤɨɪɧɟɣ ɭɪɚɜɧɟɧɢɹ. Ɏɨɪɦɭɥɵ ɜɵɱɢɫɥɟɧɢɹ ɤɨɪɧɟɣ ɭɪɚɜɧɟɧɢɹ ɨɬɫɭɬɫɬɜɭɸɬ. Ɍɨɱɧɨɟ ɜɵɱɢɫɥɟɧɢɟ ɤɨɪɧɟɣ ɩɪɨɢɡɜɟɞɟɦ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɩɪɨɰɟɞɭɪɵ ɉɨɢɫɤ ɪɟɲɟɧɢɹ. ɍɪɚɜɧɟɧɢɹ ɱɚɫɬɨ ɢɦɟɸɬ ɫɥɨɠɧɵɣ ɜɢɞ. ɉɨɷɬɨɦɭ ɰɟɥɟɫɨɨɛɪɚɡɧɨ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨ ɨɩɪɟɞɟɥɢɬɶ ɧɚɥɢɱɢɟ ɤɨɪɧɟɣ ɭɪɚɜɧɟɧɢɹ, ɨɛɥɚɫɬɢ ɢɯ ɧɚɯɨɠɞɟɧɢɹ ɢ ɩɪɢɛɥɢɠɟɧɧɵɟ ɡɧɚɱɟɧɢɹ. ɉɪɢ ɧɚɯɨɠɞɟɧɢɢ ɤɨɪɧɟɣ ɫɧɚɱɚɥɚ ɩɪɢɦɟɧɢɦ ɝɪɚɮɨɚɧɚɥɢɬɢɱɟɫɤɢɣ ɦɟɬɨɞ ɧɚɯɨɠɞɟɧɢɹ ɤɨɪɧɟɣ ɭɪɚɜɧɟɧɢɹ, ɭɫɥɨɜɧɨɝɨ ɮɨɪɦɚɬɢɪɨɜɚɧɢɹ ɢ ɡɚɬɟɦ ɩɪɨɰɟɞɭɪɵ ɉɨɢɫɤɚ ɪɟɲɟɧɢɹ. Ƚɪɚɮɨɚɧɚɥɢɬɢɱɟɫɤɢɣ ɦɟɬɨɞ ɩɨɡɜɨɥɹɟɬ ɧɚɝɥɹɞɧɨ ɨɩɪɟɞɟɥɢɬɶ ɧɚɥɢɱɢɟ ɤɨɪɧɟɣ, ɢɯ ɤɨɥɢɱɟɫɬɜɨ ɢ ɩɪɢɛɥɢɠɟɧɧɵɟ ɡɧɚɱɟɧɢɹ. ɋ ɩɨɦɨɳɶɸ ɭɫɥɨɜɧɨɝɨ ɮɨɪɦɚɬɢɪɨɜɚɧɢɹ ɝɪɚɮɢɱɟɫɤɢ ɜɵɞɟɥɹɟɦ ɧɚ ɝɪɚɮɢɤɟ ɢɧɬɟɪɜɚɥɵ ɧɚɯɨɠɞɟɧɢɹ ɤɨɪɧɟɣ. ɉɪɨɰɟɞɭɪɚ ɉɨɢɫɤ ɪɟɲɟɧɢɹ ɨɛɟɫɩɟɱɢɜɚɟɬ ɬɨɱɧɨɟ ɨɩɪɟɞɟɥɟɧɢɟ ɡɧɚɱɟɧɢɣ ɜɫɟɯ ɤɨɪɧɟɣ ɭɪɚɜɧɟɧɢɹ. ȼ ɤɚɱɟɫɬɜɟ ɩɪɢɦɟɪɚ ɪɚɫɫɦɨɬɪɢɦ ɜɵɱɢɫɥɟɧɢɟ ɤɨɪɧɟɣ ɧɚ ɨɩɪɟɞɟɥɟɧɧɨɦ ɢɧɬɟɪɜɚɥɟ ɫɥɟɞɭɸɳɟɝɨ ɭɪɚɜɧɟɧɢɹ ͹ ‫•‘… כ‬ሺ͵ ‫ݔ כ‬ሻ ൅ ͵ ൌ ‫ ݔ‬ଶ . Ⱦɥɹ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨɝɨ ɨɩɪɟɞɟɥɟɧɢɹ ɡɧɚɱɟɧɢɣ ɤɨɪɧɟɣ ɢ ɢɯ ɤɨɥɢɱɟɫɬɜɚ ɩɪɢɦɟɧɹɟɦ ɝɪɚɮɨɚɧɚɥɢɬɢɱɟɫɤɢɣ ɦɟɬɨɞ. ɉɪɟɨɛɪɚɡɭɟɦ ɢɫɯɨɞɧɨɟ ɭɪɚɜɧɟɧɢɟ. ɉɟɪɟɧɟɫɟɦ ɜɫɟ ɱɥɟɧɵ ɢɡ ɩɪɚɜɨɣ ɱɚɫɬɢ ɜ ɥɟɜɭɸ ɱɚɫɬɶ ɭɪɚɜɧɟɧɢɹ. ȼ ɩɪɚɜɨɣ ɱɚɫɬɢ ɭɪɚɜɧɟɧɢɹ ɰɟɥɟɫɨɨɛɪɚɡɧɨ ɨɫɬɚɜɢɬɶ ɡɧɚɱɟɧɢɟ ɧɭɥɶ ͹ ‫•‘… כ‬ሺ͵ ‫ݔ כ‬ሻ െ ‫ ݔ‬ଶ ൅ ͵ ൌ Ͳ. Ɍɟɩɟɪɶ ɩɪɟɞɫɬɚɜɥɹɟɦ ɥɟɜɭɸ ɱɚɫɬɶ ɭɪɚɜɧɟɧɢɹ ɤɚɤ ɮɭɧɤɰɢɸ ‫ݕ‬ ‫ ݕ‬ൌ ͹ ‫•‘… כ‬ሺ͵ ‫ݔ כ‬ሻ െ ‫ ݔ‬ଶ ൅ ͵. Ɉɫɭɳɟɫɬɜɥɹɟɦ ɬɚɛɭɥɹɰɢɸ ɮɭɧɤɰɢɢ y ɜ ɡɚɞɚɧɧɨɦ ɞɢɚɩɚɡɨɧɟ ɡɧɚɱɟɧɢɣ x ɫ ɲɚɝɨɦ, ɤɨɬɨɪɵɣ ɨɛɟɫɩɟɱɢɜɚɥ ɞɨɫɬɚɬɨɱɧɨ ɬɨɱɧɨɟ ɝɪɚɮɢɱɟɫɤɨɟ ɢɡɨɛɪɚɠɟɧɢɟ ɮɭɧɤɰɢɢ (Ⱥ2:ȼ22). Ɂɧɚɱɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɨɜ (7,3,-1 ɢ 3) ɩɪɢ ɫɬɚɧɞɚɪɬɧɵɯ ɮɭɧɤɰɢɹɯ ɰɟɥɟɫɨɨɛɪɚɡɧɨ ɨɮɨɪɦɢɬɶ ɜ ɜɢɞɟ ɩɚɪɚɦɟɬɪɨɜ (ɤɨɧɫɬɚɧɬ). ɗɬɨ ɩɨɡɜɨɥɢɬ ɩɪɢ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɩɪɨɜɟɫɬɢ ɞɨɩɨɥɧɢɬɟɥɶɧɵɣ ɚɧɚɥɢɡ ɮɭɧɤɰɢɢ ɩɪɢ ɢɯ ɢɡɦɟɧɟɧɢɢ (ɩɚɪɚɦɟɬɪɨɜ). ɉɨɫɥɟ ɬɚɛɭɥɹɰɢɢ ɢ ɩɨɫɬɪɨɟɧɢɹ ɝɪɚɮɢɤɚ ɮɭɧɤɰɢɢ ɨɩɪɟɞɟɥɹɟɦ ɢɧɬɟɪɜɚɥɵ ɡɧɚɱɟɧɢɣ‫ݔ‬, ɝɞɟ ɝɪɚɮɢɤ ɮɭɧɤɰɢɢ ɩɟɪɟɫɟɤɚɟɬɫɹ ɫ ɨɫɶɸ ɨɪɞɢɧɚɬ. ɉɪɢ ɩɨɫɬɪɨɟɧɢɢ ɝɪɚɮɢɤɚ ɮɭɧɤɰɢɢ ɜɵɛɢɪɚɟɦ ɞɢɚɝɪɚɦɦɭ Ɍɨɱɟɱɧɚɹ ɫ ɝɥɚɞɤɢɦɢ ɤɪɢɜɵɦɢ ɢ ɦɚɪɤɟɪɚɦɢ. Ⱦɥɹ ɧɚɝɥɹɞɧɨɫɬɢ ɩɪɨɜɨɞɢɦ ɭɫɥɨɜɧɨɟ ɮɨɪɦɚɬɢɪɨɜɚɧɢɟ ɡɧɚɱɟɧɢɣ ɮɭɧɤɰɢɢ y, ɤɨɬɨɪɵɟ ɧɚɯɨɞɹɬɫɹ ɪɹɞɨɦ ɫ ɬɨɱɤɚɦɢ ɩɟɪɟɫɟɱɟɧɢɹ ɫ ɨɫɶɸ ɨɪɞɢɧɚɬ. ȼɵɞɟɥɹɟɦ ɫɬɨɥɛɟɰ ɹɱɟɟɤ ɡɧɚ55

2. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ MS Excel

ɱɟɧɢɣ ɮɭɧɤɰɢɢ. ɇɚ ɥɢɧɟɣɤɟ Ƚɥɚɜɧɚɹ, ɜ ɪɚɡɞɟɥɟ ɋɬɢɥɢ ɳɟɥɤɚɟɦ ɧɚ ɫɩɢɫɤɟ ɍɫɥɨɜɧɨɟ ɮɨɪɦɚɬɢɪɨɜɚɧɢɟ ɢ ɜɵɛɢɪɚɟɦ ɩɭɧɤɬ Ɇɟɠɞɭ ɜ ɉɪɚɜɢɥɚɯ ɜɵɞɟɥɟɧɢɹ ɹɱɟɟɤ. ȼ ɨɤɧɟ Ɇɟɠɞɭ ɡɚɧɨɫɢɦ ɡɧɚɱɟɧɢɹ -3 ɢ 1,5, ɤɨɬɨɪɵɟ ɜɵɛɢɪɚɟɦ ɢɫɯɨɞɹ ɢɡ ɡɧɚɱɟɧɢɣ ɬɚɛɭɥɢɪɨɜɚɧɧɨɣ ɮɭɧɤɰɢɢ ɜ ɪɚɣɨɧɟ ɩɟɪɟɫɟɱɟɧɢɹ ɫ ɨɫɶɸ x. ɇɚɛɥɸɞɚɟɦ ɩɪɢ ɷɬɨɦ, ɤɚɤɢɟ ɹɱɟɣɤɢ ɡɧɚɱɟɧɢɣ ɮɭɧɤɰɢɢ y ɮɨɪɦɚɬɢɪɭɸɬɫɹ. ɉɪɢ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɢɡɦɟɧɹɟɦ ɡɧɚɱɟɧɢɹ ɝɪɚɧɢɰ ɞɢɚɩɚɡɨɧɚ ɭɫɥɨɜɧɨɝɨ ɮɨɪɦɚɬɢɪɨɜɚɧɢɹ ɞɥɹ ɛɨɥɟɟ ɱɟɬɤɨɝɨ ɜɵɞɟɥɟɧɢɹ ɧɚ ɝɪɚɮɢɤɟ ɨɛɥɚɫɬɟɣ ɩɟɪɟɫɟɱɟɧɢɹ ɮɭɧɤɰɢɢ y ɫ ɨɫɶɸ‫ݔ‬. ȼ ɨɛɥɚɫɬɹɯ ɩɟɪɟɫɟɱɟɧɢɹ ɫ ɨɫɶɸ ɨɪɞɢɧɚɬ ɦɨɠɧɨ ɢɡɦɟɧɢɬɶ ɰɜɟɬ ɨɬɪɟɡɤɨɜ ɮɭɧɤɰɢɢ y ɩɪɢ ɮɨɪɦɚɬɢɪɨɜɚɧɢɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɦɚɪɤɟɪɨɜ ɬɨɱɟɤ, ɩɪɢɧɚɞɥɟɠɚɳɢɯ ɞɢɚɩɚɡɨɧɚɦ ɭɫɥɨɜɧɨɝɨ ɮɨɪɦɚɬɢɪɨɜɚɧɢɹ. ɇɚɜɨɞɢɦ ɤɭɪɫɨɪ ɧɚ ɧɭɠɧɭɸ ɬɨɱɤɭ ɨɬɪɟɡɤɚ ɮɭɧɤɰɢɢ, ɞɜɚɠɞɵ ɳɟɥɤɚɟɦ ɧɚ ɧɟɣ ɢ ɱɟɪɟɡ ɤɨɧɬɟɤɫɬɧɨɟ ɦɟɧɸ ɜɵɯɨɞɢɦ ɧɚ ɩɭɧɤɬ Ɏɨɪɦɚɬ ɬɨɱɤɢ ɞɚɧɧɵɯ. Ⱦɚɥɟɟ ɭɫɬɚɧɚɜɥɢɜɚɟɦ ɧɟɨɛɯɨɞɢɦɵɟ ɩɚɪɚɦɟɬɪɵ ɪɹɞɚ. ɐɟɥɟɫɨɨɛɪɚɡɧɨ ɬɚɤɠɟ ɩɪɨɜɟɫɬɢ ɮɨɪɦɚɬɢɪɨɜɚɧɢɟ ɨɫɟɣ ɝɪɚɮɢɤɚ ɞɥɹ ɢɯ ɛɨɥɟɟ ɱɟɬɤɨɝɨ ɜɵɞɟɥɟɧɢɹ. ɉɨɫɥɟ ɮɨɪɦɚɬɢɪɨɜɚɧɢɹ ɷɥɟɦɟɧɬɨɜ ɝɪɚɮɢɤɚ ɬɚɛɭɥɢɪɨɜɚɧɧɨɣ ɮɭɧɤɰɢɢ, ɩɪɟɞɜɚɪɢɬɟɥɶɧɨɣ ɨɰɟɧɤɢ ɤɨɥɢɱɟɫɬɜɚ ɤɨɪɧɟɣ ɢ ɢɯ ɩɪɢɛɥɢɠɟɧɧɵɯ ɡɧɚɱɟɧɢɣ ɩɪɢɦɟɧɹɟɦ ɩɪɨɰɟɞɭɪɭ ɉɨɞɛɨɪ ɩɚɪɚɦɟɬɪɚ ɞɥɹ ɬɨɱɧɨɝɨ ɧɚɯɨɠɞɟɧɢɹ ɡɧɚɱɟɧɢɣ ɤɨɪɧɟɣ ɭɪɚɜɧɟɧɢɹ. Ʉɨɪɧɢ ɭɪɚɜɧɟɧɢɹ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɬɨɱɤɚɦ ɩɟɪɟɫɟɱɟɧɢɹ ɝɪɚɮɢɤɚ ɮɭɧɤɰɢɢ y ɫ ɨɫɶɸ x. ȼ ɤɚɱɟɫɬɜɟ ɩɪɟɞɜɚɪɢɬɟɥɶɧɵɯ ɡɧɚɱɟɧɢɣ ɤɨɪɧɟɣ ɰɟɥɟɫɨɨɛɪɚɡɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɡɧɚɱɟɧɢɹ x ɜ ɜɵɞɟɥɟɧɧɵɯ ɢɧɬɟɪɜɚɥɚɯ. ȼ ɤɚɱɟɫɬɜɟ ɡɧɚɱɟɧɢɹ ɩɟɪɜɨɝɨ ɤɨɪɧɹ ɜɵɛɟɪɟɦ ɹɱɟɣɤɭ Ⱥ4. ȼ ɹɱɟɣɤɟ ȼ4 ɡɧɚɱɟɧɢɟ ɮɭɧɤɰɢɢ y ɞɨɫɬɚɬɨɱɧɨ ɛɥɢɡɤɨ ɤ ɧɭɥɸ. Ⱦɚɥɟɟ ɚɤɬɢɜɢɡɢɪɭɟɦ ɹɱɟɣɤɭ ɮɭɧɤɰɢɢ ȼ4 ɢ ɨɛɪɚɳɚɟɦɫɹ ɤ ɩɪɨɰɟɞɭɪɟ ɉɨɞɛɨɪ ɩɚɪɚɦɟɬɪɚ, ɤɨɬɨɪɨɟ ɧɚɯɨɞɢɬɫɹ ɧɚ ɜɤɥɚɞɤɟ Ⱦɚɧɧɵɟ ɜ ɪɚɡɞɟɥɟ Ɋɚɛɨɬɚ ɫ ɞɚɧɧɵɦɢ ɜ ɫɩɢɫɤɟ Ⱥɧɚɥɢɡ “ɱɬɨ-ɟɫɥɢ“. ȼ ɨɤɧɟ ɉɨɞɛɨɪ ɩɚɪɚɦɟɬɪɚ ɭɫɬɚɧɚɜɥɢɜɚɟɦ ɚɞɪɟɫ ȼ4, ɡɧɚɱɟɧɢɟ ɧɭɥɶ ɢ ɚɞɪɟɫ ɢɡɦɟɧɹɟɦɨɣ ɹɱɟɣɤɢ Ⱥ4. ɓɟɥɤɚɟɦ ɧɚ ɤɧɨɩɤɟ ɈɄ ɢ ɫɨɯɪɚɧɹɟɦ ɪɟɡɭɥɶɬɚɬ. ɉɟɪɜɵɣ ɤɨɪɟɧɶ ɪɚɜɧɹɟɬɫɹ 1,54098, ɚ ɡɧɚɱɟɧɢɟ ɮɭɧɤɰɢɢ ɪɚɜɧɨ -4ȿ-06, ɤɨɬɨɪɨɟ ɨɱɟɧɶ ɛɥɢɡɤɨ ɤ ɧɭɥɸ. ɑɬɨɛɵ ɡɧɚɱɟɧɢɟ ɮɭɧɤɰɢɢ ɜ ɬɚɛɥɢɰɟ ɪɚɜɧɹɥɨɫɶ ɧɭɥɸ ɰɟɥɟɫɨɨɛɪɚɡɧɨ ɩɪɨɢɡɜɟɫɬɢ ɮɨɪɦɚɬɢɪɨɜɚɧɢɟ ɹɱɟɟɤ ɮɭɧɤɰɢɢ ɢ ɭɫɬɚɧɨɜɢɬɶ ɱɢɫɥɨɜɨɣ ɮɨɪɦɚɬ 2 ɢɥɢ 3 ɡɧɚɤɚ ɩɨɫɥɟ ɡɚɩɹɬɨɣ. Ɂɚɬɟɦ ɩɪɨɜɨɞɢɦ ɚɧɚɥɨɝɢɱɧɨɟ ɩɪɢɦɟɧɟɧɢɟ ɩɪɨɰɟɞɭɪɵ ɉɨɞɛɨɪ ɩɚɪɚɦɟɬɪɚ ɞɥɹ ɜɵɱɢɫɥɟɧɢɹ ɞɪɭɝɢɯ ɤɨɪɧɟɣ. ɇɟ ɡɚɛɵɜɚɹ ɤɨɪɪɟɤɬɢɪɨɜɚɬɶ ɚɞɪɟɫɚ ɹɱɟɟɤ ɜ ɨɤɧɚɯ. ɉɨ ɦɟɪɟ ɧɚɯɨɠɞɟɧɢɹ ɬɨɱɧɵɯ ɡɧɚɱɟɧɢɣ ɤɨɪɧɟɣ ɧɚ ɝɪɚɮɢɤɟ ɧɚɛɥɸɞɚɟɦ 56

2.1. Ɇɚɬɟɦɚɬɢɤɚ

ɫɦɟɳɟɧɢɹ ɦɚɪɤɟɪɨɜ ɬɨɱɟɤ ɤɨɪɧɟɣ ɮɭɧɤɰɢɢ ‫ ݕ‬ɧɚ ɨɫɶ ɨɪɞɢɧɚɬ ‫ݔ‬. Ⱦɨɩɨɥɧɢɬɟɥɶɧɨ ɦɨɠɧɨ ɩɪɨɜɟɫɬɢ ɩɪɨɜɟɪɤɭ ɤɨɪɧɟɣ ɩɭɬɟɦ ɩɨɞɫɬɚɧɨɜɤɢ ɢɯ ɡɧɚɱɟɧɢɣ ɜ ɢɫɯɨɞɧɨɟ ɜɵɪɚɠɟɧɢɟ ɭɪɚɜɧɟɧɢɹ. ɉɪɟɞɥɨɠɟɧɧɚɹ ɦɟɬɨɞɢɤɚ ɞɨɥɠɧɚ ɨɛɟɫɩɟɱɢɬɶ ɥɭɱɲɟɟ ɩɨɧɢɦɚɧɢɟ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɩɪɨɰɟɞɭɪɵ ɉɨɞɛɨɪ ɩɚɪɚɦɟɬɪɚ ɢ ɧɚɯɨɠɞɟɧɢɟ ɜɫɟɯ ɤɨɪɧɟɣ ɭɪɚɜɧɟɧɢɣ ɜ ɡɚɞɚɧɧɨɦ ɞɢɚɩɚɡɨɧɟ ɡɧɚɱɟɧɢɣ x. ɉɪɢ ɢɡɦɟɧɟɧɢɢ ɡɧɚɱɟɧɢɣ ɩɚɪɚɦɟɬɪɨɜ (ɤɨɧɫɬɚɧɬ) ɮɭɧɤɰɢɢ ɦɨɠɧɨ ɨɫɭɳɟɫɬɜɥɹɬɶ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɢɡɦɟɧɟɧɢɹ ɤɨɪɧɟɣ ɭɪɚɜɧɟɧɢɹ. 2.1.3. Ɉɩɪɟɞɟɥɟɧɢɟ ɩɪɟɞɟɥɨɜ ɋɨɡɞɚɞɢɦ ɝɪɚɮɢɱɟɫɤɢɟ ɦɨɞɟɥɢ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɡɚɦɟɱɚɬɟɥɶɧɵɯ ɩɪɟɞɟɥɨɜ. Ƚɪɚɮɢɱɟɫɤɚɹ ɦɨɞɟɥɶ ɛɭɞɟɬ ɨɫɧɨɜɵɜɚɬɶɫɹ ɧɚ ɬɚɛɥɢɰɚɯ ɬɚɛɭɥɢɪɨɜɚɧɧɵɯ ɮɭɧɤɰɢɣ, ɝɞɟ ɚɪɝɭɦɟɧɬɵ ɛɭɞɭɬ ɮɨɪɦɢɪɨɜɚɬɶɫɹ ɫ ɭɱɟɬɨɦ ɨɫɨɛɟɧɧɨɫɬɟɣ ɡɚɦɟɱɚɬɟɥɶɧɵɯ ɩɪɟɞɟɥɨɜ. ɋɨɡɞɚɞɢɦ ɫɧɚɱɚɥɚ ɦɨɞɟɥɶ ɞɥɹ ɡɚɦɟɱɚɬɟɥɶɧɨɝɨ ɩɪɟɞɟɥɚ Ž‹ •‹ ‫ ݔ‬Τ‫ ݔ‬ൌ ͳǤ ௫՜଴

Ⱦɟɥɟɧɢɟ ɧɚ ɧɨɥɶ ɨɫɭɳɟɫɬɜɥɹɬɶ ɧɟɥɶɡɹ. ɉɨɷɬɨɦɭ ɫɨɡɞɚɞɢɦ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɚɪɝɭɦɟɧɬɨɜ ɫ 0,1 ɞɨ 2. Ⱦɚɥɟɟ ɫɨɡɞɚɞɢɦ ɫɬɨɥɛɟɰ ɞɥɹ ɜɵɱɢɫɥɟɧɢɹ ‫ ݕ‬ൌ •‹ ‫ݔ‬Τ‫ ݔ‬. ȼɵɞɟɥɢɦ ɹɱɟɣɤɢ ɬɚɛɭɥɢɪɨɜɚɧɧɨɣ ɮɭɧɤɰɢɢ (Ⱥ3:ȼ22) ɢ ɨɛɪɚɬɢɦɫɹ ɤ ɞɢɚɝɪɚɦɦɟ Ɍɨɱɟɱɧɚɹ ɫ ɝɥɚɞɤɢɦɢ ɤɪɢɜɵɦɢ ɢ ɦɚɪɤɟɪɚɦɢ. ɓɟɥɤɧɟɦ ɩɨ ɨɫɢ ɚɪɝɭɦɟɧɬɨɜ ɢ ɱɟɪɟɡ ɤɨɧɬɟɤɫɬɧɨɟ ɦɟɧɸ ɜɵɣɞɟɦ ɧɚ ɩɭɧɤɬ Ɏɨɪɦɚɬ ɨɫɢ. Ⱦɚɥɟɟ ɜ ɨɤɧɟ ɜ ɉɚɪɚɦɟɬɪɵ ɨɫɢ ɭɫɬɚɧɨɜɢɦ ɨɛɪɚɬɧɵɣ ɩɨɪɹɞɨɤ ɡɧɚɱɟɧɢɣ. ɇɚ ɝɪɚɮɢɤɟ ɧɚɛɥɸɞɚɟɦ ɫɬɪɟɦɥɟɧɢɟ ɡɧɚɱɟɧɢɣ ɮɭɧɤɰɢɢ ɤ 1. ɂɡɦɟɧɢɦ ɩɟɪɜɨɟ ɡɧɚɱɟɧɢɟ ‫ ݔ‬ɫ 0,1 ɧɚ 0,01 ɢ ɡɧɚɱɟɧɢɟ ɮɭɧɤɰɢɢ ɢɡɦɟɧɢɬɶɫɹ ɫ 0,999983 ɧɚ 1. ɗɬɨ ɟɳɟ ɪɚɡ ɩɨɞɬɜɟɪɠɞɚɟɬ ɫɬɪɟɦɥɟɧɢɟ ɩɪɟɞɟɥɚ ɤ 1. ɋɨɡɞɚɞɢɦ ɦɨɞɟɥɶ ɞɥɹ ɩɪɟɞɟɥɚ ͳ ௡ Ž‹ ൬ͳ ൅ ൰ ൌ ݁Ǥ ௡՜ஶ ݊ Ɂɞɟɫɶ ɢɡɦɟɧɟɧɢɟ ɚɪɝɭɦɟɧɬɚ ɨɛɟɫɩɟɱɢɦ ɫ 1 ɞɨ 107 . Ɋɚɫɱɟɬ ɡɧɚɱɟɧɢɣ ɮɭɧɤɰɢɢ ɩɪɨɢɡɜɨɞɢɦ ଵ ௡

ɩɨ ɮɨɪɦɭɥɟ ‫ ݕ‬ൌ ቀͳ ൅ ቁ Ǥ ௡ Ⱦɚɥɟɟ ɫɬɪɨɢɦ ɝɪɚɮɢɤ ɬɚɛɭɥɢɪɨɜɚɧɧɨɣ ɮɭɧɤɰɢɢ, ɝɞɟ ɡɧɚɱɟɧɢɹ ɨɫɢ ɚɪɝɭɦɟɧɬɨɜ ɮɨɪɦɚɬɢɪɭɟɦ ɤɚɤ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɵɟ ɫ ɱɢɫɥɨɦ ɞɟɫɹɬɢɱɧɵɯ ɡɧɚɤɨɜ 57

2. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ MS Excel

ɪɚɜɧɵɯ ɧɭɥɸ. ɇɚ ɝɪɚɮɢɤɟ ɜɢɞɢɦ, ɱɬɨ ɩɪɟɞɟɥ ɫɬɪɟɦɢɬɶɫɹ ɤ ɡɚɦɟɱɚɬɟɥɶɧɨɦɭ ɱɢɫɥɭ ݁ =2,7182. ɉɪɢɜɟɞɟɦ ɝɪɚɮɢɱɟɫɤɢɟ ɦɨɞɟɥɢ ɞɥɹ ɩɪɟɞɟɥɨɜ ௡ ௫

Ž‹௫՜ஶ ቀͳ ൅ ቁ ൌ ݁ ௡ ɢ ௫ ɢ Ž‹ ሺሺͳ ൅ ‫ݔ‬ሻఈ െ ͳሻΤ‫ ݔ‬ൌ ߙǤ

௫՜଴

ɉɨɫɥɟ ɩɪɨɫɦɨɬɪɚ ɝɪɚɮɢɱɟɫɤɢɯ ɦɨɞɟɥɟɣ ɨɩɪɟɞɟɥɟɧɢɹ ɡɧɚɱɟɧɢɣ ɩɪɟɞɟɥɨɜ ɦɨɠɧɨ ɛɨɥɟɟ ɨɫɦɵɫɥɟɧɧɨ ɩɪɢɫɬɭɩɢɬɶ ɤ ɜɵɱɢɫɥɟɧɢɟɦ ɩɪɟɞɟɥɨɜ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɚɧɚɥɢɬɢɱɟɫɤɢɯ ɦɟɬɨɞɨɜ. 2.1.4. ȼɫɬɪɟɱɚ ɩɭɬɧɢɤɨɜ ɂɡ ɩɭɧɤɬɚ Ⱥ ɢ ȼ ɨɞɧɨɜɪɟɦɟɧɧɨ ɜɵɲɥɢ ɩɭɬɧɢɤɢ. ɋɤɨɪɨɫɬɢ ɞɜɢɠɟɧɢɹ ɭ ɧɢɯ ɪɚɡɧɵɟ. Ɋɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɩɭɧɤɬɚɦɢ (‫ܮ‬஺஻ ) ɡɚɞɚɧɨ ɢ ɪɚɜɧɨ 21ɤɦ. ɑɟɪɟɡ ɫɤɨɥɶɤɨ ɜɪɟɦɟɧɢ ɨɧɢ ɜɫɬɪɟɬɹɬɫɹ? ɉɨɫɬɪɨɢɦ ɝɪɚɮɢɤɢ ɬɪɚɟɤɬɨɪɢɣ ɞɜɢɠɟɧɢɹ ɩɭɬɧɢɤɨɜ ɢɡ ɩɭɧɤɬɨɜ ɨɬɩɪɚɜɥɟɧɢɹ ɞɥɹ ɧɚɯɨɠɞɟɧɢɹ ɜɪɟɦɟɧɢ ɜɫɬɪɟɱɢ. Ɍɪɚɟɤɬɨɪɢɢ ɩɪɟɞɫɬɚɜɢɦ ɜ ɜɢɞɟ ɨɬɪɟɡɤɨɜ ɩɪɹɦɵɯ, ɞɥɢɧɚ ɤɨɬɨɪɵɯ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɫɤɨɪɨɫɬɢ ɞɜɢɠɟɧɢɹ ɢ ɬɟɤɭɳɟɝɨ ɜɪɟɦɟɧɢ ɫɱɟɬɱɢɤɚ. Ɇɨɦɟɧɬ ɜɫɬɪɟɱɢ ɮɢɤɫɢɪɭɟɬɫɹ ɩɪɢ ɫɨɩɪɢɤɨɫɧɨɜɟɧɢɢ ɬɪɚɟɤɬɨɪɢɣ. ɂɡɨɛɪɚɠɟɧɢɟ ɬɪɚɟɤɬɨɪɢɣ ɛɭɞɟɦ ɧɚɱɢɧɚɬɶ ɞɥɹ ɤɚɠɞɨɝɨ ɩɭɬɧɢɤɚ ɢɡ ɫɜɨɟɝɨ ɩɭɧɤɬɚ ɨɬɩɪɚɜɥɟɧɢɹ. Ⱦɥɹ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɞɜɢɠɟɧɢɹ ɩɭɬɧɢɤɨɜ ɫɨɡɞɚɟɦ ɬɚɛɥɢɰɭ, ɝɞɟ ɨɫɧɨɜɧɵɦɢ ɩɚɪɚɦɟɬɪɚɦɢ ɛɭɞɭɬ ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɩɭɧɤɬɚɦɢ ɢ ɢɧɬɟɪɜɚɥ ɪɚɫɫɬɨɹɧɢɹ. ȼɟɥɢɱɢɧɚ ɢɧɬɟɪɜɚɥɚ ɨɩɪɟɞɟɥɹɟɬ ɬɨɱɧɨɫɬɶ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɞɜɢɠɟɧɢɹ. ȼɨɡɶɦɟɦ ɢɧɬɟɪɜɚɥ ɪɚɜɧɵɣ 1ɤɦ. ɇɚɱɚɥɨ ɤɨɨɪɞɢɧɚɬ ɭɫɬɚɧɨɜɢɦ ɜ ɩɭɧɤɬɟ Ⱥ. Ɍɨɝɞɚ ɞɥɹ ɨɬɨɛɪɚɠɟɧɢɹ ɩɪɨɣɞɟɧɧɨɝɨ ɩɭɬɢ ɨɬ ɩɭɧɤɬɚ Ⱥ (‫ܮ‬஺ ) ɢɫɩɨɥɶɡɭɟɦ ɜɵɪɚɠɟɧɢɟ ‫ܮ‬஺ ൌ ܸ஺ ‫ܶ כ‬, ɚ ɞɥɹ ɨɬɨɛɪɚɠɟɧɢɹ ɩɪɨɣɞɟɧɧɨɝɨ ɩɭɬɢ ɨɬ ɩɭɧɤɬɚ Ȼ (‫ܮ‬஻ ) – ‫ܮ‬஻ ൌ ‫ܮ‬஺஻ െ ܸ஻ ‫ܶ כ‬. ȼ ɜɵɪɚɠɟɧɢɹɯ ܸ஺ ɢ ܸ஻ ɫɤɨɪɨɫɬɢ ɩɟɪɟɞɜɢɠɟɧɢɹ ɩɭɬɧɢɤɨɜ ɢɡ ɩɭɧɤɬɚ Ⱥ ɢ Ȼ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ, ɚ T – ɬɟɤɭɳɢɟ ɜɪɟɦɹ ɫ ɦɨɦɟɧɬɚ ɧɚɱɚɥɚ ɞɜɢɠɟɧɢɹ ɩɭɬɧɢɤɨɜ. 58

2.1. Ɇɚɬɟɦɚɬɢɤɚ

ɋɨɡɞɚɞɢɦ ɫɬɨɥɛɟɰ ɪɚɫɫɬɨɹɧɢɣ (G3:G24) ɨɬ ɩɭɧɤɬɚ Ⱥ ɞɨ Ȼ ɫ ɢɧɬɟɪɜɚɥɨɦ 1ɤɦ. Ⱦɥɹ ɢɡɨɛɪɚɠɟɧɢɹ ɧɚ ɞɢɚɝɪɚɦɦɟ ɬɪɚɟɤɬɨɪɢɢ ɩɪɨɣɞɟɧɧɨɝɨ ɩɭɬɢ ɤɚɠɞɵɦ ɩɭɬɧɢɤɨɦ ɧɚ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɢɧɬɟɪɜɚɥɚɯ ɞɚɥɶɧɨɫɬɢ ɡɚɞɚɟɦ ɨɩɪɟɞɟɥɟɧɧɵɟ ɡɧɚɱɟɧɢɹ ɨɪɞɢɧɚɬ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɢɫɤɥɸɱɢɦ ɫɥɢɹɧɢɟ ɬɪɚɟɤɬɨɪɢɣ ɞɜɢɠɟɧɢɹ. Ⱦɥɹ ɩɭɬɧɢɤɚ, ɜɵɲɟɞɲɟɝɨ ɢɡ ɩɭɧɤɬɚ Ⱥ ɭɫɬɚɧɨɜɢɦ 0,8 ɭɫɥɨɜɧɵɯ ɟɞɢɧɢɰ, ɚ ɞɥɹ ɞɪɭɝɨɝɨ ɩɭɬɧɢɤɚ – 1. ɗɬɢɦ ɢɫɤɥɸɱɚɟɬɫɹ ɧɟɨɞɧɨɡɧɚɱɧɨɫɬɶ ɜ ɨɩɪɟɞɟɥɟɧɢɢ ɦɨɦɟɧɬɚ ɜɫɬɪɟɱɢ, ɤɨɬɨɪɚɹ ɦɨɠɟɬ ɛɵɬɶ ɩɪɢ ɩɟɪɟɫɟɱɟɧɢɢ ɬɪɚɟɤɬɨɪɢɣ ɩɪɢ ɨɞɢɧɚɤɨɜɵɯ ɡɧɚɱɟɧɢɹɯ ɨɪɞɢɧɚɬ. Ɉɬɨɛɪɚɠɚɬɶ ɬɪɚɟɤɬɨɪɢɢ ɩɪɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ ɧɟɨɛɯɨɞɢɦɨ ɜ ɥɸɛɨɟ ɡɚɞɚɧɧɨɟ ɜɪɟɦɹ. Ⱦɥɹ ɷɬɨɝɨ ɜ ɫɬɨɥɛɰɚɯ ‫ܮ‬஺ ɢ ‫ܮ‬஻ (H3:I24) ɩɪɨɜɟɪɹɟɬɫɹ ɭɫɥɨɜɢɟ ɩɪɨɯɨɠɞɟɧɢɹ ɤɚɠɞɨɝɨ ɭɱɚɫɬɤɚ ɩɭɬɢ ɧɚ ɬɟɤɭɳɟɟ ɜɪɟɦɹ (ɫɦ. ɩɪɢɦɟɱɚɧɢɟ) ɢ ɩɪɢ ɜɵɩɨɥɧɟɧɢɢ ɭɫɥɨɜɢɹ ɮɨɪɦɢɪɭɟɬɫɹ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɡɧɚɱɟɧɢɟ ɨɪɞɢɧɚɬɵ ɢɥɢ ɜ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ ɜ ɹɱɟɣɤɭ ɡɚɩɢɫɵɜɚɟɬɫɹ ɮɭɧɤɰɢɹ ɇȾ() ɞɥɹ ɢɫɤɥɸɱɟɧɢɹ ɜɨɡɦɨɠɧɨɫɬɢ ɢɧɞɢɤɚɰɢɢ ɭɱɚɫɬɤɨɜ ɬɪɚɟɤɬɨɪɢɢ ɩɭɬɢ, ɤɨɬɨɪɵɟ ɟɳɟ ɧɟ ɩɪɨɲɥɢ. Ⱦɥɹ ɮɨɪɦɢɪɨɜɚɧɢɹ ɦɚɪɤɟɪɨɜ, ɤɨɬɨɪɵɟ ɨɬɨɛɪɚɠɚɥɢ ɛɵ ɦɟɫɬɨ ɧɚɯɨɠɞɟɧɢɹ ɩɭɬɧɢɤɨɜ ɧɚ ɢɯ ɬɪɚɟɤɬɨɪɢɹɯ ɞɜɢɠɟɧɢɹ, ɜ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɹɱɟɣɤɚɯ ɩɟɪɜɨɝɨ ɫɬɨɥɛɰɚ ‫ܮ‬஺஻ ɬɚɛɥɢɰɵ ɪɚɫɫɱɢɬɵɜɚɟɦ ɬɟɤɭɳɢɟ ɩɨɥɨɠɟɧɢɹ ɩɭɬɧɢɤɨɜ ɩɨ ɜɵɲɟɩɪɢɜɟɞɟɧɧɵɦ ɜɵɪɚɠɟɧɢɹɦ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɡɧɚɱɟɧɢɹ ɫɱɟɬɱɢɤɚ ɜɪɟɦɟɧɢ. əɱɟɣɤɢ (ɉɭɬɶ, ɩɪɨɣɞɟɧɧɵɣ ɢɡ Ⱥ ɢ ɉɭɬɶ, ɨɫɬɚɜɲɢɣɫɹ ɞɨ Ⱥ) ɨɬɞɟɥɹɸɬɫɹ ɨɬ ɫɬɪɨɤ ɬɚɛɥɢɰɵ ɞɥɹ ɭɞɨɛɫɬɜɚ ɡɚɞɚɧɢɹ ɧɭɠɧɵɯ ɩɚɪɚɦɟɬɪɨɜ ɮɨɪɦɚɬɢɪɨɜɚɧɢɹ. Ɂɧɚɱɟɧɢɹ ɨɪɞɢɧɚɬ ɞɥɹ ɦɚɪɤɟɪɨɜ ɤɚɠɞɨɝɨ ɩɭɬɧɢɤɚ ɡɚɞɚɟɦ ɡɚɪɚɧɟɟ, ɤɨɬɨɪɵɟ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɡɧɚɱɟɧɢɹɦ 0,8 ɢ 1. Ʉɨɧɟɱɧɨ, ɨɛɹɡɚɬɟɥɶɧɨ ɫɨɡɞɚɟɦ ɫɱɟɬɱɢɤ ɬɟɤɭɳɟɝɨ ɜɪɟɦɟɧɢ (ɋɱɟɬɱɢɤ Ɍ) ɢ ɹɱɟɣɤɢ ɞɥɹ ɡɚɞɚɧɢɹ ɫɤɨɪɨɫɬɟɣ ɞɜɢɠɟɧɢɹ ɩɭɬɧɢɤɨɜ (ܸ஺ ɢ ܸ஻ ), ɜ ɤɨɬɨɪɵɟ ɡɚɩɢɫɵɜɚɟɦ ɫɤɨɪɨɫɬɢ ɞɜɢɠɟɧɢɹ ɩɭɬɧɢɤɨɜ. Ɍɟɩɟɪɶ ɜɵɞɟɥɢɜ ɜɫɟ ɫɬɨɥɛɰɵ ɬɚɛɥɢɰɵ (G3:I28), ɨɛɪɚɳɚɟɦɫɹ ɤ Ɇɚɫɬɟɪɭ ɞɢɚɝɪɚɦɦ. Ⱦɚɥɟɟ ɜɵɛɢɪɚɟɦ ɜ ɞɢɚɥɨɝɨɜɨɦ ɨɤɧɟ ɬɢɩ Ɍɨɱɟɱɧɚɹ, ɚ ɜɢɞ – Ɍɨɱɟɱɧɚɹ ɞɢɚɝɪɚɦɦɚ, ɧɚ ɤɨɬɨɪɨɣ ɡɧɚɱɟɧɢɹ ɫɨɟɞɢɧɟɧɵ ɨɬɪɟɡɤɚɦɢ. ɉɪɨɢɡɜɨɞɢɦ ɧɟɨɛɯɨɞɢɦɨɟ ɬɟɤɫɬɨɜɨɟ ɨɮɨɪɦɥɟɧɢɟ ɞɢɚɝɪɚɦɦɵ. Ⱦɥɹ ɮɨɪɦɢɪɨɜɚɧɢɹ ɦɚɪɤɟɪɨɜ ɩɭɬɧɢɤɨɜ ɧɚɜɨɞɢɦ ɭɤɚɡɚɬɟɥɶ ɦɵɲɢ ɧɚ ɧɭɠɧɭɸ ɬɨɱɤɭ ɝɪɚɮɢɤɚ, ɳɟɥɤɚɟɦ ɧɚ ɧɟɣ ɢ ɩɨɫɥɟ ɩɨɹɜɥɟɧɢɹ ɤɪɟɫɬɨɨɛɪɚɡɧɨɝɨ ɭɤɚɡɚɬɟɥɹ ɫɨ ɫɬɪɟɥɤɚɦɢ ɜɵɡɵɜɚɟɦ ɤɨɧɬɟɤɫɬɧɨɟ ɦɟɧɸ ɬɨɱɤɢ. ɉɟɪɟɯɨɞɢɦ ɧɚ ɩɭɧɤɬ Ɏɨɪɦɚɬ ɬɨɱɤɢ ɞɚɧɧɵɯ ɢ ɜ ɞɢɚɥɨ59

2. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ MS Excel

ɝɨɜɨɦ ɨɤɧɟ ɭɫɬɚɧɚɜɥɢɜɚɟɦ ɧɭɠɧɵɟ ɩɚɪɚɦɟɬɪɵ ɦɚɪɤɟɪɚ. Ⱥɧɚɥɨɝɢɱɧɵɦ ɨɛɪɚɡɨɦ ɦɨɠɧɨ ɡɚɞɚɬɶ ɩɚɪɚɦɟɬɪɵ ɥɢɧɢɢ ɬɪɚɟɤɬɨɪɢɢ ɞɜɢɠɟɧɢɹ. Ɍɨɥɶɤɨ ɩɨɫɥɟ ɧɚɜɟɞɟɧɢɹ ɭɤɚɡɚɬɟɥɹ ɦɵɲɢ ɧɚ ɧɭɠɧɭɸ ɬɪɚɟɤɬɨɪɢɸ ɜɵɯɨɞɢɦ ɧɚ ɤɨɧɬɟɤɫɬɧɨɟ ɦɟɧɸ ɪɹɞɚ ɢ ɩɭɧɤɬ Ɏɨɪɦɚɬ ɪɹɞɨɜ ɞɚɧɧɵɯ. Ɉɫɬɚɟɬɫɹ ɬɨɥɶɤɨ ɜ ɹɱɟɣɤɭ ɋɱɟɬɱɢɤɚ Ɍ ɡɚɞɚɜɚɬɶ ɜɪɟɦɹ ɞɥɹ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɞɜɢɠɟɧɢɹ ɩɭɬɧɢɤɨɜ ɢ ɡɚɮɢɤɫɢɪɨɜɚɬɶ ɦɨɦɟɧɬ ɜɫɬɪɟɱɢ. ɉɨ ɦɟɪɟ ɩɪɢɛɥɢɠɟɧɢɹ ɩɭɬɧɢɤɨɜ ɤ ɬɨɱɤɟ ɜɫɬɪɟɱɢ ɡɧɚɱɟɧɢɟ ɜɪɟɦɟɧɢ ɧɭɠɧɨ ɡɚɧɨɫɢɬɶ ɫ ɞɪɨɛɧɨɣ ɱɚɫɬɶɸ. Ⱦɥɹ ɩɨɜɵɲɟɧɢɹ ɬɨɱɧɨɫɬɢ ɨɩɪɟɞɟɥɟɧɢɹ ɦɨɦɟɧɬɚ ɜɫɬɪɟɱɢ ɧɭɠɧɨ ɭɦɟɧɶɲɢɬɶ ɜɟɥɢɱɢɧɭ ɢɧɬɟɪɜɚɥɚ ɞɚɥɶɧɨɫɬɢ. 2.1.5. ɉɟɪɟɩɪɚɜɚ ɱɟɪɟɡ ɪɟɱɤɭ ɑɟɪɟɡ ɪɟɱɤɭ ɧɟɨɛɯɨɞɢɦɨ ɩɟɪɟɩɪɚɜɢɬɶɫɹ ɧɚ ɥɨɞɤɟ. Ɂɚɞɚɧɚ ɫɤɨɪɨɫɬɶ ɬɟɱɟɧɢɹ ɪɟɤɢ (ܸ˕ˈ˚ ) ɢ ɫɨɛɫɬɜɟɧɧɚɹ ɫɤɨɪɨɫɬɶ ɥɨɞɤɢ (ܸˎ ), ɜɟɤɬɨɪ ɤɨɬɨɪɨɣ ɩɟɪɩɟɧɞɢɤɭɥɹɪɟɧ ɛɟɪɟɝɭ. Ɉɩɪɟɞɟɥɢɬɶ ɬɨɱɤɭ ɩɪɢɱɚɥɢɜɚɧɢɹ ɢ ɜɪɟɦɹ ɩɟɪɟɩɪɚɜɵ ɩɪɢ ɡɚɞɚɧɧɨɣ ɲɢɪɢɧɟ ɪɟɤɢ. ɋ ɭɱɟɬɨɦ ɧɚɩɪɚɜɥɟɧɧɨɫɬɢ ɜɟɤɬɨɪɨɜ ɫɤɨɪɨɫɬɟɣ ɦɨɠɧɨ ɜɵɱɢɫɥɢɬɶ ɤɨɨɪɞɢɧɚɬɵ ɥɨɞɤɢ ɩɨ ɮɨɪɦɭɥɚɦ ܺ ൌ ܸ˕ˈ˚ ‫כ‬ ܶ ɢ ܻ ൌ ܸˎ ‫ܶ כ‬, ɝɞɟ T - ɜɪɟɦɹ ɫ ɦɨɦɟɧɬɚ ɧɚɱɚɥɚ ɩɟɪɟɩɪɚɜɵ. Ʉɨɨɪɞɢɧɚɬɚ ܺ ɧɚɩɪɚɜɥɟɧɚ ɜɞɨɥɶ ɛɟɪɟɝɚ ɩɨ ɜɟɤɬɨɪɭ ɬɟɱɟɧɢɹ, ɤɨɨɪɞɢɧɚɬɚ ܻ – ɩɨ ɧɚɩɪɚɜɥɟɧɢɸ ɜɟɤɬɨɪɚ ɫɨɛɫɬɜɟɧɧɨɣ ɫɤɨɪɨɫɬɢ ɥɨɞɤɢ. ȼɟɤɬɨɪ ɫɨɛɫɬɜɟɧɧɨɣ ɫɤɨɪɨɫɬɢ ɥɨɞɤɢ ɩɟɪɩɟɧɞɢɤɭɥɹɪɟɧ ɥɢɧɢɢ ɛɟɪɟɝɚ. ɋɨɡɞɚɟɦ ɹɱɟɣɤɢ ɞɥɹ ɡɚɞɚɧɧɵɯ ɫɤɨɪɨɫɬɟɣ ɢ ɫɱɟɬɱɢɤɚ ɬɟɤɭɳɟɝɨ ɜɪɟɦɟɧɢ. Ⱦɚɥɟɟ ɮɨɪɦɢɪɭɟɦ ɬɚɛɥɢɰɭ ɞɥɹ ɪɚɫɱɟɬɚ ɤɨɨɪɞɢɧɚɬ ɥɨɞɤɢ. ȼ ɩɟɪɜɵɣ ɫɬɨɥɛɟɰ ɡɚɧɨɫɢɦ ɡɧɚɱɟɧɢɹ ɜɪɟɦɟɧɢ T (F3:F24) ɫ ɡɚɞɚɧɧɵɦ ɢɧɬɟɪɜɚɥɨɦ. Ɇɚɤɫɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɜɪɟɦɟɧɢ ɡɚɜɢɫɢɬ ɨɬ ɜɨɡɦɨɠɧɨɝɨ ɜɪɟɦɟɧɢ ɩɟɪɟɩɪɚɜɵ ɩɪɢ ɪɚɡɥɢɱɧɵɯ ɧɚɱɚɥɶɧɵɯ ɭɫɥɨɜɢɹɯ ɡɚɞɚɱɢ. Ʉɚɤ ɢ ɜ ɩɪɟɞɵɞɭɳɟɣ ɡɚɞɚɱɟ, ɪɚɫɱɟɬɧɵɟ ɤɨɨɪɞɢɧɚɬɵ ɬɪɚɟɤɬɨɪɢɢ ɥɨɞɤɢ ɡɚɩɢɫɵɜɚɸɬɫɹ ɜ ɹɱɟɣɤɢ ɩɨɫɥɟ ɩɪɨɜɟɪɤɢ ɭɫɥɨɜɢɹ. Ɂɞɟɫɶ ɩɪɨɜɟɪɹɟɬɫɹ ɧɟ ɩɪɟɜɵɲɟɧɢɟ ɜɪɟɦɟɧɢ, ɤɨɬɨɪɨɟ ɡɚɮɢɤɫɢɪɨɜɚɧɨ ɜ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɹɱɟɣɤɟ ɬɚɛɥɢɰɵ, ɬɟɤɭɳɟɝɨ ɜɪɟɦɟɧɢ ɫɱɟɬɱɢɤɚ. ɇɚ ɷɬɨɦ ɦɨɠɧɨ ɨɫɬɚɧɨɜɢɬɶɫɹ ɢ, ɜɵɞɟɥɢɜ ɫɬɨɥɛɰɵ ɫ ɤɨɨɪɞɢɧɚɬɚɦɢ ɏ ɢ Y (G3:H24), ɨɛɪɚɬɢɬɶɫɹ ɤ Ɇɚɫɬɟɪɭ ɞɢɚɝɪɚɦɦ ɞɥɹ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɬɪɚɟɤɬɨɪɢɢ ɥɨɞɤɢ. ɋɚɦɨɟ ɝɥɚɜɧɨɟ ɡɚɮɢɤɫɢɪɨɜɚɬɶ ɦɚɤɫɢɦɚɥɶɧɵɟ ɡɧɚɱɟɧɢɹ ɤɨɨɪɞɢɧɚɬ ɩɨ ɨɫɢ ɏ ɢܻ. Ɇɚɤɫɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɩɨ ɨɫɢ ܻ ɞɨɥɠɧɨ ɪɚɜɧɹɬɶɫɹ ɲɢɪɢɧɟ ɪɟɤɢ. 60

2.1. Ɇɚɬɟɦɚɬɢɤɚ

ɉɪɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ ɩɟɪɟɩɪɚɜɵ ɢɧɬɟɪɟɫɧɨ ɩɨɤɚɡɚɬɶ ɩɨɥɨɠɟɧɢɟ ɥɨɞɤɢ. ɉɪɟɞɫɬɚɜɢɦ ɥɨɞɤɭ ɜ ɜɢɞɟ ɩɪɹɦɨɭɝɨɥɶɧɢɤɚ. ɉɭɫɬɶ ɩɨɥɨɜɢɧɚ ɲɢɪɢɧɵ ɥɨɞɤɢ ɪɚɜɧɹɟɬɫɹ dx , ɩɨɥɨɜɢɧɚ ɞɥɢɧɵ – dy (D29:D30). ȼ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɹɱɟɣɤɚɯ ɨɩɪɟɞɟɥɢɦ ɩɨɥɨɠɟɧɢɟ ɰɟɧɬɪɚ ɥɨɞɤɢ ɧɚ ɬɟɤɭɳɢɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ ɩɨ ɜɵɲɟɩɪɢɜɟɞɟɧɧɵɦ ɮɨɪɦɭɥɚɦ (F26:H26). Ⱦɚɥɟɟ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɞɜɢɝɚɹɫɶ ɜ ɜɵɛɪɚɧɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ, ɜɵɱɢɫɥɹɟɦ ɤɨɨɪɞɢɧɚɬɵ ɤɪɚɣɧɢɯ ɬɨɱɟɤ ɫɬɨɪɨɧ ɩɪɹɦɨɭɝɨɥɶɧɢɤɚ (G29:H33). Ⱦɥɹ ɡɚɦɵɤɚɧɢɹ ɤɨɧɬɭɪɚ ɥɨɞɤɢ ɜ ɩɨɫɥɟɞɧɢɯ ɹɱɟɣɤɚɯ (G33, H33) ɞɨɥɠɧɵ ɛɵɬɶ ɩɨɜɬɨɪɟɧɵ ɤɨɨɪɞɢɧɚɬɵ ɩɟɪɜɨɣ ɜɵɛɪɚɧɧɨɣ ɬɨɱɤɢ (F29, H29). ȿɫɥɢ ɩɪɢ ɨɛɪɚɳɟɧɢɢ ɤ Ɇɚɫɬɟɪɭ ɞɢɚɝɪɚɦɦ ɜ ɢɫɯɨɞɧɵɣ ɞɢɚɩɚɡɨɧ ɹɱɟɟɤ ɛɭɞɭɬ ɜɤɥɸɱɟɧɵ ɹɱɟɣɤɢ ɫ ɤɨɨɪɞɢɧɚɬɚɦɢ ɤɨɧɬɭɪɚ ɥɨɞɤɢ, ɬɨ ɫɨɜɦɟɫɬɧɨ ɫ ɬɪɚɟɤɬɨɪɢɟɣ ɩɭɬɢ ɩɨɥɭɱɢɦ ɤɨɧɬɭɪ ɥɨɞɤɢ. ɉɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɢɡɥɨɠɟɧɧɨɝɨ ɩɪɢɧɰɢɩɚ ɦɨɠɧɨ ɢɡɨɛɪɚɠɚɬɶ ɢ ɞɪɭɝɢɟ ɮɢɝɭɪɵ ɧɚ ɞɢɚɝɪɚɦɦɚɯ. Ɉɛ ɷɬɨɦ ɧɚɩɢɫɚɧɨ ɪɚɧɟɟ. ɂɡɦɟɧɹɹ ɡɧɚɱɟɧɢɹ ɬɟɤɭɳɟɝɨ ɜɪɟɦɟɧɢ ɦɨɠɧɨ ɧɚɝɥɹɞɧɨ ɩɪɨɞɟɦɨɧɫɬɪɢɪɨɜɚɬɶ ɦɨɞɟɥɶ ɩɟɪɟɩɪɚɜɵ ɱɟɪɟɡ ɪɟɤɭ ɧɚ ɥɨɞɤɟ, ɬɪɚɟɤɬɨɪɢɹ ɤɨɬɨɪɨɣ ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɥɨɠɟɧɢɟɦ ɜɟɤɬɨɪɨɜ ɫɤɨɪɨɫɬɟɣ ɬɟɱɟɧɢɹ ɪɟɤɢ ɢ ɫɨɛɫɬɜɟɧɧɨɣ ɫɤɨɪɨɫɬɢ ɥɨɞɤɢ. 2.1.6. Ɍɭɪɢɫɬ Ɍɭɪɢɫɬ ɩɪɨɲɟɥ 3 ɤɦ ɩɨ ɲɨɫɫɟ ɢ 6 ɤɦ – ɩɨ ɩɪɨɫɟɥɨɱɧɨɣ ɞɨɪɨɝɟ ɫɨ ɫɪɟɞɧɟɣ ɫɤɨɪɨɫɬɶɸ 4,5 ɤɦ/ɱ. ɉɨ ɲɨɫɫɟ ɨɧ ɲɟɥ ɫɨ ɫɤɨɪɨɫɬɶɸ ɧɚ 2 ɤɦ/ɱ ɛɨɥɶɲɟ, ɱɟɦ ɩɨ ɩɪɨɫɟɥɤɭ. ɋ ɤɚɤɨɣ ɫɤɨɪɨɫɬɶɸ ɲɟɥ ɬɭɪɢɫɬ ɩɨ ɩɪɨɫɟɥɨɱɧɨɣ ɞɨɪɨɝɟ? ɉɨ ɭɫɥɨɜɢɸ ɡɚɞɚɱɢ ɢɡɜɟɫɬɧɨ, ɫɤɨɥɶɤɨ ɜɫɟɝɨ ɩɪɨɲɟɥ ɬɭɪɢɫɬ ɢ ɟɝɨ ɫɪɟɞɧɹɹ ɫɤɨɪɨɫɬɶ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɦɨɠɟɦ ɩɨɫɬɪɨɢɬɶ ɜɟɤɬɨɪ ɜ ɤɨɨɪɞɢɧɚɬɚɯ «ɜɪɟɦɹɞɚɥɶɧɨɫɬɶ», ɝɞɟ ɧɚɱɚɥɨ ɜɟɤɬɨɪɚ ɩɪɢɜɹɡɵɜɚɟɦ ɤ ɧɚɱɚɥɭ ɤɨɨɪɞɢɧɚɬ. Ʉɨɧɟɰ ɜɟɤɬɨɪɚ ɨɩɪɟɞɟɥɢɬ ɤɨɧɟɱɧɭɸ ɬɨɱɤɭ ɩɭɬɢ ɬɭɪɢɫɬɚ ɜ ɡɚɞɚɧɧɵɯ ɤɨɨɪɞɢɧɚɬɚɯ. Ⱦɚɥɟɟ ɞɥɹ ɩɟɪɜɨɝɨ ɭɱɚɫɬɤɚ ɩɭɬɢ ɫɬɪɨɢɦ ɬɚɤɠɟ ɜɟɤɬɨɪ, ɤɨɬɨɪɵɣ ɧɚɱɢɧɚɟɬɫɹ ɨɬ ɧɚɱɚɥɚ ɤɨɨɪɞɢɧɚɬ. Ⱥɧɚɥɨɝɢɱɧɨ ɫɬɪɨɢɦ ɜɟɤɬɨɪ ɞɥɹ ɜɬɨɪɨɝɨ ɭɱɚɫɬɤɚ, ɧɨ ɧɚɱɚɥɨ ɟɝɨ ɫɨɜɦɟɳɚɟɦ ɫ ɨɤɨɧɱɚɧɢɟɦ ɜɟɤɬɨɪɚ ɩɟɪɜɨɝɨ ɭɱɚɫɬɤɚ. Ɏɚɤɬɢɱɟɫɤɢ ɩɪɨɢɡɜɨɞɢɦ ɫɥɨɠɟɧɢɟ ɞɜɭɯ ɜɟɤɬɨɪɨɜ. ɉɥɨɯɨ, ɱɬɨ ɧɟ ɡɧɚɟɦ ɫɤɨɪɨɫɬɶ ɞɜɢɠɟɧɢɹ ɩɨ ɩɪɨɫɟɥɨɱɧɨɣ ɞɨɪɨɝɟ. ɇɨ ɟɟ ɦɨɠɧɨ ɡɚɞɚɬɶ. ȿɫɥɢ ɷɬɚ ɫɤɨɪɨɫɬɶ ɛɭɞɟɬ ɭɞɨɜɥɟɬɜɨɪɹɬɶ ɭɫɥɨɜɢɹɦ ɡɚɞɚɱɢ, ɬɨ ɤɨɧɟɰ ɜɟɤɬɨɪɚ ɩɨ ɜɬɨɪɨɦɭ ɭɱɚɫɬɤɭ ɩɭɬɢ ɫɨɜɦɟɫɬɢɬɶɫɹ ɫ ɤɨɧɰɨɦ ɜɟɤɬɨɪɚ, ɩɨɫɬɪɨɟɧɧɨɦɭ ɫ ɭɱɟɬɨɦ ɫɪɟɞɧɟɣ ɫɤɨɪɨɫɬɢ ɞɜɢɠɟɧɢɹ. ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɭɫɥɨɜɢɹɦɢ ɡɚɞɚɱɢ ɮɨɪɦɢɪɭɟɦ ɹɱɟɣɤɢ ɩɚɪɚɦɟɬɪɨɜ ɦɨɞɟɥɢ. Ɂɚɩɢɫɵɜɚɟɦ ɡɚɝɨɥɨɜɤɢ ɩɚɪɚɦɟɬɪɨɜ ɢ ɡɚɧɨɫɢɦ ɢɯ ɱɢɫɥɨɜɵɟ ɡɧɚɱɟɧɢɹ (B5, C5, E5). ȿɫɥɢ ɡɧɚɱɟɧɢɟ ɨɬɫɭɬɫɬɜɭɟɬ ɜ ɡɚɞɚɱɟ ɢɥɢ ɡɧɚɱɟɧɢɟ ɧɭɠɧɨ ɧɚɣɬɢ ɜ ɯɨɞɟ ɪɟɲɟɧɢɹ, ɬɨ ɩɪɢ ɨɬɫɭɬɫɬɜɢɢ ɜɡɚɢɦɨɫɜɹɡɢ ɫ ɞɪɭɝɢɦɢ ɩɚɪɚɦɟɬɪɚɦɢ ɡɚɩɢɫɵɜɚɟɦ ɥɸɛɨɟ ɪɚɡɭɦɧɨɟ ɟɟ ɡɧɚɱɟɧɢɟ (F5). ȼ ɧɚɲɟɦ ɫɥɭɱɚɟ ɷɬɨ ɫɤɨɪɨɫɬɶ ɩɨ ɩɪɨɫɟɥɨɱ61

2. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ MS Excel

ɧɨɣ ɞɨɪɨɝɟ (2 ɱɚɫɬɶ ɩɭɬɢ). Ⱦɚɥɟɟ ɮɨɪɦɢɪɭɟɦ ɡɚɜɢɫɢɦɵɟ ɩɚɪɚɦɟɬɪɵ ɩɨ ɭɫɥɨɜɢɹɦ ɡɚɞɚɱɢ (D5). ɋɤɨɪɨɫɬɶ ɞɜɢɠɟɧɢɹ ɧɚ ɩɟɪɜɨɦ ɭɱɚɫɬɤɟ ɩɭɬɢ ɩɨ ɭɫɥɨɜɢɸ ɡɚɞɚɱɢ ɞɨɥɠɧɚ ɛɵɬɶ ɛɨɥɶɲɟ ɧɚ 2 ɤɦ, ɱɟɦ ɧɚ ɜɬɨɪɨɦ ɭɱɚɫɬɤɟ ɩɭɬɢ (ɫɦ. ɩɪɢɦɟɱɚɧɢɟ). ɉɨɫɥɟ ɡɚɩɢɫɢ ɩɚɪɚɦɟɬɪɨɜ ɢ ɨɩɪɟɞɟɥɟɧɢɹ ɢɯ ɡɚɜɢɫɢɦɨɫɬɟɣ ɩɪɢɫɬɭɩɚɟɦ ɤ ɮɨɪɦɢɪɨɜɚɧɢɸ ɤɨɨɪɞɢɧɚɬ ɧɚɱɚɥɚ ɢ ɤɨɧɰɚ ɜɟɤɬɨɪɨɜ ɞɜɢɠɟɧɢɹ ɨɛɴɟɤɬɨɜ ɡɚɞɚɱɢ. Ɂɚɞɚɞɢɦ ɤɨɨɪɞɢɧɚɬɵ ɜɟɤɬɨɪɚ ɜɫɟɝɨ ɩɭɬɢ. ɇɚɱɚɥɨ ɜɟɤɬɨɪɚ ɩɨɦɟɳɚɟɦ ɜ ɧɚɱɚɥɨ ɫɢɫɬɟɦɵ ɤɨɨɪɞɢɧɚɬ (0,0). Ʉɨɨɪɞɢɧɚɬɚ ɤɨɧɰɚ ɜɟɤɬɨɪɚ ɩɨ ɞɚɥɶɧɨɫɬɢ ɪɚɜɧɚ ɫɭɦɦɟ ɞɚɥɶɧɨɫɬɟɣ ɞɜɭɯ ɭɱɚɫɬɤɨɜ ɩɭɬɢ (C10),ɚ ɤɨɨɪɞɢɧɚɬɚ ɩɨ ɜɪɟɦɟɧɢ – ɱɚɫɬɧɨɦɭ ɨɬ ɞɟɥɟɧɢɹ ɨɛɳɟɣ ɞɚɥɶɧɨɫɬɢ ɧɚ ɫɪɟɞɧɸɸ ɫɤɨɪɨɫɬɶ (B10). Ɉɬɫɬɭɩɢɜ ɨɞɧɭ ɫɬɪɨɤɭ, ɡɚɞɚɟɦ ɤɨɨɪɞɢɧɚɬɵ ɜɟɤɬɨɪɚ 1-ɣ ɱɚɫɬɢ ɩɭɬɢ (B12:C13). ɇɚɱɚɥɨ ɜɟɤɬɨɪɚ ɩɨɦɟɳɚɟɦ ɜ ɧɚɱɚɥɨ ɤɨɨɪɞɢɧɚɬ (0,0). Ʉɨɨɪɞɢɧɚɬɚ ɤɨɧɰɚ ɜɟɤɬɨɪɚ ɩɨ ɜɪɟɦɟɧɢ ɪɚɜɧɚ ɱɚɫɬɧɨɦɭ ɨɬ ɞɟɥɟɧɢɹ ɞɥɢɧɵ 1-ɣ ɱɚɫɬɢ ɩɭɬɢ (C5) ɧɚ ɫɤɨɪɨɫɬɶ ɞɜɢɠɟɧɢɹ (D5), ɚ ɩɨ ɞɚɥɶɧɨɫɬɢ – ɞɥɢɧɟ 1-ɣ ɱɚɫɬɢ ɩɭɬɢ (C5). ɇɚɱɚɥɨ ɜɟɤɬɨɪɚ 2-ɣ ɱɚɫɬɢ ɩɭɬɢ ɫɨɜɩɚɞɚɟɬ ɫ ɤɨɧɰɨɦ ɜɟɤɬɨɪɚ 1-ɣ ɱɚɫɬɢ ɩɭɬɢ (B13,C13). Ʉɨɧɟɰ ɜɟɤɬɨɪɚ ɡɚɜɢɫɢɬ ɨɬ ɩɪɨɣɞɟɧɧɨɝɨ ɩɭɬɢ ɢ ɡɚɬɪɚɱɟɧɧɨɝɨ ɜɪɟɦɟɧɢ, ɤɨɬɨɪɨɟ ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɤɨɪɨɫɬɶɸ (F5). Ɍɟɩɟɪɶ ɦɨɠɧɨ ɩɨɫɬɪɨɢɬɶ ɞɢɚɝɪɚɦɦɭ Ɍɨɱɟɱɧɚɹ ɞɢɚɝɪɚɦɦɚ, ɧɚ ɤɨɬɨɪɨɣ ɡɧɚɱɟɧɢɹ ɫɨɟɞɢɧɟɧɵ ɨɬɪɟɡɤɚɦɢ, ɜɵɞɟɥɢɜ ɹɱɟɣɤɢ ɫ ɤɨɨɪɞɢɧɚɬɚɦɢ ɜɟɤɬɨɪɨɜ (ȼ9:ɋ16). ȿɫɥɢ ɩɪɚɜɢɥɶɧɨ ɡɚɞɚɥɢ ɪɚɡɦɟɪɧɨɫɬɢ ɩɚɪɚɦɟɬɪɨɜ, ɨɩɪɟɞɟɥɢɥɢ ɢɯ ɡɚɜɢɫɢɦɨɫɬɢ ɢ ɡɚɞɚɥɢ ɤɨɨɪɞɢɧɚɬɵ ɜɟɤɬɨɪɨɜ, ɬɨ ɩɨɥɭɱɢɦ ɜɟɪɧɭɸ ɬɪɚɤɬɨɜɤɭ ɡɚɞɚɱɢ ɜ ɤɨɨɪɞɢɧɚɬɚɯ «ɜɪɟɦɹ-ɞɚɥɶɧɨɫɬɶ». ɉɪɢ ɷɬɨɦ ɧɚɤɥɨɧ ɜɟɤɬɨɪɨɜ ɞɨɥɠɟɧ ɨɩɪɟɞɟɥɹɬɶɫɹ ɫɤɨɪɨɫɬɶɸ ɞɜɢɠɟɧɢɹ ɬɭɪɢɫɬɚ ɢ ɥɟɝɤɨ ɩɪɨɜɟɪɹɟɬɫɹ ɩɨ ɞɢɚɝɪɚɦɦɟ. ɐɟɥɟɫɨɨɛɪɚɡɧɨ ɡɚɮɢɤɫɢɪɨɜɚɬɶ ɦɚɤɫɢɦɚɥɶɧɵɟ ɢ ɦɢɧɢɦɚɥɶɧɵɟ ɡɧɚɱɟɧɢɹ ɨɫɟɣ ɤɨɨɪɞɢɧɚɬ ɞɢɚɝɪɚɦɦɵ ɱɟɪɟɡ ɩɭɧɤɬ Ɏɨɪɦɚɬ ɨɫɢ ɤɨɧɬɟɤɫɬɧɨɝɨ ɦɟɧɸ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɨɫɢ ɞɥɹ ɢɫɤɥɸɱɟɧɢɹ ɢɡɦɟɧɟɧɢɹ ɪɚɡɦɟɪɨɜ ɞɢɚɝɪɚɦɦɵ ɩɪɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ. Ⱦɥɹ ɧɚɝɥɹɞɧɨɫɬɢ ɜɵɞɟɥɢɦ ɡɚɥɢɜɤɨɣ ɹɱɟɣɤɭ ɧɚɡɜɚɧɢɹ ɩɚɪɚɦɟɬɪɚ, ɤɨɬɨɪɵɣ ɧɭɠɧɨ ɧɚɣɬɢ ɩɨ ɭɫɥɨɜɢɹɦ ɡɚɞɚɱɢ (F4), ɢ ɹɱɟɣɤɭ ɩɚɪɚɦɟɬɪɚ, ɤɨɬɨɪɵɣ ɛɭɞɟɦ ɢɫɩɨɥɶɡɨɜɚɬɶ ɩɪɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ ɪɟɲɟɧɢɹ (F5). ɂɡɦɟɧɹɹ ɡɧɚɱɟɧɢɟ ɫɤɨɪɨɫɬɢ ɧɚ 2-ɦ ɭɱɚɫɬɤɟ ɩɭɬɢ, ɞɨɛɢɜɚɟɦɫɹ ɫɨɜɦɟɳɟɧɢɹ ɤɨɧɰɚ ɜɟɤɬɨɪɚ ɜɫɟɝɨ ɩɭɬɢ ɫ ɤɨɧɰɨɦ ɜɟɤɬɨɪɚ 2-ɝɨ ɭɱɚɫɬɤɚ ɩɭɬɢ. Ʉɨɧɰɵ ɜɟɤɬɨɪɨɜ ɫɨɜɩɚɞɭɬ ɩɪɢ ɫɤɨɪɨɫɬɢ 4 ɤɦ/ɱ. Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɦɨɦɟɧɬɚ ɬɨɱɧɨɝɨ ɫɨɜɩɚɞɟɧɢɹ ɰɟɥɟɫɨɨɛɪɚɡɧɨ ɜɵɜɟɫɬɢ ɡɧɚɱɟɧɢɹ ɤɨɨɪɞɢɧɚɬ ɤɨɧɰɨɜ ɜɟɤɬɨɪɨɜ, ɤɨɬɨɪɵɟ ɜ ɧɚɲɟɦ ɫɥɭɱɚɟ ɞɨɥɠɧɵ ɫɬɚɬɶ 62

2.1. Ɇɚɬɟɦɚɬɢɤɚ

ɪɚɜɧɵɦɢ. Ⱦɥɹ ɧɚɝɥɹɞɧɨɫɬɢ ɦɨɠɧɨ ɭɫɬɚɧɨɜɢɬɶ ɦɚɪɤɟɪɵ ɜ ɜɢɞɟ «ɫɬɪɟɥɨɤ» ɧɚ ɤɨɧɰɚɯ ɜɟɤɬɨɪɨɜ. Ⱦɥɹ ɮɨɪɦɚɬɢɪɨɜɚɧɢɹ «ɫɬɪɟɥɨɤ» ɧɟɨɛɯɨɞɢɦɨ ɧɚɜɟɫɬɢ ɭɤɚɡɚɬɟɥɶ ɦɵɲɢ ɧɚ ɬɨɱɤɭ ɤɨɧɰɚ ɜɟɤɬɨɪɚ ɳɟɥɤɧɭɬɶ ɧɚ ɧɟɣ ɢ ɩɨɫɥɟ ɩɨɹɜɥɟɧɢɹ ɤɪɟɫɬɨɨɛɪɚɡɧɨɝɨ ɭɤɚɡɚɬɟɥɹ ɫɨ ɫɬɪɟɥɤɚɦɢ ɜɵɡɜɚɬɶ ɤɨɧɬɟɤɫɬɧɨɟ ɦɟɧɸ, ɚ ɡɚɬɟɦ ɩɟɪɟɣɬɢ ɧɚ ɩɭɧɤɬ Ɏɨɪɦɚɬ ɬɨɱɤɢ ɞɚɧɧɵɯ. ɉɪɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ ɫɥɟɞɭɟɬ ɨɛɪɚɬɢɬɶ ɜɧɢɦɚɧɢɟ, ɱɬɨ ɧɚɤɥɨɧ ɜɟɤɬɨɪɨɜ ɡɚɜɢɫɢɬ ɨɬ ɫɤɨɪɨɫɬɢ ɞɜɢɠɟɧɢɹ, ɩɪɨɟɤɰɢɹ ɜɟɤɬɨɪɚ ɧɚ ɨɫɶ ɞɚɥɶɧɨɫɬɢ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɩɪɨɣɞɟɧɧɨɦɭ ɩɭɬɢ, ɚ ɩɨɥɨɠɟɧɢɟ ɤɨɧɰɨɜ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ ɜɪɟɦɟɧɢ ɨɩɪɟɞɟɥɹɸɬ ɜɪɟɦɟɧɹ ɞɜɢɠɟɧɢɹ. 2.1.7. Ⱦɜɚ ɩɥɨɜɰɚ Ⱦɜɚ ɩɥɨɜɰɚ ɫɬɚɪɬɨɜɚɥɢ ɨɞɧɨɜɪɟɦɟɧɧɨ ɧɚ ɞɥɢɧɧɭɸ ɞɢɫɬɚɧɰɢɸ ɜ ɫɬɨɦɟɬɪɨɜɨɦ ɛɚɫɫɟɣɧɟ. ɑɟɪɟɡ ɤɚɤɨɟ ɜɪɟɦɹ ɨɧɢ ɩɟɪɜɵɣ ɪɚɡ ɨɤɚɠɭɬɫɹ ɜ ɪɚɡɧɵɯ ɤɨɧɰɚɯ ɛɚɫɫɟɣɧɚ, ɟɫɥɢ ɢɯ ɫɤɨɪɨɫɬɢ ɪɚɜɧɵ 1 ɦ/ɫ ɢ 0,8ɦ/ɫ. ɋɨɫɬɚɜɥɟɧɢɟ ɭɪɚɜɧɟɧɢɣ ɞɥɹ ɪɟɲɟɧɢɹ ɷɬɨɣ ɡɚɞɚɱɢ ɜɵɡɵɜɚɟɬ ɨɩɪɟɞɟɥɟɧɧɵɟ ɬɪɭɞɧɨɫɬɢ. Ɉɞɧɚɤɨ ɫ ɩɨɦɨɳɶɸ ɦɨɞɟɥɢ ɪɟɲɟɧɢɟ ɧɚɯɨɞɢɬɫɹ ɞɨɜɨɥɶɧɨ ɩɪɨɫɬɨ. ɇɭɠɧɨ ɫɮɨɪɦɢɪɨɜɚɬɶ ɜɟɤɬɨɪɚ ɞɜɢɠɟɧɢɹ ɞɥɹ ɤɚɠɞɨɝɨ ɩɥɨɜɰɚ ɜ ɤɨɨɪɞɢɧɚɬɚɯ «ɜɪɟɦɹ-ɞɚɥɶɧɨɫɬɶ» ɢ ɩɨ ɞɢɚɝɪɚɦɦɟ ɨɩɪɟɞɟɥɢɬɶ ɦɨɦɟɧɬ, ɤɨɝɞɚ ɨɧɢ ɛɭɞɭɬ ɧɚɯɨɞɢɬɶɫɹ ɧɚ ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɯ ɤɨɧɰɚɯ ɛɚɫɫɟɣɧɚ. ɉɪɢ ɷɬɨɦ ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɧɢɦɢ ɞɨɥɠɧɨ ɛɵɬɶ 100ɦ, ɚ ɩɪɨɩɥɵɬɶ ɤɚɠɞɵɣ ɩɥɨɜɟɰ ɞɨɥɠɟɧ ɪɚɫɫɬɨɹɧɢɟ ɤɪɚɬɧɨɟ 100ɦ. Ɏɨɪɦɢɪɭɟɦ ɧɚɱɚɥɶɧɵɟ ɩɚɪɚɦɟɬɪɵ ɦɨɞɟɥɢ (Ⱥ5:D5) ɩɨ ɜɵɲɟɩɪɢɜɟɞɟɧɧɨɣ ɦɟɬɨɞɢɤɟ. ȼ ɹɱɟɣɤɭ (D5), ɤɨɬɨɪɭɸ ɢɫɩɨɥɶɡɭɟɦ ɩɪɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ, ɛɭɞɟɦ ɡɚɧɨɫɢɬɶ ɡɧɚɱɟɧɢɟ ɜɪɟɦɟɧɢ. Ⱦɚɥɟɟ ɡɚɞɚɟɦ ɤɨɨɪɞɢɧɚɬɵ ɜɟɤɬɨɪɨɜ ɩɥɨɜɰɨɜ. ɇɚɱɚɥɨ ɜɟɤɬɨɪɨɜ ɞɜɢɠɟɧɢɹ ɨɛɨɢɯ ɩɥɨɜɰɨɜ ɩɨɦɟɳɚɟɦ ɜ ɧɚɱɚɥɨ ɤɨɨɪɞɢɧɚɬ, ɚ ɤɨɨɪɞɢɧɚɬɵ ɤɨɧɰɨɜ ɨɩɪɟɞɟɥɹɸɬɫɹ ɡɧɚɱɟɧɢɟɦ ɜɪɟɦɟɧɢ (D5) ɢ ɪɚɫɫɬɨɹɧɢɟɦ, ɤɨɬɨɪɨɟ ɨɧɢ ɩɪɨɩɥɵɥɢ, ɬɨ ɟɫɬɶ ɩɪɨɢɡɜɟɞɟɧɢɟɦ ɫɤɨɪɨɫɬɢ ɧɚ ɜɪɟɦɹ (B10, B13). ɋɬɪɨɢɦ ɞɢɚɝɪɚɦɦɭ ɢ ɩɨɫɥɟ ɟɟ ɮɨɪɦɚɬɢɪɨɜɚɧɢɹ ɦɨɞɟɥɢɪɭɟɦ ɞɜɢɠɟɧɢɟ ɩɥɨɜɰɨɜ, ɢɡɦɟɧɹɹ ɡɧɚɱɟɧɢɟ ɜɪɟɦɟɧɢ ɜ ɹɱɟɣɤɟ D5 ɨɬ 0 ɞɨ 500ɫ. Ɋɟɲɟɧɢɟ ɧɚɯɨɞɢɦ ɩɪɢ 500ɫ ɩɨɫɥɟ ɫɬɚɪɬɚ ɩɥɨɜɰɨɜ, ɱɬɨ ɯɨɪɨɲɨ ɜɢɞɧɨ ɧɚ ɞɢɚɝɪɚɦɦɟ. ɉɪɢ ɞɚɥɶɧɟɣɲɟɦ ɭɜɟɥɢɱɟɧɢɢ ɡɧɚɱɟɧɢɹ ɜɪɟɦɟɧɢ (D5) ɦɨɠɧɨ ɫɦɨɞɟɥɢɪɨɜɚɬɶ ɧɚɯɨɠɞɟɧɢɟ ɩɥɨɜɰɨɜ ɧɚ ɪɚɡɥɢɱɧɵɯ ɤɨɧɰɚɯ ɛɚɫɫɟɣɧɚ ɜ ɞɪɭɝɢɟ ɦɨɦɟɧɬɵ ɜɪɟɦɟɧɢ.

63

2. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ MS Excel

2.1.8. Ʉɚɬɟɪ ɢ ɩɥɨɬ Ʉɚɬɟɪ, ɫɤɨɪɨɫɬɶ ɤɨɬɨɪɨɝɨ ɜ ɫɬɨɹɱɟɣ ɜɨɞɟ 15 ɤɦ/ɱ, ɨɬɩɪɚɜɢɥɫɹ ɨɬ ɩɪɢɱɚɥɚ ɜɧɢɡ ɩɨ ɬɟɱɟɧɢɸ ɪɟɤɢ ɢ, ɩɪɨɣɞɹ 36 ɤɦ, ɞɨɝɧɚɥ ɩɥɨɬ, ɨɬɩɪɚɜɥɟɧɧɵɣ ɨɬ ɬɨɝɨ ɠɟ ɩɪɢɱɚɥɚ ɡɚ 10 ɱɚɫɨɜ ɞɨ ɨɬɯɨɞɚ ɤɚɬɟɪɚ. ɇɚɣɬɢ ɫɤɨɪɨɫɬɶ ɬɟɱɟɧɢɹ ɪɟɤɢ. ɉɨ ɭɫɥɨɜɢɸ ɡɚɞɚɱɢ ɤɚɬɟɪ ɢ ɩɥɨɬ ɞɨɥɠɧɵ ɜɫɬɪɟɬɢɬɶɫɹ ɜ ɤɨɧɤɪɟɬɧɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ, ɬɨ ɟɫɬɶ ɤɨɧɰɵ ɢɯ ɜɟɤɬɨɪɨɜ ɞɜɢɠɟɧɢɹ ɞɨɥɠɧɵ ɫɨɜɦɟɫɬɢɬɶɫɹ ɜ ɪɟɡɭɥɶɬɚɬɟ ɦɨɞɟɥɢɪɨɜɚɧɢɹ. ɉɨ ɭɫɥɨɜɢɹɦ ɡɚɞɚɱɢ (Ⱥ5:ȿ5) ɮɨɪɦɢɪɭɟɦ ɤɨɨɪɞɢɧɚɬɵ ɜɟɤɬɨɪɨɜ ɩɨ ɭɠɟ ɢɡɜɟɫɬɧɨɣ ɦɟɬɨɞɢɤɟ ɜ ɤɨɨɪɞɢɧɚɬɚɯ «ɜɪɟɦɹɞɚɥɶɧɨɫɬɶ». Ɍɚɤ ɤɚɤ ɤɚɬɟɪ ɨɬɩɪɚɜɢɥɫɹ ɜɧɢɡ ɩɨ ɬɟɱɟɧɢɸ, ɬɨ ɡɚɧɨɫɢɦ ɩɨɥɨɠɢɬɟɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɫɤɨɪɨɫɬɢ ɬɟɱɟɧɢɹ ɪɟɤɢ. ɉɪɢ ɷɬɨɦ ɤɨɨɪɞɢɧɚɬɚ ɧɚɱɚɥɚ ɜɟɤɬɨɪɚ ɩɥɨɬɚ ɩɨ ɜɪɟɦɟɧɢ ɪɚɜɧɚ ɦɢɧɭɫ 10 ɱɚɫɚɦ ɜ ɫɜɹɡɢ ɫ ɨɬɩɪɚɜɥɟɧɢɟɦ ɩɥɨɬɚ ɧɚ 10 ɱɚɫɨɜ ɪɚɧɶɲɟ ɤɚɬɟɪɚ. ɉɪɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ ɢɡɦɟɧɹɟɦ ɡɧɚɱɟɧɢɟ ɫɤɨɪɨɫɬɢ ɬɟɱɟɧɢɹ ɪɟɤɢ (D5) ɞɨ ɫɨɜɩɚɞɟɧɢɹ ɤɨɧɰɨɜ ɜɟɤɬɨɪɨɜ ɨɛɴɟɤɬɨɜ. ȼ ɦɨɦɟɧɬ ɜɫɬɪɟɱɢ ɤɨɧɰɵ ɜɟɤɬɨɪɨɜ ɞɜɢɠɟɧɢɹ ɤɚɬɟɪɚ ɢ ɩɥɨɬɚ ɫɨɜɩɚɞɭɬ ɩɪɢ ɫɤɨɪɨɫɬɢ ɬɟɱɟɧɢɹ ɪɟɤɢ ɪɚɜɧɨɣ 3ɤɦ/ɱ. 2.1.9. ȼɟɥɨɫɢɩɟɞɢɫɬ Ɋɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɩɭɧɤɬɚɦɢ Ⱥ ɢ ȼ ɜɟɥɨɫɢɩɟɞɢɫɬ ɩɪɨɟɯɚɥ ɡɚ ɬɪɢ ɱɚɫɚ. ȼɨɡɜɪɚɳɚɹɫɶ, ɨɧ ɩɟɪɜɵɟ 24 ɤɦ ɟɯɚɥ ɫ ɩɪɟɠɧɟɣ ɫɤɨɪɨɫɬɶɸ, ɚ ɡɚɬɟɦ ɭɜɟɥɢɱɢɥ ɫɤɨɪɨɫɬɶ ɧɚ 2 ɤɦ/ɱ ɢ ɩɪɢɛɵɥ ɜ ɩɭɧɤɬ Ⱥ, ɡɚɬɪɚɬɢɜ ɧɚ ɨɛɪɚɬɧɵɣ ɩɭɬɶ ɧɚ 10 ɦɢɧɭɬ ɦɟɧɶɲɟ, ɱɟɦ ɧɚ ɩɭɬɶ ɢɡ Ⱥ ɜ ȼ. ɇɚɣɬɢ ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɩɭɧɤɬɚɦɢ Ⱥ ɢ ȼ. Ɉɫɨɛɟɧɧɨɫɬɢ ɞɚɧɧɨɣ 64

2.1. Ɇɚɬɟɦɚɬɢɤɚ

ɡɚɞɚɱɢ ɡɚɤɥɸɱɚɸɬɫɹ ɜ ɧɚɥɢɱɢɢ ɛɨɥɶɲɨɝɨ ɤɨɥɢɱɟɫɬɜɚ ɭɫɥɨɜɢɣ ɢ ɞɜɭɯ ɪɟɲɟɧɢɣ. Ɂɚɩɢɫɵɜɚɟɦ ɩɚɪɚɦɟɬɪɵ ɫ ɭɱɟɬɨɦ ɜɫɟɯ ɭɫɥɨɜɢɣ ɡɚɞɚɱɢ (Ⱥ5:ɇ5). Ɏɨɪɦɢɪɭɟɦ ɜɟɤɬɨɪ ɞɜɢɠɟɧɢɹ ɢɡ ɩɭɧɤɬɚ Ⱥ ɜ ȼ (A9:B10). Ɂɚɬɟɦ ɡɚɞɚɟɦ ɜɟɤɬɨɪ, ɤɨɬɨɪɵɣ ɫɜɹɡɚɧ ɫ ɫɨɤɪɚɳɟɧɢɟɦ ɜɪɟɦɟɧɢ ɧɚ ɨɛɪɚɬɧɭɸ ɞɨɪɨɝɭ. ɗɬɨɬ ɜɟɤɬɨɪ (Ⱥ12:ȼ13) ɩɚɪɚɥɥɟɥɟɧ ɨɫɢ ɜɪɟɦɟɧɢ, ɬɚɤ ɤɚɤ ɨɛɟɫɩɟɱɢɜɚɟɬ ɫɦɟɳɟɧɢɟ ɤɨɨɪɞɢɧɚɬɵ ɜɪɟɦɟɧɢ ɤɨɧɰɚ ɜɟɤɬɨɪɚ, ɤɨɬɨɪɵɣ ɫɜɹɡɚɧ ɫ ɩɭɧɤɬɨɦ ȼ. Ⱦɚɥɟɟ ɮɨɪɦɢɪɭɟɦ ɜɟɤɬɨɪ ɩɟɪɜɵɯ 24 ɤɦ (Ⱥ15:ȼ16), ɚ ɡɚɬɟɦ ɜɟɤɬɨɪ ɩɪɨɯɨɠɞɟɧɢɹ ɨɫɬɚɬɤɚ ɩɭɬɢ ɫ ɭɜɟɥɢɱɟɧɧɨɣ ɫɤɨɪɨɫɬɶɸ (Ⱥ18:ȼ19). ɋɥɟɞɭɟɬ ɡɚɦɟɬɢɬɶ , ɱɬɨ ɜɟɤɬɨɪ ɩɟɪɜɨɝɨ ɭɱɚɫɬɤɚ ɧɚ ɨɛɪɚɬɧɨɦ ɩɭɬɢ ɩɚɪɚɥɥɟɥɟɧ ɜɟɤɬɨɪɭ ɩɪɢ ɞɜɢɠɟɧɢɢ ɜɟɥɨɫɢɩɟɞɢɫɬɚ ɢɡ ɩɭɧɤɬɚ Ⱥ ɜ ȼ ɡɚ ɫɱɟɬ ɪɚɜɟɧɫɬɜɚ ɫɤɨɪɨɫɬɟɣ ɞɜɢɠɟɧɢɹ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɤɨɧɟɰ ɩɨɫɥɟɞɧɟɝɨ ɜɟɤɬɨɪɚ ɞɨɥɠɟɧ ɫɨɜɦɟɫɬɢɬɶɫɹ ɫ ɧɚɱɚɥɨɦ ɤɨɨɪɞɢɧɚɬ, ɬɨ ɟɫɬɶ ɫ ɩɭɧɤɬɨɦ Ⱥ. ɇɚ ɪɢɫɭɧɤɟ ɩɪɟɞɫɬɚɜɥɟɧɚ ɞɢɚɝɪɚɦɦɚ ɜɟɤɬɨɪɨɜ ɜ ɪɚɣɨɧɟ ɧɚɱɚɥɚ ɤɨɨɪɞɢɧɚɬ ɞɥɹ ɛɨɥɟɟ ɱɟɬɤɨɣ ɮɢɤɫɚɰɢɢ ɫɨɜɩɚɞɟɧɢɹ ɜɟɤɬɨɪɨɜ. ɋɨɜɦɟɳɟɧɢɟ ɤɨɧɰɨɜ ɜɟɤɬɨɪɨɜ ɦɨɠɧɨ ɧɚɛɥɸɞɚɬɶ ɩɨ ɡɧɚɱɟɧɢɸ ɹɱɟɣɤɢ Ⱥ19. ȼ ɦɨɦɟɧɬ ɫɨɜɦɟɳɟɧɢɹ ɫɨɞɟɪɠɢɦɨɟ ɹɱɟɣɤɢ ɞɨɥɠɧɨ ɪɚɜɧɹɬɶɫɹ ɧɭɥɸ. ɇɚɯɨɠɞɟɧɢɟ ɪɟɲɟɧɢɹ ɨɫɭɳɟɫɬɜɥɹɟɦ ɩɭɬɟɦ ɢɡɦɟɧɟɧɢɹ ɡɧɚɱɟɧɢɹ ɜ ɹɱɟɣɤɟ Ⱥ5, ɜ ɤɨɬɨɪɨɣ ɮɨɪɦɢɪɭɟɬɫɹ ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɩɭɧɤɬɚɦɢ. ɗɬɨ ɩɪɨɢɫɯɨɞɢɬ, ɤɨɝɞɚ ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɩɭɧɤɬɚɦɢ ɪɚɜɧɹɟɬɫɹ 48 ɤɦ ɢɥɢ 54 ɤɦ. ɉɪɢ ɪɚɫɫɦɨɬɪɟɧɢɢ ɩɪɟɞɥɚɝɚɟɦɨɝɨ ɦɟɬɨɞɚ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɭɫɥɨɜɢɹ ɡɚɞɚɱ ɧɟ ɢɡɦɟɧɹɥɢɫɶ ɞɥɹ ɤɨɪɪɟɤɬɧɨɣ ɩɪɨɜɟɪɤɢ ɜɨɡɦɨɠɧɨɫɬɟɣ ɦɟɬɨɞɚ. Ɉɞɧɚɤɨ ɞɥɹ ɛɨɥɶɲɨɣ ɧɚɝɥɹɞɧɨɫɬɢ ɰɟɥɟɫɨɨɛɪɚɡɧɨ ɦɨɞɢɮɢɰɢɪɨɜɚɬɶ ɧɚɱɚɥɶɧɵɟ ɡɧɚɱɟɧɢɹ ɜ ɡɚɞɚɱɟ ɞɥɹ ɛɨɥɟɟ «ɹɪɤɨɝɨ» ɝɪɚɮɢɱɟɫɤɨɝɨ ɩɪɟɞɫɬɚɜɥɟɧɢɹ ɦɨɞɟɥɢ ɪɟɲɟɧɢɹ ɫ ɩɨɦɨɳɶɸ ɜɟɤɬɨɪɨɜ ɞɜɢɠɟɧɢɹ.

2.1.10. Ɇɨɞɟɥɢɪɨɜɚɧɢɹ ɤɚɫɚɬɟɥɶɧɨɣ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ ɮɭɧɤɰɢɢ ȼ ɦɚɬɟɦɚɬɢɤɟ ɦɧɨɝɨ ɡɚɞɚɱ ɫɜɹɡɚɧɨ ɫ ɜɵɱɢɫɥɟɧɢɟɦ ɩɪɨɢɡɜɨɞɧɵɯ ɮɭɧɤɰɢɣ ɢ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɝɟɨɦɟɬɪɢɱɟɫɤɨɣ ɢɧɬɟɪɩɪɟɬɚɰɢɢ ɩɟɪɜɨɣ ɩɪɨɢɡɜɨɞɧɨɣ ɮɭɧɤɰɢɢ. Ɋɚɫɫɦɨɬɪɢɦ ɦɟɬɨɞɢɤɭ ɩɨɫɬɪɨɟɧɢɹ ɤɚɫɚɬɟɥɶɧɨɣ ɤ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ ɮɭɧɤɰɢɢ ɢ ɨɩɪɟɞɟɥɟɧɢɹ ɩɚɪɚɦɟɬɪɨɜ ɟɟ ɭɪɚɜɧɟɧɢɹ. ȿɫɥɢ ɡɚɞɚɧɚ ɮɭɧɤɰɢɹ f(x), ɬɨ ɩɟɪɜɚɹ ɩɪɨɢɡɜɨɞɧɚɹ ɮɭɧɤɰɢɢ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ ɫ ɤɨɨɪɞɢɧɚɬɚɦɢ x0 ɢ y0 ɹɜɥɹɟɬɫɹ ɭɝɥɨɜɵɦ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɤɚɫɚɬɟɥɶɧɨɣ ɜ ɷɬɨɣ ɬɨɱɤɟ. ɍɪɚɜɧɟɧɢɟ ɤɚɫɚɬɟɥɶɧɨɣ, ɩɪɨɯɨɞɹɳɟɣ ɱɟɪɟɡ ɬɨɱɤɭ ɫ ɤɨɨɪɞɢɧɚɬɚɦɢ x0 ɢ y0, ɢɦɟɟɬ ɜɢɞ: ‫ ݕ‬െ ‫ݕ‬଴ ൌ ݇ ‫ כ‬ሺ‫ ݔ‬െ ‫ݔ‬଴ ሻ, 65

2. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ MS Excel

ɝɞɟ ݇ ൌ ݂ ᇱ ሺ‫ݔ‬଴ ሻ – ɭɝɥɨɜɨɣ ɤɨɷɮɮɢɰɢɟɧɬ; ‫ݔ‬଴ ɢ‫ݕ‬଴ - ɤɨɨɪɞɢɧɚɬɵ ɬɨɱɤɢ. Ɍɪɟɛɭɟɬɫɹ ɩɨɫɬɪɨɢɬɶ ɝɪɚɮɢɤ ɮɭɧɤɰɢɢ ݂ሺ‫ݔ‬ሻ ɢ ɤɚɫɚɬɟɥɶɧɭɸ ɜ ɩɪɹɦɨɭɝɨɥɶɧɨɣ ɨɛɥɚɫɬɢ ɞɢɚɝɪɚɦɦɵ, ɨɝɪɚɧɢɱɟɧɧɨɣ ɦɢɧɢɦɚɥɶɧɵɦɢ ɢ ɦɚɤɫɢɦɚɥɶɧɵɦɢ ɡɧɚɱɟɧɢɹɦɢ ɚɛɫɰɢɫɫ (‫ˋˏݔ‬ː ɢ ‫ ) ˔ˍ˃ˏݔ‬ɢ ɨɪɞɢɧɚɬ (‫ˋˏݕ‬ː ɢ ‫) ˔ˍ˃ˏݕ‬. Ɍɚɤ ɤɚɤ ɤɚɫɚɬɟɥɶɧɚɹ ɹɜɥɹɟɬɫɹ ɩɪɹɦɨɣ ɥɢɧɢɟɣ, ɩɪɨɯɨɞɹɳɟɣ ɱɟɪɟɡ ɡɚɞɚɧɧɭɸ ɬɨɱɤɭ, ɬɨ ɟɟ ɦɨɠɧɨ ɩɨɫɬɪɨɢɬɶ ɩɨ ɤɨɨɪɞɢɧɚɬɚɦ ɞɜɭɯ ɬɨɱɟɤ: (‫ݔ‬ଵ ǡ ‫ݕ‬ଵ ) ɢ (‫ݔ‬ଶ ǡ ‫ݕ‬ଶ ), ɤɨɬɨɪɵɟ ɪɚɫɩɨɥɚɝɚɸɬɫɹ ɧɚ ɝɪɚɧɢɰɚɯ ɩɪɹɦɨɭɝɨɥɶɧɢɤɚ. y

(x1,y1)

yɦɚɤɫ

(x2,y2)

k0 (x1,y1)

f(x)

xɦɚɤɫ

x (x2,y2)

yɦɢɧ

Ɋɚɫɫɦɨɬɪɢɦ ɪɚɫɱɟɬ ɤɨɨɪɞɢɧɚɬ ɬɨɱɟɤ ɤɚɫɚɬɟɥɶɧɨɣ ɫ ɭɱɟɬɨɦ ɡɧɚɱɟɧɢɹ ɭɝɥɨɜɨɝɨ ɤɨɷɮɮɢɰɢɟɧɬɚ݇ ൌ ݂ ᇱ ሺ‫ݔ‬଴ ሻ . Ɂɧɚɱɟɧɢɹ ɭɝɥɨɜɨɝɨ ɤɨɷɮɮɢɰɢɟɧɬɚ ɦɨɝɭɬ ɛɵɬɶ ɩɨɥɨɠɢɬɟɥɶɧɵɦɢ, ɨɬɪɢɰɚɬɟɥɶɧɵɦɢ, ɧɭɥɟɜɵɦɢ ɢɥɢ ɢɦɟɬɶ ɛɟɫɤɨɧɟɱɧɨ ɛɨɥɶɲɢɟ ɡɧɚɱɟɧɢɹ. ɉɭɫɬɶ݇ ൐ Ͳ. Ɉɫɬɚɧɨɜɢɦɫɹ ɧɚ ɜɫɟɯ ɜɨɡɦɨɠɧɵɯ ɜɚɪɢɚɧɬɚɯ ɪɚɫɩɨɥɨɠɟɧɢɹ ɬɨɱɟɤ. ɉɪɢ ‫ݔ‬ଵ ൌ ‫ˋˏݔ‬ː ɫ ɭɱɟɬɨɦ ɮɨɪɦɭɥɵ ‫ݕ‬ଵ ൌ ݇ ‫ כ‬ሺ‫ˋˏݔ‬ː െ ‫ݔ‬଴ ሻ ൅ ‫ݕ‬଴ . ȿɫɥɢ ɜɵɩɨɥɧɹɟɬɫɹ ɧɟɪɚɜɟɧɫɬɜɨ ‫ˋˏݕ‬ː ൏ ‫ݕ‬ଵ ൏ ‫ ˔ˍ˃ˏݕ‬, ɬɨ ɤɨɨɪɞɢɧɚɬɵ ɩɟɪɜɨɣ ɬɨɱɤɢ ɨɩɪɟɞɟɥɟɧɵ. ȼ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ ɪɚɫɫɦɚɬɪɢɜɚɟɦ ɞɪɭɝɢɟ ɜɚɪɢɚɧɬɵ ɪɚɫɩɨɥɨɠɟɧɢɟ ɬɨɱɤɢ. ɉɪɢ ‫ݕ‬ଵ ൏ ‫ˋˏݕ‬ː ɡɚɞɚɟɦ ‫ݕ‬ଵ ൌ ‫ˋˏݕ‬ː ɢ ɩɨɥɭɱɚɟɦ ‫ݔ‬ଵ ൌ ሺ‫ˋˏݕ‬ː െ ‫ݕ‬଴ ൅ ݇ ‫ݔ כ‬଴ ሻȀ݇. ɉɪɢ ‫ݕ‬ଵ ൐ ‫ ˔ˍ˃ˏݕ‬ɡɚɞɚɟɦ ‫ݕ‬ଵ ൌ ‫ ˔ˍ˃ˏݕ‬ɢ ɜɵɱɢɫɥɹɟɦ ‫ݔ‬ଵ ൌ ሺ‫ ˔ˍ˃ˏݕ‬െ ‫ݕ‬଴ ൅ ݇ ‫ݔ כ‬଴ ሻȀ݇. Ʉɨɨɪɞɢɧɚɬɵ ɜɬɨɪɨɣ ɬɨɱɤɢ ɤɚɫɚɬɟɥɶɧɨɣ ɪɚɫɫɱɢɬɵɜɚɸɬɫɹ ɚɧɚɥɨɝɢɱɧɵɦ ɨɛɪɚɡɨɦ. ɉɪɢ ɷɬɨɦ ɡɚɞɚɟɦ ‫ݔ‬ଶ ൌ ‫ ˔ˍ˃ˏݔ‬ɢ ‫ݕ‬ଶ ൌ ݇ ‫ כ‬ሺ‫ ˔ˍ˃ˏݔ‬െ ‫ݔ‬଴ ሻ ൅ ‫ݕ‬଴ . ȿɫɥɢ ɜɵɩɨɥɧɹɟɬɫɹ ɧɟɪɚɜɟɧɫɬɜɨ ‫ˋˏݕ‬ː ൏ ‫ݕ‬ଶ ൏ ‫ ˔ˍ˃ˏݕ‬, ɬɨ ɤɨɨɪɞɢɧɚɬɵ ɜɬɨɪɨɣ ɬɨɱɤɢ ɨɩɪɟɞɟɥɟɧɵ. ȼ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ ɪɚɫɫɦɚɬɪɢɜɚɟɦ ɫɥɟɞɭɸɳɢɟ ɜɚɪɢɚɧɬɵ ɪɚɫɩɨɥɨɠɟɧɢɹ ɬɨɱɤɢ. ɉɪɢ ‫ݕ‬ଶ ൏ ‫ˋˏݕ‬ː ɡɚɞɚɟɦ ‫ݕ‬ଶ ൌ ‫ˋˏݕ‬ː ɢ ‫ݔ‬ଶ ൌ ሺ‫ˋˏݕ‬ː െ ‫ݕ‬଴ ൅ ݇ ‫ݔ כ‬଴ ሻȀ݇. ɉɪɢ ɜɵɩɨɥɧɟɧɢɢ ɧɟɪɚɜɟɧɫɬɜɚ ‫ݕ‬ଶ ൏ ‫ ˔ˍ˃ˏݕ‬ɡɚɞɚɟɦ ‫ݕ‬ଶ ൌ ‫ ˔ˍ˃ˏݕ‬ɢ ɩɨɞɫɱɢɬɵɜɚɟɦ ‫ݔ‬ଶ ൌ ሺ‫ ˔ˍ˃ˏݕ‬െ ‫ݕ‬଴ ൅ ݇ ‫ݔ כ‬଴ ሻȀ݇. 66

2.1. Ɇɚɬɟɦɚɬɢɤɚ

ȿɫɥɢ ݇ ൏ Ͳ, ɬɨ ɩɨɥɭɱɚɟɦ ɚɧɚɥɨɝɢɱɧɵɟ ɜɵɪɚɠɟɧɢɹ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɤɨɨɪɞɢɧɚɬ ɬɨɱɟɤ ɤɚɫɚɬɟɥɶɧɨɣ. ɉɪɢ ɷɬɨɦ ɜɫɟɝɞɚ ɜ ɩɟɪɜɭɸ ɨɱɟɪɟɞɶ ɪɚɫɫɱɢɬɵɜɚɟɦ ɩɪɚɜɭɸ ɬɨɱɤɭ ɤɚɫɚɬɟɥɶɧɨɣ (ɫɦ. ɪɢɫɭɧɨɤ). ɉɪɢ ݇ ൌ Ͳ ɤɚɫɚɬɟɥɶɧɚɹ ɹɜɥɹɟɬɫɹ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɥɢɧɢɟɣ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ ɚɪɝɭɦɟɧɬɨɜ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ‫ݔ‬ଵ ൌ ‫ˋˏݔ‬ː , ‫ݕ‬ଵ ൌ ‫ݕ‬଴ ɢ ‫ݔ‬ଶ ൌ ‫ ˔ˍ˃ˏݔ‬, ‫ݕ‬ଶ ൌ ‫ݕ‬଴ . ɉɪɢ ݇ ՜ േλ ɤɚɫɚɬɟɥɶɧɚɹ ɫɬɚɧɨɜɢɬɶɫɹ ɜɟɪɬɢɤɚɥɶɧɨɣ ɥɢɧɢɟɣ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ,‫ݔ‬ଵ ൌ ‫ݔ‬଴ , ‫ݕ‬ଵ ൌ ‫ˋˏݕ‬ː ɢ ‫ݔ‬ଶ ൌ ‫ݔ‬଴ , ‫ݕ‬ଶ ൌ ‫ ˔ˍ˃ˏݕ‬. Ɍɟɩɟɪɶ ɦɨɠɧɨ ɨɫɬɚɧɨɜɢɬɶɫɹ ɧɚ ɦɟɬɨɞɢɤɟ ɩɨɫɬɪɨɟɧɢɹ ɝɪɚɮɢɤɚ ɮɭɧɤɰɢɢ ɢ ɤɚɫɚɬɟɥɶɧɨɣ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ ɮɭɧɤɰɢɢ. Ɉɩɪɟɞɟɥɹɟɦ ɝɪɚɧɢɱɧɵɟ ɡɧɚɱɟɧɢɹ ɞɢɚɩɚɡɨɧɨɜ ɞɥɹ ‫ ݔ‬ɢ ‫ˋˏݔ( ݕ‬ː , ‫ ˔ˍ˃ˏݔ‬, ‫ˋˏݕ‬ː ,‫ ) ˔ˍ˃ˏݕ‬ɩɪɢ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨɦ ɩɨɫɬɪɨɟɧɢɢ ɝɪɚɮɢɤɚ ɡɚɞɚɧɧɨɣ ɮɭɧɤɰɢɢ ɧɚ ɨɫɧɨɜɟ ɬɚɛɭɥɢɪɨɜɚɧɧɨɣ ɮɭɧɤɰɢɢ (B5:C25) ‫ ݕ‬ൌ ʹ ‫ݔ ‹• כ‬. Ɏɨɪɦɢɪɭɟɦ ɬɚɛɥɢɰɵ ɧɚɱɚɥɶɧɵɯ ɭɫɥɨɜɢɣ ɡɚɞɚɱɢ. Ɂɚɞɚɟɦ ɹɱɟɣɤɢ: x ɤɨɨɪɞɢɧɚɬ ɡɚɞɚɧɧɨɣ ɬɨɱɤɢ ɮɭɧɤɰɢɢ(‫ݔ‬଴ ,‫ݕ‬଴ ) (F2 ɢ G2); x ɭɝɥɨɜɨɝɨ ɤɨɷɮɮɢɰɢɟɧɬɚ ݇ ൌ ݂ ᇱ ሺ‫ݔ‬଴ ሻ (ɇ2); x ɝɪɚɧɢɱɧɵɯ ɡɧɚɱɟɧɢɣ ɞɢɚɩɚɡɨɧɨɜ (‫ˋˏݔ‬ː , ‫ ˔ˍ˃ˏݔ‬, ‫ˋˏݕ‬ː ,‫( ) ˔ˍ˃ˏݕ‬A2:D5). Ɉɬɫɬɭɩɢɜ ɨɞɧɭ ɹɱɟɣɤɭ ɨɬ ɬɚɛɥɢɰɵ ɮɭɧɤɰɢɢ (B5:C25), ɪɚɫɫɱɢɬɵɜɚɟɦ ɤɨɨɪɞɢɧɚɬɵ ɬɨɱɟɤ ɤɚɫɚɬɟɥɶɧɨɣ (B27:C28) ɫ ɭɱɟɬɨɦ ɩɪɢɜɟɞɟɧɧɵɯ ɜɵɲɟ ɪɚɫɫɭɠɞɟɧɢɣ (ɧɚ ɪɢɫɭɧɤɟ ɜ ɩɪɢɦɟɱɚɧɢɹɯ ɨɬɨɛɪɚɠɟɧɵ ɮɨɪɦɭɥɵ ɪɚɫɱɟɬɨɜ). ɉɪɟɞɜɚɪɢɬɟɥɶɧɨ ɞɥɹ ɭɞɨɛɫɬɜɚ ɜɵɱɢɫɥɹɟɦ ɜɨ ɜɫɩɨɦɨɝɚɬɟɥɶɧɵɯ ɹɱɟɣɤɚɯ ɡɧɚɱɟɧɢɹ ‫ݕ‬ଵ ɩɪɢ ‫ݔ‬ଵ ൌ ‫ˋˏݔ‬ː ɢ ‫ݕ‬ଶ ɩɪɢ ‫ݔ‬ଶ ൌ ‫( ˔ˍ˃ˏݔ‬F8 ɢ G8). Ⱦɥɹ ɨɬɨɛɪɚɠɟɧɢɹ ɬɨɱɤɢ ɧɚ ɝɪɚɮɢɤɟ ɮɭɧɤɰɢɢ ɞɨɛɚɜɥɹɟɦ ɹɱɟɣɤɢ ɫ ɟɟ ɡɚɞɚɧɧɵɦɢ ɤɨɨɪɞɢɧɚɬɚɦɢ (ȼ30 ɢ ɋ30). ȼɵɞɟɥɢɜ ɞɢɚɩɚɡɨɧ ɹɱɟɟɤ (B5:C30), ɜ ɤɨɬɨɪɵɣ ɜɤɥɸɱɚɸɬɫɹ ɹɱɟɣɤɢ ɬɚɛɥɢɰɵ ɮɭɧɤɰɢɢ ɢ ɤɨɨɪɞɢɧɚɬ ɬɨɱɟɤ ɤɚɫɚɬɟɥɶɧɨɣ, ɨɛɪɚɳɚɟɦɫɹ ɤ ɦɚɫɬɟɪɭ ɞɢɚɝɪɚɦɦ ɞɥɹ ɩɨɫɬɪɨɟɧɢɹ ɝɪɚɮɢɤɚ ɮɭɧɤɰɢɢ ɢ ɤɚɫɚɬɟɥɶɧɨɣ. Ɂɚɞɚɟɦ ɬɢɩ ɞɢɚɝɪɚɦɦɵ - Ɍɨɱɟɱɧɚɹ, ɚ ɜɢɞ - Ɍɨɱɟɱɧɚɹ ɞɢɚɝɪɚɦɦɚ ɫɨ ɡɧɚɱɟɧɢɹɦɢ, ɫɨɟɞɢɧɟɧɧɵɦɢ ɫɝɥɚɠɢɜɚɸɳɢɦɢ ɥɢɧɢɹɦɢ ɛɟɡ ɦɚɪɤɟɪɨɜ. Ɏɢɤɫɢɪɭɟɦ ɦɢɧɢɦɚɥɶɧɵɟ ɢ ɦɚɤɫɢɦɚɥɶɧɵɟ ɡɧɚɱɟɧɢɹ ɲɤɚɥ ɨɫɟɣ x ɢ y ɜ ɞɢɚɥɨɝɨɜɨɦ ɨɤɧɟ Ɏɨɪɦɚɬ ɨɫɢ. Ⱦɥɹ ɡɚɞɚɧɧɨɣ ɬɨɱɤɢ, ɤ ɤɨɬɨɪɨɣ ɫɬɪɨɢɬɫɹ ɤɚɫɚɬɟɥɶɧɚɹ, ɦɨɠɧɨ ɭɫɬɚɧɨɜɢɬɶ ɨɬɥɢɱɢɬɟɥɶɧɵɣ ɦɚɪɤɟɪ ɢ ɜɵɜɟɫɬɢ ɟɟ ɤɨɨɪɞɢɧɚɬ. ɑɬɨɛɵ ɭɫɬɚɧɨɜɢɬɶ ɰɜɟɬ ɢ ɬɨɥɳɢɧɭ ɥɢɧɢɢ ɤɚɫɚɬɟɥɶɧɨɣ ɧɭɠɧɨ ɚɤɤɭɪɚɬɧɨ ɳɟɥɤɧɭɬɶ ɩɨ ɥɢɧɢɢ ɤɚɫɚɬɟɥɶɧɨɣ. ɉɪɢ ɩɨɹɜɥɟɧɢɢ ɦɚɪɤɟɪɨɜ ɬɨɱɟɤ ɤɚɫɚɬɟɥɶɧɨɣ ɜɵɡɜɚɬɶ ɤɨɧɬɟɤɫɬɧɨɟ ɦɟɧɸ ɢ ɳɟɥɤɧɭɬɶ ɩɨ ɩɭɧɤɬɭ Ɏɨɪɦɚɬ ɬɨɱɤɢ ɞɚɧɧɵɯ. ȼ ɞɢɚɥɨɝɨɜɨɦ ɨɤɧɟ ɭɫɬɚɧɨɜɢɬɶ ɬɢɩ, ɰɜɟɬ ɢ ɬɨɥɳɢɧɭ ɥɢɧɢɢ ɤɚɫɚɬɟɥɶɧɨɣ. Ⱦɥɹ ɧɚɝɥɹɞɧɨɫɬɢ ɨɞɧɨɜɪɟɦɟɧɧɨ ɜɵɱɢɫɥɹɟɦ ɩɚɪɚɦɟɬɪɵ ɭɪɚɜɧɟɧɢɹ ɤɚɫɚɬɟɥɶɧɨɣ ‫ ݕ‬ൌ ܽ ‫ ݔ כ‬൅ ܾ, ɝɞɟ ɢɡ ɭɪɚɜɧɟɧɢɹ ܽ ൌ ݇, ܾ ൌ ‫ݕ‬଴ െ ݇ ‫ݔ כ‬଴ . ɗɬɢ ɩɚɪɚɦɟɬɪɵ ɪɚɫɫɱɢɬɵɜɚɟɦ ɜ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɹɱɟɣɤɚɯ, ɤɨɬɨɪɵɟ ɫɨɫɟɞɫɬɜɭɸɬ ɫ ɹɱɟɣɤɚɦɢ, ɜ ɤɨɬɨɪɵɯ ɡɚɧɟɫɟɧɵ ɫɢɦɜɨɥɵ Y,=,* ɞɥɹ ɩɪɟɞɫɬɚɜɥɟɧɢɹ ɭɪɚɜɧɟɧɢɹ ɤɚɫɚ67

2. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ MS Excel

ɬɟɥɶɧɨɣ. Ɍɚɤ ɤɚɤ ɡɧɚɱɟɧɢɟ ɩɚɪɚɦɟɬɪɚ b ɦɨɝɭɬ ɛɵɬɶ ɤɚɤ ɨɬɪɢɰɚɬɟɥɶɧɵɦɢ, ɬɚɤ ɢ ɩɨɥɨɠɢɬɟɥɶɧɵɦɢ, ɬɨ ɜ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɹɱɟɣɤɟ ɢɫɩɨɥɶɡɭɟɦ ɮɭɧɤɰɢɸ ȿɋɅɂ ɞɥɹ ɨɬɨɛɪɚɠɟɧɢɹ ɫɢɦɜɨɥɨɜ + ɢ -.

ɂɡɦɟɧɹɹ ɡɧɚɱɟɧɢɹ ɤɨɨɪɞɢɧɚɬɵ ‫ݔ‬଴ , ɨɫɭɳɟɫɬɜɥɹɟɦ ɢɫɫɥɟɞɨɜɚɧɢɟ ɩɨɜɟɞɟɧɢɹ ɤɚɫɚɬɟɥɶɧɨɣ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ ɮɭɧɤɰɢɢ ɢ ɢɡɦɟɧɟɧɢɹ ɩɚɪɚɦɟɬɪɨɜ ɭɪɚɜɧɟɧɢɹ ɤɚɫɚɬɟɥɶɧɨɣ. ɉɪɢ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɦɨɠɧɨ ɞɨɩɨɥɧɢɬɟɥɶɧɨ ɩɨɫɬɪɨɢɬɶ ɝɪɚɮɢɤ ɩɪɨɢɡɜɨɞɧɨɣ ɡɚɞɚɧɧɨɣ ɮɭɧɤɰɢɢ. 2.1.11. ȿɞɢɧɢɱɧɚɹ ɨɤɪɭɠɧɨɫɬɶ ɢ ɫɢɧɭɫ ɭɝɥɚ Ⱦɥɹ ɜɵɹɫɧɟɧɢɹ ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ ɢɡɦɟɧɟɧɢɹ ɨɫɧɨɜɧɵɯ ɬɪɢɝɨɧɨɦɟɬɪɢɱɟɫɤɢɯ ɮɭɧɤɰɢɣ ɢɫɩɨɥɶɡɭɸɬ ɟɞɢɧɢɱɧɭɸ ɨɤɪɭɠɧɨɫɬɶ ɢ ɟɟ ɪɚɞɢɭɫ-ɜɟɤɬɨɪ. ɉɪɢ ɷɬɨɦ ɪɚɞɢɭɫ-ɜɟɤɬɨɪ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɭɝɥɚ ɡɚɧɢɦɚɟɬ ɨɩɪɟɞɟɥɟɧɧɨɟ ɩɨɥɨɠɟɧɢɟ. ɋɨɡɞɚɞɢɦ ɞɢɧɚɦɢɱɟɫɤɭɸ ɦɨɞɟɥɶ ɞɜɢɠɟɧɢɹ ɟɞɢɧɢɱɧɨɝɨ ɪɚɞɢɭɫɚ-ɜɟɤɬɨɪɚ ɢ ɩɨɫɬɪɨɟɧɢɹ ɝɪɚɮɢɤɚ ɮɭɧɤɰɢɢ ɫɢɧɭɫɚ. Ɂɚɞɚɞɢɦ ɭɝɥɨɜɭɸ ɫɤɨɪɨɫɬɶ ɞɜɢɠɟɧɢɹ ɪɚɞɢɭɫɚ (ȼ3). ɍɝɨɥ ɩɨɜɨɪɨɬɚ ɪɚɞɢɭɫɚ ɛɭɞɟɬ ɨɩɪɟɞɟɥɹɬɶɫɹ ɩɪɨɢɡɜɟɞɟɧɢɟɦ ɡɚɞɚɧɧɨɣ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɢ ɧɚ ɡɧɚɱɟɧɢɟ ɫɱɟɬɱɢɤɚ ɬɟɤɭɳɟɝɨ ɜɪɟɦɟɧɢ (D3). Ɂɧɚɱɟɧɢɟ ɮɭɧɤɰɢɢ ɫɢɧɭɫɚ ɪɚɜɧɹɟɬɫɹ ɩɪɨɟɤɰɢɢ ɪɚɞɢɭɫɚ-ɜɟɤɬɨɪɚ ɧɚ ɨɫɶ Y. 68

2.1. Ɇɚɬɟɦɚɬɢɤɚ

ɂɫɯɨɞɹ ɢɡ ɭɫɥɨɜɢɣ, ɫɨɡɞɚɟɦ ɬɚɛɥɢɰɭ, ɝɞɟ ɜ ɩɟɪɜɨɦ ɫɬɨɥɛɰɟ ɫ ɡɚɞɚɧɧɵɦ ɢɧɬɟɪɜɚɥɨɦ ɡɚɧɨɫɢɦ ɜɪɟɦɹ (F3:F26). ȼɨ ɜɬɨɪɨɦ ɫɬɨɥɛɰɟ (G3:G26) ɪɚɫɫɱɢɬɵɜɚɟɦ ɭɝɨɥ ɩɨɜɨɪɨɬɚ ɩɪɢ ɫɨɛɥɸɞɟɧɢɢ ɭɫɥɨɜɢɹ: ɭɝɨɥ ɩɨɜɨɪɨɬɚ ɧɟ ɩɪɟɜɵɲɚɟɬ ɭɝɨɥ ɩɨɜɨɪɨɬɚ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɬɟɤɭɳɟɦɭ ɜɪɟɦɟɧɢ ɫɱɟɬɱɢɤɚ. ɉɪɢ ɧɟɜɵɩɨɥɧɟɧɢɢ ɭɫɥɨɜɢɹ ɜ ɹɱɟɣɤɢ ɭɝɥɚ ɡɚɩɢɫɵɜɚɟɬɫɹ ɮɭɧɤɰɢɹ ɇȾ(). ȼ ɬɪɟɬɶɟɦ ɫɬɨɥɛɰɟ ɜɵɱɢɫɥɹɟɬɫɹ ɡɧɚɱɟɧɢɟ ɮɭɧɤɰɢɢ ɫɢɧɭɫɚ.

Ⱦɥɹ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɞɜɢɠɟɧɢɹ ɜɟɤɬɨɪɚ ɜ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɹɱɟɣɤɚɯ ɢɫɯɨɞɧɨɣ ɬɚɛɥɢɰɵ ɡɚɞɚɟɦ ɤɨɨɪɞɢɧɚɬɵ ɧɚɱɚɥɚ ɪɚɞɢɭɫɚ ɢ ɜɵɱɢɫɥɹɟɦ ɤɨɨɪɞɢɧɚɬɵ ɤɨɧɰɚ ɪɚɞɢɭɫɚ (G28:H29). ɇɟ ɡɚɛɵɜɚɟɦ ɩɪɨɩɭɫɬɢɬɶ ɨɞɧɭ ɫɬɪɨɤɭ ɞɥɹ ɢɫɤɥɸɱɟɧɢɹ ɫɥɢɹɧɢɹ ɢɡɨɛɪɚɠɟɧɢɹ ɪɚɞɢɭɫɚ ɫ ɝɪɚɮɢɤɨɦ ɮɭɧɤɰɢɢ ɫɢɧɭɫɚ. Ɉɬɨɛɪɚɠɟɧɢɟ ɟɞɢɧɢɱɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɩɪɨɢɡɜɨɞɢɦ ɫ ɩɨɦɨɳɶɸ ɞɨɩɨɥɧɢɬɟɥɶɧɨɣ ɬɚɛɥɢɰɵ, ɝɞɟ ɜ ɩɟɪɜɨɦ ɫɬɨɥɛɰɟ (F31:F67 ) ɡɚɞɚɟɦ ɤɨɥɢɱɟɫɬɜɨ ɬɨɱɟɤ, ɤɨɬɨɪɨɟ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɧɨɪɦɚɥɶɧɨɝɨ ɢɡɨɛɪɚɠɟɧɢɹ ɨɤɪɭɠɧɨɫɬɢ. ȼ ɨɫɬɚɥɶɧɵɯ ɫɬɨɥɛɰɚɯ ɜɵɱɢɫɥɹɟɦ ɤɨɨɪɞɢɧɚɬɵ ɬɨɱɟɤ ɨɤɪɭɠɧɨɫɬɢ (G31:H67). ȼɵɞɟɥɢɜ ɹɱɟɣɤɢ ɫɬɨɥɛɰɨɜ ɍɝɨɥ ɩɨɜɨɪɨɬɚ ɢ Ɂɧɚɱɟɧɢɟ ɫɢɧɭɫɚ ɬɚɛɥɢɰɵ, ɨɛɪɚɳɚɟɦɫɹ ɤ Ɇɚɫɬɟɪɭ ɞɢɚɝɪɚɦɦ ɢ ɩɨɫɥɟ ɡɚɞɚɧɢɹ ɩɚɪɚɦɟɬɪɨɜ ɩɟɪɟɯɨɞɢɦ ɤ ɦɨɞɟɥɢɪɨɜɚɧɢɸ, ɢɡɦɟɧɹɹ ɡɧɚɱɟɧɢɹ ɫɱɟɬɱɢɤɚ (ɋ3). əɫɧɨ, ɱɬɨ ɩɪɢ ɩɨɫɬɪɨɟɧɢɢ ɞɢɚɝɪɚɦɦɵ ɜɵɛɢɪɚɟɦ ɜɢɞ Ɍɨɱɟɱɧɚɹ ɞɢɚɝɪɚɦɦɚ ɫɨ ɡɧɚɱɟɧɢɹɦɢ, ɫɨɟɞɢɧɟɧɧɵɦɢ ɫɝɥɚɠɢɜɚɸɳɢɦɢ ɥɢɧɢɹɦɢ. ȿɫɥɢ ɟɞɢɧɢɱɧɚɹ ɨɤɪɭɠɧɨɫɬɶ ɧɚ ɞɢɚɝɪɚɦɦɟ ɩɨɥɭ69

2. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ MS Excel

ɱɢɥɚɫɶ ɞɟɮɨɪɦɢɪɨɜɚɧɧɨɣ (ɜ ɜɢɞɟ ɷɥɥɢɩɫɚ), ɬɨ ɧɭɠɧɨ ɪɚɫɬɹɧɭɬɶ ɞɢɚɝɪɚɦɦɭ ɩɨ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɫɬɨɪɨɧɟ. 2.1.12. ɉɨɫɬɪɨɟɧɢɟ ɩɪɨɫɬɟɣɲɢɯ ɨɛɴɟɦɧɵɯ ɮɢɝɭɪ ɉɨɫɬɪɨɢɦ ɤɚɪɤɚɫɧɵɟ ɦɨɞɟɥɢ ɷɥɟɦɟɧɬɚɪɧɵɯ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɯ ɮɢɝɭɪ, ɤɨɬɨɪɵɟ ɹɜɥɹɸɬɫɹ ɨɫɧɨɜɧɵɦɢ ɷɥɟɦɟɧɬɚɦɢ ɬɪɟɯɦɟɪɧɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ. Ɂɚɞɚɱɢ ɫɬɟɪɟɨɦɟɬɪɢɢ ɜɵɡɵɜɚɸɬ ɨɩɪɟɞɟɥɟɧɧɵɟ ɬɪɭɞɧɨɫɬɢ. ɉɪɢ ɢɯ ɪɟɲɟɧɢɢ ɧɭɠɧɨ ɨɛɥɚɞɚɬɶ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɵɦ ɜɨɨɛɪɚɠɟɧɢɟɦ. ȼɨɡɶɦɟɦ ɤɭɛ, ɱɟɬɵɪɟɯɭɝɨɥɶɧɭɸ ɩɢɪɚɦɢɞɭ, ɩɨɥɭɫɮɟɪɭ ɢ ɰɢɥɢɧɞɪ ɞɥɹ ɨɛɴɟɦɧɨɝɨ ɢɡɨɛɪɚɠɟɧɢɹ ɜɨ ɮɪɨɧɬɚɥɶɧɨɣ ɞɢɦɟɬYɷɤɪ ɪɢɱɟɫɤɨɣ ɢ ɤɨɫɨɭɝɨɥɶɧɨɣ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɢɡɨɦɟɬZ ɪɢɱɟɫɤɨɣ ɩɪɨɟɤɰɢɹɯ. ɗɬɢ ɩɪɨɟɤɰɢɢ ɧɚɢɛɨɥɟɟ ɱɚ(X,Y,Z) ɫɬɨ ɢɫɩɨɥɶɡɭɸɬɫɹ. ȼ ɩɟɪɜɭɸ ɨɱɟɪɟɞɶ ɧɟɨɛɯɨɞɢɦɨ Y Xɷɤɪ ɨɛɟɫɩɟɱɢɬɶ ɩɟɪɟɫɱɟɬ ɤɨɨɪɞɢɧɚɬ ɢɡ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɩɪɨɟɤɰɢɢ XYZ ɧɚ ɩɥɨɫɤɭɸ ɩɨɜɟɪɯɧɨɫɬɶ, ɤɨ450 450 ɬɨɪɭɸ ɧɚɡɨɜɟɦ ɷɤɪɚɧɧɨɣ ɫɢɫɬɟɦɨɣ ɤɨɨɪɞɢɧɚɬ (X,Y) X ɏɷɤɪYɷɤɪ. Ɇɚɫɲɬɚɛɧɵɟ ɤɨɷɮɮɢɰɢɟɧɬɵ ɩɨ ɨɫɹɦ ɩɪɨɟɤɰɢɣ ɭɱɢɬɵɜɚɬɶ ɧɟ ɛɭɞɟɦ. ɉɟɪɟɫɱɟɬ ɤɨɨɪɞɢɧɚɬ ɢɡ ɮɪɨɧɬɚɥɶɧɨɣ ɞɢɦɟɬɪɢɱɟɫɤɨɣ ɩɪɨɟɤɰɢɢ ɜ ɷɤɪɚɧɧɭɸ ɫɢɫɬɟɦɭ ɤɨɨɪɞɢɧɚɬ ɨɫɭɳɟɫɬɜɥɹɟɦ ɩɨ ɮɨɪɦɭɥɚɦ (ɫɦ. ɪɢɫɭɧɨɤ) ܺˠˍ˓ ൌ ܻ െ ܺ ‫ ‹• כ‬Ͷͷ଴ , ܻˠˍ˓ ൌ ܼ െ ܺ ‫כ‬ Yɷɤɪ …‘• Ͷͷ଴ . Z ɉɟɪɟɫɱɟɬ ɢɡ ɤɨɫɨɭɝɨɥɶɧɨɣ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ (X,Y,Z) ɢɡɨɦɟɬɪɢɱɟɫɤɨɣ ɩɪɨɟɤɰɢɢ ɜ ɷɤɪɚɧɧɭɸ ɫɢɫɬɟɦɭ Xɷɤɪ ɩɪɨɢɡɜɨɞɢɦ ɩɨ ɮɨɪɦɭɥɚɦ (ɫɦ. ɪɢɫɭɧɨɤ) 0 0 ȕ ܺˠˍ˓ ൌ ܴ ‫•‘… כ‬ሺߚሻ, ܻˠˍ˓ ൌ ܼ െ ܴ ‫‹• כ‬ሺߚሻ, 45 45 ɝɞɟ ܴ ൌ ሺܺ ଶ ൅ ܻ ଶ ሻ଴ǡହ , Į X Y ߚ ൌ ͳ͵ͷ଴ െ ܽ‫݃ݐܿݎ‬ሺܻΤܺሻ. (X,Y) Ɇɨɠɧɨ ɥɟɝɤɨ ɩɟɪɟɣɬɢ ɤ ɞɪɭɝɢɦ ɩɪɨɟɤɰɢɹɦ ɡɚɞɚɜ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɭɝɥɵ ɨɪɢɟɧɬɚɰɢɢ ɨɫɟɣ ɩɪɨɟɤɰɢɣ, ɧɨ ɩɪɢ ɷɬɨɦ ɮɨɪɦɭɥɵ ɪɚɫɱɟɬɚ ɭɫɥɨɠɧɹɬɫɹ. ɉɟɪɟɯɨɞ ɨɬ ɞɢɦɟɬɪɢɱɟɫɤɨɣ ɤ ɢɡɨɦɟɬɪɢɱɟɫɤɨɣ ɩɪɨɟɤɰɢɢ ɩɪɨɢɡɜɨɞɢɬɫɹ ɩɨ ɡɧɚɱɟɧɢɸ ɩɪɢɡɧɚɤɚ «ɉɪɨɟɤɰɢɹ» ɜ ɹɱɟɣɤɟ F2. ɉɪɢ ɧɭɥɟ ɮɢɝɭɪɵ ɢɡɨɛɪɚɠɚɸɬɫɹ ɜ ɞɢɦɟɬɪɢɱɟɫɤɨɣ ɩɪɨɟɤɰɢɢ, ɚ ɩɪɢ ɪɚɜɟɧɫɬɜɟ ɟɞɢɧɢɰɟ – ɜ ɢɡɨɦɟɬɪɢɱɟɫɤɨɣ. ȼ ɹɱɟɣɤɚɯ ɋ1 ɢ ɋ2 ɡɚɪɚɧɟɟ ɜɵɱɢɫɥɢɦ ɡɧɚɱɟɧɢɹ ɤɨɫɢɧɭɫɚ ɢ ɫɢɧɭɫɚ 450, ɤɨɬɨɪɵɟ ɢɫɩɨɥɶɡɭɸɬɫɹ ɩɪɢ ɩɟɪɟɫɱɟɬɟ ɤɨɨɪɞɢɧɚɬ. Ɏɢɝɭɪɵ ɛɭɞɟɦ ɢɡɨɛɪɚɠɚɬɶ ɜ ɜɢɞɟ ɤɚɪɤɚɫɨɜ, ɡɚɞɚɜɚɹ ɤɨɨɪɞɢɧɚɬɵ ɤɨɧɰɨɜ ɨɬɪɟɡɤɨɜ ɢɥɢ ɷɥɟɦɟɧɬɚɪɧɵɯ ɮɢɝɭɪ ɜ ɬɪɟɯɦɟɪɧɨɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ XYZ. Ɂɚɬɟɦ ɤɨɨɪɞɢɧɚɬɵ ɩɟɪɟɫɱɢɬɵɜɚɸɬɫɹ ɜ ɷɤɪɚɧɧɭɸ ɫɢɫɬɟɦɭ ɤɨɨɪɞɢɧɚɬ ɩɨ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦ ɮɨɪɦɭɥɚɦ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɡɧɚɱɟɧɢɹ ɩɪɢɡɧɚɤɚ «ɉɪɨɟɤɰɢɹ». Ⱦɥɹ ɨɬɫɥɟɠɢɜɚɧɢɹ ɩɪɨɰɟɫɫɚ ɩɨɫɬɪɨɟɧɢɹ 70

2.1. Ɇɚɬɟɦɚɬɢɤɚ

ɢɡɨɛɪɚɠɟɧɢɹ ɧɚ ɞɢɚɝɪɚɦɦɟ ɮɢɝɭɪ, ɜɵɞɟɥɹɟɦ ɹɱɟɣɤɢ ɫɬɨɥɛɰɨɜ E ɢ F ɫ ɞɨɫɬɚɬɨɱɧɵɦ ɤɨɥɢɱɟɫɬɜɨɦ ɫɬɪɨɤ, ɧɚɱɢɧɚɹ ɫ 6-ɣ ɫɬɪɨɤɢ. Ɉɛɪɚɳɚɟɦɫɹ ɤ Ɇɚɫɬɟɪɭ ɞɢɚɝɪɚɦɦ ɢ ɜɵɛɢɪɚɟɦ ɬɢɩ ɞɢɚɝɪɚɦɦɵ Ɍɨɱɟɱɧɵɣ.

ɂɡɨɛɪɚɡɢɦ ɨɫɢ ɩɪɨɟɤɰɢɣ ɱɟɪɟɡ ɤɨɨɪɞɢɧɚɬɵ ɞɜɭɯ ɬɨɱɟɤ. ɉɟɪɜɚɹ ɬɨɱɤɚ ɩɪɢɧɚɞɥɟɠɢɬ ɧɚɱɚɥɭ ɤɨɨɪɞɢɧɚɬ (B6:D6, B9:D9, B12:D12), ɚ ɜɬɨɪɚɹ ɢɦɟɟɬ ɨɞɧɭ ɫɨɨɬɜɟɬɫɬɜɭɸɳɭɸ ɤɨɨɪɞɢɧɚɬɭ ɧɟ ɪɚɜɧɭɸ ɧɭɥɸ (B7:D7, B10:D10, B13:D13). Ɂɧɚɱɟɧɢɟ ɤɨɨɪɞɢɧɚɬɵ ɜɬɨɪɨɣ ɬɨɱɤɢ ɨɫɢ ɨɩɪɟɞɟɥɹɟɬYɷɤɪ Z ɫɹ ɜɟɥɢɱɢɧɨɣ ɨɛɥɚɫɬɢ ɩɨɫɬɪɨɟɧɢɹ ɮɢɝɭɪ. Ʉɨɨɪɞɢɧɚɬɵ ɨɬɪɟɡɤɨɜ ɨɫɟɣ ɪɚɡɞɟɥɹɟɦ ɫɬɪɨɤɚɦɢ ɞɥɹ ɨɛɟɫɩɟɱɟR ɧɢɹ ɢɯ ɪɚɡɞɟɥɶɧɨɝɨ ɢɡɨɛɪɚɠɟɧɢɹ. ȼ ɫɨɨɬɜɟɬɫɬɜɭɸij Y Xɷɤɪ ɳɢɯ ɹɱɟɣɤɚɯ ɫɬɨɥɛɰɨɜ E ɢ F ɜɵɱɢɫɥɹɟɦ ɷɤɪɚɧɧɵɟ ɤɨɨɪɞɢɧɚɬɵ ɫ ɩɪɨɜɟɪɤɨɣ ɡɧɚɱɟɧɢɹ ɩɪɢɡɧɚɤɚ «ɉɪɨɟɤɰɢɹ» ɢ ɢɫɤɥɸɱɟɧɢɟɦ ɞɟɥɟɧɢɹ ɧɚ ɧɨɥɶ ɩɪɢ ɜɵɱɢɫɥɟȜ X ɧɢɢ ɮɭɧɤɰɢɢ ɬɚɧɝɟɧɫɚ (ɫɦ. ɩɪɢɦɟɱɚɧɢɟ). ɉɨɫɥɟ ɩɨɹɜɥɟɧɢɹ ɨɫɟɣ ɧɚ ɞɢɚɝɪɚɦɦɟ ɩɪɢɫɬɭɩɚɟɦ ɤ ɢɡɨɛɪɚɠɟɧɢɸ ɤɚɪɤɚɫɚ ɤɭɛɚ. Ɉɬɦɟɬɢɦ, ɱɬɨ ɨɫɧɨɜɚɧɢɹ ɜɫɟɯ ɮɢɝɭɪ ɪɚɫɩɨɥɨɠɟɧɵ ɜ ɩɥɨɫɤɨɫɬɢ XY ɞɥɹ ɩɪɨɫɬɨɬɵ ɡɚɞɚɧɢɹ ɤɨɨɪɞɢɧɚɬ ɷɥɟɦɟɧɬɨɜ ɤɚɪɤɚɫɚ. ɋɧɚɱɚɥɚ ɡɚɞɚɟɦ ɤɨɨɪɞɢɧɚɬɵ ɞɧɚ ɤɭɛɚ (B17:D21), ɞɚɥɟɟ ɤɨɨɪɞɢɧɚɬɵ ɤɨɧɰɨɜ ɪɟɛɟɪ (B23:D33) ɢ ɜɟɪɯɚ ɤɭɛɚ (B35:D39). Ɍɚɤ ɤɚɤ ɰɟɥɟɫɨɨɛɪɚɡɧɨ ɫ ɩɨɦɨɳɶɸ ɚɜɬɨɡɚɩɨɥɧɟɧɢɹ ɡɚɪɚɧɟɟ ɨɛɟɫɩɟɱɢɬɶ ɩɟɪɟɫɱɟɬ ɤɨɨɪɞɢɧɚɬ ɜ ɷɤɪɚɧɧɭɸ ɫɢɫɬɟɦɭ, ɬɨ ɩɨ ɦɟɪɟ ɡɚɞɚɧɢɹ ɤɨɨɪɞɢɧɚɬ ɢ ɮɨɪɦɢɪɨɜɚɧɢɹ ɩɭɫɬɵɯ ɫɬɨɤ ɦɟɠɞɭ ɷɥɟɦɟɧɬɚɦɢ ɤɭɛɚ ɛɭɞɟɦ ɧɚɛɥɸɞɚɬɶ ɩɪɨɰɟɫɫ ɩɨɹɜɥɟɧɢɹ ɢɡɨɛɪɚɠɟɧɢɹ ɤɭɛɚ. ɉɪɢ ɪɚɫɱɟɬɟ ɭɝɥɚ ȕ ɢɫɩɨɥɶɡɭɟɦ ɮɭɧɤɰɢɸ ATAN2(X;Y), ɤɨɬɨɪɚɹ ɨɩɪɟɞɟɥɹɟɬ ɭɝɨɥ ɨɬ –ʌ ɞɨ ʌ. 71

2. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ MS Excel

Ⱥɧɚɥɨɝɢɱɧɨ ɥɟɝɤɨ ɩɨɥɭɱɚɟɦ ɢɡɨɛɪɚɠɟɧɢɟ ɱɟɬɵɪɟɯɭɝɨɥɶɧɨɣ ɩɪɢɡɦɵ. ɉɨɫɥɟ ɡɚɞɚɧɢɹ ɤɨɨɪɞɢɧɚɬ ɞɧɚ, ɨɩɪɟɞɟɥɹɟɦ ɤɨɨɪɞɢɧɚɬɵ ɜɵɫɨɬɵ ɩɪɢɡɦɵ ɢ ɡɚɞɚɟɦ ɤɨɨɪɞɢɧɚɬɵ ɪɟɛɟɪ. ɉɪɢ ɩɨɫɬɪɨɟɧɢɢ ɤɚɪɤɚɫɚ ɩɨɥɭɫɮɟɪɵ ɪɚɫɩɨɥɨɠɢɦ ɰɟɧɬɪ ɮɢɝɭɪɵ ɜ ɧɚɱɚɥɟ ɤɨɨɪɞɢɧɚɬ. Ɍɨɝɞɚ ɞɥɹ ɪɚɫɱɟɬɚ ɤɚɪɤɚɫɚ ɦɨɠɧɨ ɜɨɫɩɨɥɶɡɨɜɚɬɶɫɹ ɮɨɪɦɭɥɚɦɢ ɫɮɟɪɵ ܺ ൌ ܴ˔˗ ‫•‘… כ‬ሺ߮ሻ ‫•‘… כ‬ሺߣሻ, Yൌ ܴ˔˗ ‫•‘… כ‬ሺ߮ሻ ‫‹• כ‬ሺߣሻ, ܼ ൌ ܴ˔˗ ‫‹• כ‬ሺ߮ሻ, ɝɞɟ ܴ˔˗ – ɪɚɞɢɭɫ ɫɮɟɪɵ, ߮ – ɜɫɩɨɦɨɝɚɬɟɥɶɧɵɣ ɭɝɨɥ, ɡɧɚɱɟɧɢɹ ɤɨɬɨɪɨɝɨ ɢɡɦɟɧɹɸɬɫɹ ɨɬ -900 ɞɨ 900, ߣ – ɜɫɩɨɦɨɝɚɬɟɥɶɧɵɣ ɭɝɨɥ, ɡɧɚɱɟɧɢɹ ɤɨɬɨɪɨɝɨ ɢɡɦɟɧɹɸɬɫɹ ɨɬ 00 ɞɨ 3600. Ɋɚɞɢɭɫ ɩɨɥɭɫɮɟɪɵ ɡɚɞɚɞɢɦ ɜ ɹɱɟɣɤɟ ɇ61. Ⱦɥɹ ɩɨɫɬɪɨɟɧɢɹ ɤɚɪɤɚɫɚ ɩɨɥɭɫɮɟɪɵ ɜɨɫɩɨɥɶɡɭɟɦɫɹ «ɝɨɪɢɡɨɧɬɚɥɶɧɵɦɢ» ɨɤɪɭɠɧɨɫɬɹɦɢ ɩɪɢ ɡɚɞɚɧɧɵɯ ɡɧɚɱɟɧɢɹɯ ɭɝɥɚ ߮ =00, 300 ɢ 600. Ɋɚɫɱɟɬ ɤɨɨɪɞɢɧɚɬ 19 ɬɨɱɟɤ ɤɚɠɞɨɣ ɨɤɪɭɠɧɨɫɬɢ ɩɪɢ ɮɢɤɫɢɪɨɜɚɧɧɨɦ ɡɧɚɱɟɧɢɢ ߮ ɩɪɨɢɡɜɨɞɢɦ ɫ ɢɡɦɟɧɟɧɢɟɦ ߣ ɨɬ 00 ɞɨ 3600 ɫ ɲɚɝɨɦ οߣ =200 (ɇ65). Ɋɚɫɱɟɬ ɤɨɨɪɞɢɧɚɬ 10 ɬɨɱɟɤ «ɜɟɪɬɢɤɚɥɶɧɵɯ» ɩɨɥɭɨɤɪɭɠɧɨɫɬɟɣ ɞɟɥɚɟɦ ɩɪɢ ɮɢɤɫɢɪɨɜɚɧɧɵɯ ɡɧɚɱɟɧɢɹɯ ߣ =450, 900, 1350 ɢ 1800, ɧɨ ɫ ɢɡɦɟɧɟɧɢɟɦ ɡɧɚɱɟɧɢɣ ɭɝɥɚ ߮ ɨɬ ɨɬ 00 ɞɨ 1800 ɫ ɲɚɝɨɦ ο߮ =200. ɇɟ ɡɚɛɵɜɚɟɦ ɨ ɪɚɡɞɟɥɟɧɢɢ ɹɱɟɟɤ ɫ ɤɨɨɪɞɢɧɚɬɚɦɢ ɨɬɞɟɥɶɧɵɯ ɷɥɟɦɟɧɬɨɜ ɤɚɪɤɚɫɚ ɩɨɥɭɫɮɟɪɵ ɩɭɫɬɵɦɢ ɫɬɪɨɤɚɦɢ. Ɍɟɩɟɪɶ ɨɫɬɚɟɬɫɹ ɢɡɨɛɪɚɡɢɬɶ ɤɚɪɤɚɫ ɰɢɥɢɧɞɪɚ. ɐɟɧɬɪ ɨɫɧɨɜɚɧɢɹ ɰɢɥɢɧɞɪɚ ɢɦɟɟɬ ɤɨɨɪɞɢɧɚɬɵ ܺ଴ ɢ ܻ଴ (H168:H169). Ɋɚɞɢɭɫ ɰɢɥɢɧɞɪɚ ܴ˙ ɡɚɞɚɧ ɜ ɹɱɟɣɤɟ ɇ167. Ʉɚɪɤɚɫ ɰɢɥɢɧɞɪɚ ɫɨɫɬɚɜɢɦ ɢɡ ɨɤɪɭɠɧɨɫɬɟɣ ɨɫɧɨɜɚɧɢɹ (ȼ169:D178) ɢ ɜɟɪɯɚ (ȼ180:D189), ɚ ɬɚɤɠɟ ɨɛɪɚɡɭɸɳɢɯ 9 ɪɟɛɟɪ. Ɉɤɪɭɠɧɨɫɬɢ ɢɡɨɛɪɚɠɚɟɦ 10 ɬɨɱɤɚɦɢ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɮɨɪɦɭɥ ɞɥɹ ɫɮɟɪɵ, ɧɨ ɫ ɭɱɟɬɨɦ ɤɨɨɪɞɢɧɚɬ ɰɟɧɬɪɚ (ɇ168:ɇ169). ɉɪɢ ɡɚɞɚɧɢɢ ɤɨɨɪɞɢɧɚɬ ɨɤɪɭɠɧɨɫɬɢ ɜɟɪɯɚ ɰɢɥɢɧɞɪɚ ɤɨɨɪɞɢɧɚɬɵ X ɢ Y ɤɨɩɢɪɭɟɦ, ɚ ɤɨɨɪɞɢɧɚɬɭ Z ɩɪɢɪɚɜɧɹɟɦ ɜɵɫɨɬɟ ɰɢɥɢɧɞɪɚ (ɇ171). Ʉɨɨɪɞɢɧɚɬɵ ɤɨɧɰɨɜ ɪɟɛɟɪ ɮɨɪɦɢɪɭɟɦ ɤɨɩɢɪɨɜɚɧɢɟɦ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɤɨɨɪɞɢɧɚɬ ɨɤɪɭɠɧɨɫɬɟɣ ɞɧɚ ɢ ɜɟɪɯɚ ɰɢɥɢɧɞɪɚ.

72

2.1. Ɇɚɬɟɦɚɬɢɤɚ

ɉɪɢ ɪɚɜɟɧɫɬɜɟ ɟɞɢɧɢɰɟ ɩɪɢɡɧɚɤɚ «ɉɪɨɟɤɰɢɹ» ɩɨɥɭɱɚɟɦ ɢɡɨɛɪɚɠɟɧɢɟ ɮɢɝɭɪ ɜ ɢɡɨɦɟɬɪɢɢ. ɗɬɨ ɩɨɡɜɨɥɢɬ ɨɩɪɟɞɟɥɢɬɶɫɹ ɫ ɧɚɝɥɹɞɧɨɫɬɶɸ ɢɡɨɛɪɚɠɟɧɢɹ ɮɢɝɭɪ ɜ ɤɚɠɞɨɣ ɩɪɨɟɤɰɢɢ ɢ ɩɪɢɧɹɬɶ ɪɟɲɟɧɢɟ ɨɛ ɢɯ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɩɪɢ ɬɪɟɯɦɟɪɧɨɦ ɦɨɞɟɥɢɪɨɜɚɧɢɢ. ɉɪɢ ɡɚɞɚɧɢɢ ɤɨɨɪɞɢɧɚɬ ɤɚɪɤɚɫɚ ɮɢɝɭɪ ɰɟɥɟɫɨɨɛɪɚɡɧɨ ɢɯ ɩɪɢɜɹɡɚɬɶ ɤ ɨɞɧɨɣ ɯɚɪɚɤɬɟɪɧɨɣ ɬɨɱɤɟ ɮɢɝɭɪɵ ɞɥɹ ɨɛɥɟɝɱɟɧɢɹ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɩɟɪɟɦɟɳɟɧɢɹ. Ⱦɥɹ ɪɚɫɲɢɪɟɧɢɹ ɜɨɡɦɨɠɧɨɫɬɟɣ ɩɨ ɦɨɞɟɥɢɪɨɜɚɧɢɸ ɨɛɴɟɦɧɨɝɨ ɢɡɨɛɪɚɠɟɧɢɹ ɮɢɝɭɪ ɦɨɠɧɨ ɜɜɟɫɬɢ ɦɚɫɲɬɚɛɧɵɟ ɤɨɷɮɮɢɰɢɟɧɬɵ ɩɨ ɤɨɨɪɞɢɧɚɬɧɵɦ ɨɫɹɦ. 2.1.13. Ɋɟɲɟɧɢɟ ɝɪɚɮɨɚɧɚɥɢɬɢɱɟɫɤɢɦ ɦɟɬɨɞɨɦ ɡɚɞɚɱ ɥɢɧɟɣɧɨɝɨ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ ɋɨɡɞɚɞɢɦ ɝɪɚɮɢɱɟɫɤɭɸ ɦɨɞɟɥɶ ɪɟɲɟɧɢɹ ɨɩɬɢɦɚɥɶɧɨɣ ɡɚɞɚɱɢ. Ɂɚɞɚɱɚ ɥɢɧɟɣɧɨɝɨ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ ɫɨɫɬɨɢɬ ɜ ɧɚɯɨɠɞɟɧɢɢ ɧɚɢɛɨɥɶɲɟɝɨ ɢɥɢ ɧɚɢɦɟɧɶɲɟɝɨ ɡɧɚɱɟɧɢɹ ɥɢɧɟɣɧɨɣ ɰɟɥɟɜɨɣ ɮɭɧɤɰɢɢ ‫ ܨ‬ൌ ‫ܥ‬ଵ ‫ܺ כ‬ଵ ൅ ‫ ڮ‬൅ ‫ܥ‬௡ ‫ܺ כ‬௡ ɜ ɨɛɥɚɫɬɢ n-ɦɟɪɧɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ, ɡɚɞɚɧɧɨɣ ɩɨɫɪɟɞɫɬɜɨɦ ɫɢɫɬɟɦɵ ɧɟɪɚɜɟɧɫɬɜ: ܽ௜ଵ ‫ܺ כ‬ଵ ൅ ܽ௜ଶ ‫ܺ כ‬ଶ ൅ ‫ ڮ‬൅ ܽ௜௡ ‫ܺ כ‬௡ ൑ ܾ௜ Ǣ i=1,2,…,m; ܺଵ ൒ ͲǢܺଶ ൒ ͲǢ ǥ Ǣ ܺ௡ ൒ Ͳ. Ɋɚɫɫɦɨɬɪɢɦ ɦɨɞɟɥɶ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɝɪɚɮɨɚɧɚɥɢɬɢɱɟɫɤɢɦ ɫɩɨɫɨɛɨɦ ɩɪɢ n=2. ɋɭɳɧɨɫɬɶ ɝɪɚɮɨɚɧɚɥɢɬɢɱɟɫɤɨɝɨ ɦɟɬɨɞɚ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɧɚɯɨɠɞɟɧɢɢ ɫɨɜ73

2. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ MS Excel

ɦɟɫɬɧɵɯ ɬɨɱɟɤ ɨɛɥɚɫɬɢ ɞɨɩɭɫɬɢɦɵɯ ɪɟɲɟɧɢɣ ɫ ɥɢɧɢɟɣ ɭɪɨɜɧɹ ɰɟɥɟɜɨɣ ɮɭɧɤɰɢɢ. Ⱦɥɹ ɷɬɨɝɨ ɧɟɨɛɯɨɞɢɦɨ ɩɨɫɬɪɨɢɬɶ ɨɛɥɚɫɬɶ ɪɟɲɟɧɢɣ ɢ ɨɛɟɫɩɟɱɢɬɶ ɩɟɪɟɦɟɳɟɧɢɟ ɧɚ ɩɥɨɫɤɨɫɬɢ ɥɢɧɢɢ ɭɪɨɜɧɹ ɰɟɥɟɜɨɣ ɮɭɧɤɰɢɢ ɞɨ ɩɨɥɭɱɟɧɢɹ ɫɨɜɦɟɫɬɧɵɯ ɬɨɱɟɤ. ɉɭɫɬɶ ɨɛɥɚɫɬɶ ɞɨɩɭɫɬɢɦɵɯ ɪɟɲɟɧɢɣ ɢɦɟɟɬ ɮɨɪɦɭ ɬɪɟɭɝɨɥɶɧɢɤɚ (m=3). ɗɬɨ ɡɧɚɱɢɬɟɥɶɧɨ ɨɛɥɟɝɱɢɬ ɟɟ ɝɪɚɮɢɱɟɫɤɨɟ ɢɡɨɛɪɚɠɟɧɢɟ ɩɨ ɤɨɨɪɞɢɧɚɬɚɦ ɜɟɪɲɢɧ ɬɪɟɭɝɨɥɶɧɢɤɚ ɫ ɩɨɦɨɳɶɸ Ɇɚɫɬɟɪɚ ɞɢɚɝɪɚɦɦ. ɂɬɚɤ, ɰɟɥɟɜɚɹ ɮɭɧɤɰɢɹ ‫ ܨ‬ൌ ʹ ‫ܺ כ‬ଵ ൅ ܺଶ ǡ ɚ ɨɛɥɚɫɬɶ ɞɨɩɭɫɬɢɦɵɯ ɪɟɲɟɧɢɣ ɡɚɞɚɧɚ ɧɟɪɚɜɟɧɫɬɜɚɦɢ: ͵ ‫ܺ כ‬ଵ ൅ Ͷ ‫ܺ כ‬ଶ ൒ ͳͷǢെͷ ‫ܺ כ‬ଵ ൅ ͸ ‫ܺ כ‬ଶ ൒ െʹͲǢܺଵ ൅ ͺ ‫ܺ כ‬ଶ ൑ ͵Ͳ. Ɉɛɵɱɧɨ ɢɡ ɭɫɥɨɜɢɣ ɛɨɥɶɲɢɧɫɬɜɚ ɡɚɞɚɱ ɜɜɨɞɹɬ ɫɥɟɞɭɸɳɢɟ ɞɨɩɨɥɧɢɬɟɥɶɧɵɟ ɨɝɪɚɧɢɱɟɧɢɹ: ܺଵ ൒ ͲǢܺଶ ൒ Ͳ. Ɍɪɟɛɭɟɬɫɹ ɧɚɣɬɢ ɦɢɧɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɰɟɥɟɜɨɣ ɮɭɧɤɰɢɢ F ɩɪɢ ɡɚɞɚɧɧɵɯ ɨɝɪɚɧɢɱɟɧɢɹɯ. ȼɚɪɢɚɧɬ 1.ɉɨ ɭɫɥɨɜɢɸ ɡɚɞɚɱɢ ɨɛɥɚɫɬɶ ɪɟɲɟɧɢɣ ɩɨɥɧɨɫɬɶɸ ɧɚɯɨɞɢɬɫɹ ɜ ɩɟɪɜɨɦ ɤɜɚɞɪɚɧɬɟ ɫɢɫɬɟɦɵ ɤɨɨɪɞɢɧɚɬ. Ɂɚɦɟɧɹɹ ɜ ɧɟɪɚɜɟɧɫɬɜɚɯ ɡɧɚɤɢ ɛɨɥɶɲɟ ɢ ɦɟɧɶɲɟ ɧɚ ɡɧɚɤ ɪɚɜɟɧɫɬɜɚ, ɩɨɥɭɱɚɟɦ ɭɪɚɜɧɟɧɢɹ ɩɪɹɦɵɯ ɝɪɚɧɢɰ ɨɛɥɚɫɬɢ ɞɨɩɭɫɬɢɦɵɯ ɪɟɲɟɧɢɣ: ͵ ‫ܺ כ‬ଵ ൅ Ͷ ‫ܺ כ‬ଶ ൌ ͳͷǢെͷ ‫ܺ כ‬ଵ ൅ ͸ ‫ܺ כ‬ଶ ൌ െʹͲǢܺଵ ൅ ͺ ‫ܺ כ‬ଶ ൌ ͵Ͳ. Ⱦɥɹ ɩɨɫɬɪɨɟɧɢɹ ɝɪɚɧɢɰ ɨɛɥɚɫɬɢ ɞɨɫɬɚɬɨɱɧɨ ɨɩɪɟɞɟɥɢɬɶ ɤɨɨɪɞɢɧɚɬɵ ɜɟɪɲɢɧ ɬɪɟɭɝɨɥɶɧɨɣ ɨɛɥɚɫɬɢ ɞɨɩɭɫɬɢɦɵɯ ɪɟɲɟɧɢɣ. Ƚɪɭɩɩɢɪɭɟɦ ɩɨɩɚɪɧɨ ɭɪɚɜɧɟɧɢɹ ɢ ɪɟɲɚɟɦ ɫɢɫɬɟɦɵ ɫ ɩɨɦɨɳɶɸ ɮɨɪɦɭɥ Ʉɪɚɦɟɪɚ ɞɥɹ ɧɚɯɨɠɞɟɧɢɹ ɤɨɨɪɞɢɧɚɬ ɩɟɪɟɫɟɱɟɧɢɹ ɩɪɹɦɵɯ. ɇɚɩɪɢɦɟɪ, ɞɥɹ ɫɢɫɬɟɦɵ ɭɪɚɜɧɟɧɢɣ ɜ ɨɛɳɟɦ ɜɢɞɟ ܽଵଵ ‫ܺ כ‬ଵ ൅ ܽଵଶ ‫ܺ כ‬ଶ ൌ ܾଵ ɢ ܽଶଵ ‫ܺ כ‬ଵ ൅ ܽଶଶ ‫ܺ כ‬ଶ ൌ ܾଶ ɪɟɲɟɧɢɹ ɩɨɥɭɱɚɟɦ ɩɨ ɮɨɪɦɭɥɚɦ ܺଵ ൌ ሺܾଵ ‫ܽ כ‬ଶଶ െ ܾଶ ‫ܽ כ‬ଵଶ ሻȀሺܽଵଵ ‫ܽ כ‬ଶଶ െ ܽଶଵ ‫ܽ כ‬ଵଶሻ ) ɢ ܺଶ ൌ ሺܾଶ ‫ܽ כ‬ଵଵ െ ܾଵ ‫ܽ כ‬ଶଵ ሻȀሺܽଵଵ ‫ܽ כ‬ଶଶ െ ܽଶଵ ‫ܽ כ‬ଵଶሻ ). ȼ ɬɚɛɥɢɰɭ (Ⱥ4:ɋ6) ɡɚɧɨɫɢɦ ɤɨɷɮɮɢɰɢɟɧɬɵ ɩɪɹɦɵɯ. ȼ ɬɚɛɥɢɰɟ (D4:E6) ɜɵɱɢɫɥɹɟɦ ɤɨɨɪɞɢɧɚɬɵ ɬɨɱɟɤ ɩɟɪɟɫɟɱɟɧɢɹ ɩɟɪɜɨɣ ɢ ɜɬɨɪɨɣ ɩɪɹɦɵɯ, ɜɬɨɪɨɣ ɢ ɬɪɟɬɶɟɣ, ɬɪɟɬɶɟɣ ɢ ɩɟɪɜɨɣ. Ⱦɥɹ ɡɚɦɵɤɚɧɢɹ ɤɨɧɬɭɪɚ ɬɪɟɭɝɨɥɶɧɢɤɚ ɧɚ ɝɪɚɮɢɤɟ ɜ ɤɨɧɰɟ ɩɟɪɟɡɚɩɢɫɵɜɚɟɦ ɤɨɨɪɞɢɧɚɬɵ ɩɟɪɜɨɣ ɪɚɫɱɟɬɧɨɣ ɬɨɱɤɢ ɩɟɪɟɫɟɱɟɧɢɹ ɩɪɹɦɵɯ ɩɪɹɦɨɣ (D7,E7).

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2.1. Ɇɚɬɟɦɚɬɢɤɚ

ɉɟɪɟɞ ɨɛɪɚɳɟɧɢɟɦ ɤ Ɇɚɫɬɟɪɭ ɞɢɚɝɪɚɦɦ ɜɵɞɟɥɹɟɦ ɞɢɚɩɚɡɨɧ ɹɱɟɟɤ D4:E10 ɫ ɭɱɟɬɨɦ ɞɚɥɶɧɟɣɲɟɝɨ ɩɨɫɬɪɨɟɧɢɹ ɥɢɧɢɢ ɭɪɨɜɧɹ ɰɟɥɟɜɨɣ ɮɭɧɤɰɢɢ. ȼɵɛɢɪɚɟɦ ɬɢɩ ɞɢɚɝɪɚɦɦɵ Ɍɨɱɟɱɧɚɹ, ɚ ɜɢɞ, ɝɞɟ ɡɧɚɱɟɧɢɹ ɫɨɟɞɢɧɟɧɵ ɨɬɪɟɡɤɚɦɢ. ɑɬɨɛɵ ɝɪɚɮɢɤɢ ɨɛɥɚɫɬɢ ɢ ɥɢɧɢɢ ɰɟɥɟɜɨɣ ɮɭɧɤɰɢɢ ɛɵɥɢ ɨɬɨɛɪɚɠɟɧɵ ɪɚɡɞɟɥɶɧɨ ɹɱɟɣɤɢ ɫ ɢɯ ɤɨɨɪɞɢɧɚɬɚɦɢ ɨɬɞɟɥɹɟɦ ɫɬɪɨɤɨɣ. Ɏɢɤɫɢɪɭɟɦ ɦɚɤɫɢɦɚɥɶɧɵɟ ɢ ɦɢɧɢɦɚɥɶɧɵɟ ɡɧɚɱɟɧɢɹ ɲɤɚɥ ɱɟɪɟɡ ɞɢɚɥɨɝɨɜɨɟ ɨɤɧɨ Ɏɨɪɦɚɬ ɨɫɢ ɞɥɹ ɢɫɤɥɸɱɟɧɢɹ ɢɡɦɟɧɟɧɢɣ ɩɚɪɚɦɟɬɪɨɜ ɨɛɥɚɫɬɢ ɩɨɫɬɪɨɟɧɢɹ ɞɢɚɝɪɚɦɦɵ ɩɪɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ. Ⱦɥɹ ɩɨɫɬɪɨɟɧɢɹ ɥɢɧɢɢ ɭɪɨɜɧɹ ɰɟɥɟɜɨɣ ɮɭɧɤɰɢɢ ɡɚɞɚɟɦ ɧɚɱɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɮɭɧɤɰɢɢ ‫ܨ‬଴ (C13). Ɂɚɩɢɫɚɜ ɡɧɚɱɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɋ1 ɢ ɋ2 ɰɟɥɟɜɨɣ ɮɭɧɤɰɢɢ ɢ ɟɟ ɧɚɱɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ, ɦɨɠɧɨ ɩɨ ɡɚɞɚɧɧɨɦɭ ɡɧɚɱɟɧɢɸ ܺଵ ɜɵɱɢɫɥɢɬɶ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɤɨɨɪɞɢɧɚɬɵ ܺଶ ɫ ɩɨɦɨɳɶɸ ɮɨɪɦɭɥɵ ܺଶ ൌ ሺ‫ܨ‬଴ െ ‫ܥ‬ଵ ‫כ‬ ܺଵ ሻȀ‫ܥ‬ଶ ɞɥɹ ɞɜɭɯ ɤɨɧɰɨɜ ɥɢɧɢɢ ɭɪɨɜɧɹ. Ɉɩɪɟɞɟɥɢɜ ɤɨɨɪɞɢɧɚɬɵ ɤɨɧɰɨɜ ɥɢɧɢɢ ɭɪɨɜɧɹ (D9:E10), ɩɨɥɭɱɚɟɦ ɢɡɨɛɪɚɠɟɧɢɟ ɥɢɧɢɢ ɧɚ ɝɪɚɮɢɤɟ. ȼɵɛɨɪɧɨɟ ɡɧɚɱɟɧɢɟ ܺଵ ɦɨɠɧɨ ɨɬɤɨɪɪɟɤɬɢɪɨɜɚɬɶ ɞɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɛɨɥɟɟ ɧɚɝɥɹɞɧɨɝɨ ɪɚɫɩɨɥɨɠɟɧɢɹ ɥɢɧɢɢ ɭɪɨɜɧɹ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɛɥɚɫɬɢ ɞɨɩɭɫɬɢɦɵɯ ɪɟɲɟɧɢɣ. Ɍɟɩɟɪɶ ɨɫɬɚɟɬɫɹ ɢɡɦɟɧɹɬɶ ɡɧɚɱɟɧɢɟ ‫ܨ‬଴ ɞɥɹ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɩɟɪɟɦɟɳɟɧɢɹ ɥɢɧɢɢ ɭɪɨɜɧɹ ɰɟɥɟɜɨɣ ɮɭɧɤɰɢɢ ɜ ɫɬɨɪɨɧɭ ɨɛɥɚɫɬɢ ɪɟɲɟɧɢɹ. ɉɪɢ ɷɬɨɦ ɥɢɧɢɹ ɭɪɨɜɧɹ ɰɟɥɟɜɨɣ ɮɭɧɤɰɢɢ ɛɭɞɟɬ ɫɦɟɳɚɬɶɫɹ ɩɚɪɚɥɥɟɥɶɧɨ ɧɚɱɚɥɶɧɨɦɭ ɩɨɥɨɠɟɧɢɸ. ɋɦɟɳɟɧɢɟ ɩɪɨɢɡɜɨɞɢɬɫɹ ɞɨ ɩɟɪɜɨɝɨ ɫɨɩɪɢɤɨɫɧɨɜɟɧɢɹ ɫ ɨɛɥɚɫɬɶɸ ɞɨɩɭɫɬɢɦɵɯ ɪɟɲɟɧɢɣ. ȼ ɧɚɲɟɦ ɫɥɭɱɚɟ ɦɢɧɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɰɟɥɟɜɨɣ ɮɭɧɤɰɢɢ ɪɚɜɧɨ 3,75 ɩɪɢ ܺଵ ൌ Ͳ ɢ ܺଶ =3,75 (ɬɨɱɤɚ Ⱥ). ȿɫɥɢ ɧɭɠɧɨ ɧɚɣɬɢ ɦɚɤɫɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɰɟɥɟɜɨɣ ɮɭɧɤɰɢɢ, ɬɨ ɨɧɨ ɪɚɜɧɹɟɬɫɹ 17,6 ɩɪɢ ܺଵ =7,39 ɢ ܺଶ =2,82 (ɬɨɱɤɚ ȼ). Ɍɚɤɨɣ ɪɟɡɭɥɶɬɚɬ ɩɨɥɭɱɚɟɦ ɩɪɢ ɞɚɥɶɧɟɣɲɟɦ ɭɜɟɥɢɱɟɧɢɢ ɡɧɚɱɟɧɢɹ ɰɟɥɟɜɨɣ ɮɭɧɤɰɢɢ (ɋ13), ɤɨɝɞɚ ɟɟ ɥɢɧɢɹ ɫɨɩɪɢɤɚɫɚɟɬɫɹ ɫ ɩɨɫɥɟɞɧɟɣ ɬɨɱɤɨɣ ɨɛɥɚɫɬɢ ɪɟɲɟɧɢɣ ɩɪɢ ɜɵɯɨɞɟ ɢɡ ɧɟɟ. ɉɪɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ ɩɪɹɦɚɹ ɦɨɠɟɬ ɜɵɣɬɢ ɢɡ ɡɚɞɚɧɧɨɝɨ ɞɢɚɩɚɡɨɧɚ ɝɪɚɮɢɤɚ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɤɨɪɪɟɤɬɢɪɭɟɦ ɡɧɚɱɟɧɢɹ ɤɨɨɪɞɢɧɚɬ ɤɨɧɰɨɜ ɥɢɧɢɢ ɩɨ ɨɫɢ ܺଵ ɞɨ ɩɨɹɜɥɟɧɢɹ ɩɪɹɦɨɣ ɧɚ ɝɪɚɮɢɤɟ. 75 Powered by TCPDF (www.tcpdf.org)

2. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ MS Excel

ȿɫɥɢ ɜ ɩɟɪɜɨɦ ɭɪɚɜɧɟɧɢɢ ɩɪɹɦɨɣ ɤɨɷɮɮɢɰɢɟɧɬ ܽଵଵ ɩɪɢɪɚɜɧɹɬɶ ɤ 8, ɬɨ ɦɨɞɟɥɢɪɭɟɬɫɹ ɫɥɭɱɚɣ, ɤɨɝɞɚ ɥɢɧɢɹ ɰɟɥɟɜɨɣ ɮɭɧɤɰɢɢ ɫɨɩɪɢɤɚɫɚɟɬɫɹ ɧɟ ɫ ɨɞɧɨɣ ɬɨɱɤɨɣ, ɚ ɫɨ ɫɬɨɪɨɧɨɣ Ⱥɋ ɨɛɥɚɫɬɢ ɪɟɲɟɧɢɣ. ɉɪɢ ɷɬɨɦ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɧɟ ɬɨɱɤɨɣ, ɚ ɞɢɚɩɚɡɨɧɨɦ ɡɧɚɱɟɧɢɣ 0 ”ܺଵ ”2,5 ɢ -1,25” ܺଶ ”3,75 ɩɪɢ ɡɧɚɱɟɧɢɢ ɰɟɥɟɜɨɣ ɮɭɧɤɰɢɢ 3,75. ɉɪɢ ɠɟɥɚɧɢɢ ɦɨɠɧɨ ɚɜɬɨɦɚɬɢɡɢɪɨɜɚɬɶ ɢɡɦɟɧɟɧɢɟ ɡɧɚɱɟɧɢɹ ‫ܨ‬଴ (ɋ13). ȼɚɪɢɚɧɬ 2. ɋɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɟɫɥɢ ɨɛɥɚɫɬɶ ɞɨɩɭɫɬɢɦɵɯ ɪɟɲɟɧɢɣ ɢɦɟɟɬ ɛɨɥɶɲɟ ɬɪɟɯ ɫɬɨɪɨɧ, ɬɨ ɩɪɢ ɪɚɫɫɦɨɬɪɟɧɧɨɦ ɩɨɞɯɨɞɟ ɧɭɠɟɧ ɞɨɩɨɥɧɢɬɟɥɶɧɵɣ ɚɥɝɨɪɢɬɦ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɬɨɱɟɤ ɜɟɪɲɢɧ ɦɧɨɝɨɭɝɨɥɶɧɢɤɚ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɢɯ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɵɦ ɪɚɫɩɨɥɨɠɟɧɢɟɦ, ɩɨɥɭɱɚɟɦɵɦ ɩɪɢ ɨɩɪɟɞɟɥɟɧɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ ɨɛɯɨɞɚ ɜɟɪɲɢɧ ɦɧɨɝɨɭɝɨɥɶɧɢɤɚ. Ɍɚɤ ɤɚɤ ɚɥɝɨɪɢɬɦ ɩɨɫɬɪɨɟɧɢɹ ɦɧɨɝɨɭɝɨɥɶɧɢɤɚ ɨɛɥɚɫɬɢ ɞɨɩɭɫɬɢɦɵɯ ɪɟɲɟɧɢɣ ɩɨ ɤɨɨɪɞɢɧɚɬɚɦ ɟɝɨ ɜɟɪɲɢɧ ɜ ɨɛɳɟɦ ɫɥɭɱɚɟ ɫɥɨɠɟɧ, ɬɨ ɰɟɥɟɫɨɨɛɪɚɡɧɨ ɨɛɥɚɫɬɶ ɪɟɲɟɧɢɣ ɨɩɪɟɞɟɥɹɬɶ ɝɪɚɮɢɱɟɫɤɢ ɩɨɫɥɟ ɩɨɫɬɪɨɟɧɢɹ ɟɟ ɥɢɧɢɣ ɫɬɨɪɨɧ ɧɚ ɝɪɚɮɢɤɟ. ɉɟɪɜɨɧɚɱɚɥɶɧɨ ɧɟɨɛɯɨɞɢɦɨ ɨɩɪɟɞɟɥɢɬɶ ɞɢɚɩɚɡɨɧ ɤɨɨɪɞɢɧɚɬ ɨɛɥɚɫɬɢ ɨɝɪɚɧɢɱɟɧɢɣ. ɉɨɫɥɟ ɡɚɞɚɧɢɹ ɤɨɨɪɞɢɧɚɬ ɩɪɹɦɵɯ ɩɨ ܺଵ ɦɨɠɧɨ ɜɵɱɢɫɥɢɬɶ ɡɧɚɱɟɧɢɹ ɤɨɨɪɞɢɧɚɬ ɩɨܺଶ ɩɨ ɮɨɪɦɭɥɟ ܺଶ ൌ ሺܾ௜ െ ܽ௜ଵ ‫כ‬ ܺଵ ሻȀܽ௜ଶ ɞɥɹ ɞɜɭɯ ɤɨɧɰɨɜ ɤɚɠɞɨɣ ɥɢɧɢɢ ɝɪɚɧɢɰ. Ɉɬɨɛɪɚɡɢɜ ɧɚ ɝɪɚɮɢɤɟ ɩɪɹɦɵɟ ɫ ɭɱɟɬɨɦ ɡɧɚɤɨɜ ɨɝɪɚɧɢɱɟɧɢɣ, ɨɤɚɧɬɨɜɵɜɚɟɦ ɨɛɥɚɫɬɶ ɞɨɩɭɫɬɢɦɵɯ ɪɟɲɟɧɢɣ ɫ ɩɨɦɨɳɶɸ ɢɧɫɬɪɭɦɟɧɬɚ ɉɨɥɢɥɢɧɢɹ ɫ ɩɚɧɟɥɢ Ɋɢɫɨɜɚɧɢɹ ɢ ɨɩɪɟɞɟɥɹɟɦ ɰɜɟɬ ɡɚɥɢɜɤɢ. Ⱦɚɥɟɟ ɦɨɠɧɨ ɡɚɧɹɬɶɫɹ ɨɬɨɛɪɚɠɟɧɢɟɦ ɥɢɧɢɢ ɭɪɨɜɧɹ ɰɟɥɟɜɨɣ ɮɭɧɤɰɢɢ. ȼ ɩɟɪɜɨɦ ɜɚɪɢɚɧɬɟ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɤɨɨɪɞɢɧɚɬɵ ɏ1 ɤɨɧɰɨɜ ɥɢɧɢɣ ɨɫɬɚɜɚɥɢɫɶ ɩɪɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ ɮɢɤɫɢɪɨɜɚɧɧɵɦɢ. ɏɨɬɹ ɢɧɨɝɞɚ ɧɟɨɛɯɨɞɢɦɨ ɩɪɨɜɨɞɢɬɶ ɤɨɪɪɟɤɬɢɪɨɜɤɭ ɡɧɚɱɟɧɢɣ ɤɨɨɪɞɢɧɚɬ ɤɨɧɰɨɜ ɥɢɧɢɢ ɞɥɹ ɢɫɤɥɸɱɟɧɢɹ ɟɟ ɜɵɯɨɞɚ ɢɡ ɨɛɥɚɫɬɢ ɩɨɫɬɪɨɟɧɢɹ ɝɪɚɮɢɤɚ. ɗɬɨ ɦɨɠɟɬ ɩɪɢɜɟɫɬɢ ɤ ɢɫɤɚɠɟɧɢɸ ɝɟɨɦɟɬɪɢɱɟɫɤɨɝɨ ɫɦɵɫɥɚ ɩɪɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ ɩɨɢɫɤɚ ɪɟɲɟɧɢɹ ɝɪɚɮɨɚɧɚɥɢɬɢɱɟɫɤɢɦ ɦɟɬɨɞɨɦ. ɉɪɢ ɢɡɦɟɧɟɧɢɢ ɡɧɚɱɟɧɢɹ ɭɪɨɜɧɹ ɰɟɥɟɜɨɣ ɮɭɧɤɰɢɢ ɟɟ ɥɢɧɢɹ ɩɟɪɟɦɟɳɚɟɬɫɹ ɩɨ ɜɟɤɬɨɪɭ ‫ ܥ‬ൌ ሺ‫ܥ‬ଵ ǡ ‫ܥ‬ଶ ሻ. Ⱦɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɩɚɪɚɥɥɟɥɶɧɨɝɨ ɫɦɟɳɟɧɢɹ ɨɝɪɚɧɢɱɟɧɧɨɣ ɩɨ ɞɥɢɧɟ ɥɢɧɢɢ ɰɟɥɟɜɨɣ ɮɭɧɤɰɢɢ ɨɬɧɨɫɢɬɟɥɶɧɨ ɧɚɱɚɥɶɧɨɝɨ ɩɨ76

2.1. Ɇɚɬɟɦɚɬɢɤɚ

ɥɨɠɟɧɢɹ ɢ ɮɢɤɫɚɰɢɢ ɟɟ ɞɥɢɧɵ ɧɭɠɧɨ ɜɵɱɢɫɥɢɬɶ ɢɡɦɟɧɟɧɢɹ ɤɨɨɪɞɢɧɚɬ ɟɟ ɤɨɧɰɨɜ ɫ ɭɱɟɬɨɦ ɤɨɨɪɞɢɧɚɬ ɜɟɤɬɨɪɚ ɋ. Ɏɢɤɫɢɪɭɟɦ ɧɚɱɚɥɶɧɨɟ ɩɨɥɨɠɟɧɢɟ ɥɢɧɢɢ ɰɟɥɟɜɨɣ ɮɭɧɤɰɢɢ ɞɥɹ ɧɚɛɥɸɞɟɧɢɹ ɞɢɧɚɦɢɤɢ ɞɜɢɠɟɧɢɹ ɥɢɧɢɢ ɤ ɨɛɥɚɫɬɢ ɪɟɲɟɧɢɹ ɩɪɢ ɡɚɞɚɧɧɨɦ ‫ܨ‬଴ . Ʉɨɨɪɞɢɧɚɬɵ ɤɨɧɰɨɜ ɞɜɢɠɭɳɟɣɫɹ ɥɢɧɢɢ ɭɪɨɜɧɹ ɜɵɱɢɫɥɹɟɦ ɩɨ ɮɨɪɦɭɥɚɦ ܺଵ ൌ ܺ଴ଵ ൅ ‫ܥ כ ܭ‬ଵ ɢ ܺଶ ൌ ܺ଴ଶ ൅ ‫ܥ כ ܭ‬ଶ . ɐɟɥɟɜɭɸ ɮɭɧɤɰɢɸ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɤɚɤ ‫ܨ‬ଵ ൌ ‫ܥ‬ଵ ‫ כ‬ሺܺ଴ଵ ൅ ‫ܥ כ ܭ‬ଵ ሻ ൅ ‫ܥ‬ଶ ‫ כ‬ሺܺ଴ଶ ൅ ‫ܥ כ ܭ‬ଶ ሻ, ɝɞɟ ‫ܨ‬ଵ ɟɫɬɶ ɧɨɜɨɟ ɡɧɚɱɟɧɢɟ ɭɪɨɜɧɹ ɰɟɥɟɜɨɣ ɮɭɧɤɰɢɢ. Ɂɧɚɱɟɧɢɹ ܺ଴ଵ ɢ ܺ଴ଶ ɨɩɪɟɞɟɥɹɸɬ ɧɚɱɚɥɶɧɨɟ ɩɨɥɨɠɟɧɢɟ ɥɢɧɢɢ ɩɪɢ ‫ܨ‬଴ . ɂɡ ɩɨɫɥɟɞɧɟɝɨ ɜɵɪɚɠɟɧɢɟ ɧɚɯɨɞɢɦ ɤɨɷɮɮɢɰɢɟɧɬ ‫ ܭ‬ൌ ሺ‫ܨ‬଴ െ ‫ܨ‬ଵ ሻȀሺ‫ܥ‬ଵଶ ൅ ‫ܥ‬ଶଶ ሻ ɢ ɜɵɱɢɫɥɹɟɦ ɤɨɨɪɞɢɧɚɬɵ ɤɨɧɰɨɜ ɥɢɧɢɢ ɰɟɥɟɜɨɣ ɮɭɧɤɰɢɢ. ɉɪɢ ɫɨɩɪɢɤɨɫɧɨɜɟɧɢɢ ɥɢɧɢɢ ɫ ɨɛɥɚɫɬɶɸ ɧɚɯɨɞɢɦ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ ɜ ɬɨɱɤɟ Ⱥ. Ɍɨ ɟɫɬɶ, ɩɨɥɭɱɚɟɦ ɡɧɚɱɟɧɢɟ ɰɟɥɟɜɨɣ ɮɭɧɤɰɢɢ ɢ ɡɧɚɱɟɧɢɹ ܺଵ ɢ ܺଶ . 2.1.14. ȼɵɱɢɫɥɟɧɢɟ ɱɢɫɥɚ ɩɢ ɦɟɬɨɞɨɦ Ⱥɪɯɢɦɟɞɚ Ⱥɪɯɢɦɟɞ ɜɩɟɪɜɵɟ ɩɪɟɞɥɨɠɢɥ ɚɧɚɥɢɬɢɱɟɫɤɢɣ ɦɟɬɨɞ ɜɵɱɢɫɥɟɧɢɹ ɱɢɫɥɚ ߨ ɩɭɬɟɦ ɪɚɫɱɟɬɚ ɩɟɪɢɦɟɬɪɨɜ ɜɩɢɫɚɧɧɵɯ ɢ ɨɩɢɫɚɧɧɵɯ ɩɪɚɜɢɥɶɧɵɯ ɦɧɨɝɨɭɝɨɥɶɧɢɤɨɜ ɜ ɨɤɪɭɠɧɨɫɬɶ ɫ ɟɞɢɧɢɱɧɵɦ ɪɚɞɢɭɫɨɦ. ȼɵɱɢɫɥɟɧɢɹ ɧɚɱɢɧɚɥɢɫɶ ɫ ɲɟɫɬɢɭɝɨɥɶɧɢɤɨɜ, ɡɚɬɟɦ ɱɢɫɥɨ ɫɬɨɪɨɧ ɦɧɨɝɨɭɝɨɥɶɧɢɤɨɜ ɭɞɜɚɢɜɚɥɨɫɶ, ɚ ɡɚɤɨɧɱɢɥɢɫɶ ɧɚ 96-ɬɢɭɝɨɥɶɧɢɤɚɯ. Ⱥɪɯɢɦɟɞ ɩɨɥɭɱɢɥ ɧɢɠɧɸɸ ɢ ɜɟɪɯɧɸɸ ɨɰɟɧɤɢ ɱɢɫɥɚ ߨ. ȼɫɟɦ ɢɡɜɟɫɬɧɨ, ɱɬɨ ɞɥɢɧɚ ɨɤɪɭɠɧɨɫɬɢ ɜɵɱɢɫɥɹY D ɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ ‫ ܮ‬ൌ ʹߨܴ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɱɢɫɥɨ A ߨ ൌ ‫ܮ‬Τʹܴ . ɉɟɪɢɦɟɬɪ ɦɧɨɝɨɭɝɨɥɶɧɢɤɚ, ɜɩɢɫɚɧɧɨɝɨ ɜ E B ɨɤɪɭɠɧɨɫɬɶ, ɞɚɟɬ ɩɪɢɛɥɢɠɟɧɧɭɸ ɨɰɟɧɤɭ ɞɥɢɧɵ ơ R X ɨɤɪɭɠɧɨɫɬɢ. ɉɪɢ ɷɬɨɦ ɩɟɪɢɦɟɬɪ ɛɭɞɟɬ ɦɟɧɶɲɟ ɞɥɢO C F ɧɵ ɨɤɪɭɠɧɨɫɬɢ. ɉɟɪɢɦɟɬɪ ɦɧɨɝɨɭɝɨɥɶɧɢɤɚ, ɨɩɢɫɚɧɧɨɝɨ ɜɨɤɪɭɝ ɨɤɪɭɠɧɨɫɬɢ, ɛɭɞɟɬ ɜɫɟɝɞɚ ɛɨɥɶɲɟ, ɱɟɦ ɞɥɢɧɚ ɨɤɪɭɠɧɨɫɬɢ. Ȼɭɞɟɦ ɜɵɱɢɫɥɹɬɶ ɱɢɫɥɨ ߨ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɪɚɫɱɟɬɨɜ ɩɟɪɢɦɟɬɪɨɜ ɜɩɢɫɚɧɧɨɝɨ ɢ ɨɩɢɫɚɧɧɨɝɨ ɦɧɨɝɨɭɝɨɥɶɧɢɤɨɜ. ɂɫɬɢɧɧɨɟ ɱɢɫɥɨ ߨ ɛɭɞɟɬ ɧɚɯɨɞɢɬɶɫɹ ɦɟɠɞɭ ɜɵɱɢɫɥɟɧɧɵɦɢ ɡɧɚɱɟɧɢɹɦɢ. ɉɪɚɜɢɥɶɧɵɟ ɦɧɨɝɨɭɝɨɥɶɧɢɤɢ ɫɨɫɬɨɹɬ ɢɡ ɪɚɜɧɨɛɟɞɪɟɧɧɵɯ ɬɪɟɭɝɨɥɶɧɢɤɨɜ OAC ɢ ODF, ɤɨɥɢɱɟɫɬɜɨ ɤɨɬɨɪɵɯ ɪɚɜɧɨ ɱɢɫɥɭ ɫɬɨɪɨɧ ɦɧɨɝɨɭɝɨɥɶɧɢɤɚ. Ⱦɥɹ ɜɵɱɢɫɥɟɧɢɹ ɩɟɪɢɦɟɬɪɚ ɦɧɨɝɨɭɝɨɥɶɧɢɤɚ ɧɭɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɟɝɨ ɨɫɧɨɜɚɧɢɟ ɢ ɭɦɧɨɠɢɬɶ ɧɚ ɱɢɫɥɨ ɫɬɨɪɨɧ n. ȼɨɫɩɨɥɶɡɭɟɦɫɹ ɬɪɢɝɨɧɨɦɟɬɪɢɱɟɫɤɢɦɢ ɮɭɧɤɰɢɹɦɢ. Ⱥɪɯɢɦɟɞ ɩɪɢ ɜɵɱɢɫɥɟɧɢɹɯ ɢɡɜɥɟɤɚɥ ɤɨɪɧɢ ɩɪɢ ɨɩɪɟɞɟɥɟɧɢɢ ɞɥɢɧ ɫɬɨɪɨɧ. Ɋɚɫɫɦɨɬɪɢɦ ɩɪɹɦɨɭɝɨɥɶɧɵɟ ɬɪɟɭɝɨɥɶɧɢɤɢ OBC ɢ OEF. ȿɫɥɢ ɭɝɨɥ ‫ן‬ൌ ʹߨȀ݊, ɬɨ ɦɨɠɟɦ ɡɚɩɢɫɚɬɶ ‫ ܤܣ‬ൌ ʹܴ •‹ሺߙΤʹሻ ɢ DFൌ ʹܴ –ƒሺߙΤʹሻ. ɉɨɥɭɱɚɟɦ ɩɟɪɢɦɟɬɪɵ ɜɩɢɫɚɧɧɨɝɨ ɦɧɨɝɨɭɝɨɥɶɧɢɤɚ ܲ˅˒ ൌ ‫ ݊ כ ܤܣ‬ɢ ɨɩɢɫɚɧɧɨɝɨ ɦɧɨ77

2. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ MS Excel

ɝɨɭɝɨɥɶɧɢɤɚ ܲˑ˒ ൌ ‫݊ כ ܨܦ‬. ɉɨɞɫɬɚɜɢɜ ɜɦɟɫɬɨ ɞɥɢɧɵ ɨɤɪɭɠɧɨɫɬɢ ɩɟɪɢɦɟɬɪɵ ɩɨɥɭɱɢɦ ɜɵɪɚɠɟɧɢɹ ɞɥɹ ɪɚɫɱɟɬɨɜ ɱɢɫɥɚ ߨ˅˒ ൌ ܲ˅˒Τʹܴ ɢ ߨˑ˒ ൌ ܲˑ˒Τʹܴ , ɤɨɬɨɪɵɟ ɨɩɪɟɞɟɥɹɸɬ ɧɢɠɧɢɟ ɢ ɜɟɪɯɧɢɟ ɡɧɚɱɟɧɢɹ ɱɢɫɥɚ ߨ . Ɏɚɤɬɢɱɟɫɤɢ ɜ ɪɟɡɭɥɶɬɚɬɟ ɪɚɫɱɟɬɨɜ ɩɨɥɭɱɢɦ ɝɪɚɧɢɰɵ, ɜ ɤɨɬɨɪɵɯ ɛɭɞɟɬ ɧɚɯɨɞɢɬɶɫɹ ɢɫɬɢɧɧɨɟ ɡɧɚɱɟɧɢɟ ʌ: ߨ˅˒ ൏ ߨ ൏ ߨˑ˒ . Ɍɟɩɟɪɶ ɦɨɠɧɨ ɩɟɪɟɯɨɞɢɬɶ ɤ ɪɟɚɥɢɡɚɰɢɢ ɜɵɱɢɫɥɟɧɢɹ ɱɢɫɥɚ ʌ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ MS Excel. ȼ ɹɱɟɣɤɟ ɋ1 ɡɚɞɚɞɢɦ ɡɧɚɱɟɧɢɟ ɪɚɞɢɭɫɚ ɨɤɪɭɠɧɨɫɬɢ, ɜ ɹɱɟɣɤɭ ɋ2 ɛɭɞɟɦ ɡɚɧɨɫɢɬɶ ɱɢɫɥɨ ɝɪɚɧɟɣ ɦɧɨɝɨɭɝɨɥɶɧɢɤɨɜ, ɚ ɜ ɹɱɟɣɤɢ ɋ3 ɛɭɞɟɦ ɪɚɫɫɱɢɬɵɜɚɬɶ ɡɧɚɱɟɧɢɟ ɭɝɥɚ ‫ן‬. ȼ ɹɱɟɣɤɟ ɋ4 ɜɵɱɢɫɥɢɦ ɪɚɞɢɭɫ ɨɩɢɫɚɧɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɞɥɹ ɜɧɟɲɧɟɝɨ ɦɧɨɝɨɭɝɨɥɶɧɢɤɚ ɩɟɪɜɨɧɚɱɚɥɶɧɨɣ ɨɤɪɭɠɧɨɫɬɢ. ɗɬɨɬ ɪɚɞɢɭɫ ܴˑ˒ ɦɨɠɧɨ ɧɚɣɬɢ ɢɡ ɬɪɟɭɝɨɥɶɧɢɤɚ OEF ܴˑ˒ ൌ ܱ‫ ܨ‬ൌ ܴ Τ…‘•ሺ ‫ן‬Τʹሻ. ɗɬɨ ɩɨɡɜɨɥɢɬ ɭɧɢɮɢɰɢɪɨɜɚɬɶ ɮɨɪɦɭɥɵ ɪɚɫɱɟɬɚ ɤɨɨɪɞɢɧɚɬ ɜɟɪɲɢɧ ɦɧɨɝɨɭɝɨɥɶɧɢɤɨɜ. ȼ ɹɱɟɣɤɟ ɋ5 ɜɵɱɢɫɥɢɦ ɡɧɚɱɟɧɢɟ ߨ˅˒ ɩɨ ɮɨɪɦɭɥɟ ߨ˅˒ ൌ ݊ •‹ ߨΤ݊, ɚ ɜ ɹɱɟɣɤɟ ɋ6 ɡɧɚɱɟɧɢɟ ߨˑ˒ ɩɨ ɮɨɪɦɭɥɟ ߨˑ˒ ൌ ݊ –ƒ ߨΤ݊. Ɏɨɪɦɭɥɵ ɩɨɥɭɱɚɸɬɫɹ ɩɨɫɥɟ ɩɨɞɫɬɚɧɨɜɤɢ ɜɵɪɚɠɟɧɢɣ ɞɥɹ ɩɟɪɢɦɟɬɪɨɜ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɦɧɨɝɨɭɝɨɥɶɧɢɤɨɜ. Ⱦɥɹ ɫɨɩɨɫɬɚɜɥɟɧɢɹ ɜɵɱɢɫɥɟɧɧɵɯ ɡɧɚɱɟɧɢɣ ɱɢɫɥɚ ߨ ɜ ɹɱɟɣɤɭ F1 ɡɚɧɨɫɢɦ ɡɧɚɱɟɧɢɟ ɉɂ(), ɤɨɬɨɪɨɟ ɢɫɩɨɥɶɡɭɟɬɫɹ ɜ MS Excel, ɫ ɦɚɤɫɢɦɚɥɶɧɵɦ ɡɧɚɱɟɧɢɟɦ ɱɢɫɥɚ ɪɚɡɪɹɞɨɜ ɩɨɫɥɟ ɡɚɩɹɬɨɣ (ɜ ɧɟɦ ɬɨɥɶɤɨ 14 ɡɧɚɤɨɜɵɯ ɪɚɡɪɹɞɨɜ ɩɨɫɥɟ ɡɚɩɹɬɨɣ). Ⱦɥɹ ɝɪɚɮɢɱɟɫɤɨɝɨ ɢɡɨɛɪɚɠɟɧɢɹ ɜɩɢɫɵɜɚɟɦɵɯ ɢ ɨɩɢɫɵɜɚɟɦɵɯ ɩɪɚɜɢɥɶɧɵɯ ɦɧɨɝɨɭɝɨɥɶɧɢɤɨɜ ɜ ɨɤɪɭɠɧɨɫɬɶ ɧɭɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɤɨɨɪɞɢɧɚɬɵ ɜɟɪɲɢɧ ɦɧɨɝɨɭɝɨɥɶɧɢɤɨɜ. ɐɟɥɟɫɨɨɛɪɚɡɧɨ ɢɯ ɩɟɪɜɨɧɚɱɚɥɶɧɨ ɡɚɞɚɬɶ ɜ ɩɨɥɹɪɧɨɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ, ɚ ɡɚɬɟɦ ɜɵɱɢɫɥɢɬɶ ɜ ɩɪɹɦɨɭɝɨɥɶɧɨɣ ɫɢɫɬɟɦɟ ɤɨɨɪɞɢɧɚɬ. ɉɨɥɹɪɧɵɟ ɤɨɨɪɞɢɧɚɬɵ ɜɟɪɲɢɧ ɡɚɞɚɸɬɫɹ ɪɚɞɢɭɫɨɦ ɨɤɪɭɠɧɨɫɬɢ ܴ ɢ ɩɨɥɹɪɧɵɦ ɭɝɥɨɦ ߮௜ ൌ ݅ߙ, ɝɞɟ ݅ ൌ Ͳǡ ǥ ǡ ݊. ɍɝɨɥ ߮௜ ɨɬɫɱɢɬɵɜɚɟɦ ɨɬ ɨɫɢ ‫ ݔ‬ɜ ɩɨɥɨɠɢɬɟɥɶɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ (ɩɪɨɬɢɜ ɱɚɫɨɜɨɣ ɫɬɪɟɥɤɢ). ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɧɭɥɟɜɚɹ ɢɥɢ ɩɟɪɜɚɹ ɤɨɨɪɞɢɧɚɬɚ ɛɭɞɟɬ ɜɫɟɝɞɚ ɩɪɢɜɹɡɚɧɚ ɤ ɨɫɢ ‫ݔ‬. Ʉɨɥɢɱɟɫɬɜɨ ɜɵɱɢɫɥɹɟɦɵɯ ɤɨɨɪɞɢɧɚɬ ɪɚɜɧɨ ݊ ൅ ͳ. ɗɬɨ ɩɨɡɜɨɥɹɟɬ ɡɚɦɤɧɭɬɶ ɮɢɝɭɪɭ ɦɧɨɝɨɭɝɨɥɶɧɢɤɚ. ɉɟɪɟɫɱɟɬ ɤɨɨɪɞɢɧɚɬ ɜɟɪɲɢɧ ɜ ɩɪɹɦɨɭɝɨɥɶɧɭɸ ɫɢɫɬɟɦɭ ɨɫɭɳɟɫɬɜɥɹɟɦ ɩɨ ɮɨɪɦɭɥɚɦ ‫ݔ‬௜ ൌ ܴ …‘• ߮௜ ,‫ݕ‬௜ ൌ ܴ •‹ ߮௜ . Ɉɫɬɚɟɬɫɹ ɨɩɪɟɞɟɥɢɬɶ ɪɚɡɦɟɪɵ ɦɚɫɫɢɜɨɜ ɤɨɨɪɞɢɧɚɬ ɞɥɹ ɢɡɨɛɪɚɠɟɧɢɹ ɨɤɪɭɠɧɨɫɬɢ ɢ ɦɧɨɝɨɭɝɨɥɶɧɢɤɨɜ. ɐɟɥɟɫɨɨɛɪɚɡɧɨ ɫɧɚɱɚɥɚ ɢɡɨɛɪɚɡɢɬɶ ɬɪɟɭɝɨɥɶɧɢɤɢ, ɡɚɬɟɦ ɱɟɬɵɪɟɯɭɝɨɥɶɧɢɤɢ ɢ ɬ.ɞ. Ʉɚɤ ɩɨɤɚɡɵɜɚɟɬ ɩɪɚɤɬɢɤɚ, ɨɤɪɭɠɧɨɫɬɶ ɜ Excel ɯɨɪɨɲɨ ɢɡɨɛɪɚɠɚɟɬɫɹ ɦɧɨɝɨɭɝɨɥɶɧɢɤɨɦ ɫ ɱɢɫɥɨɦ ɫɬɨɪɨɧ 12-20. ȼ ɷɬɨɦ ɦɨɠɧɨ ɭɛɟɞɢɬɶɫɹ ɜ ɯɨɞɟ ɦɨɞɟɥɢɪɨɜɚɧɢɹ. ɉɨɷɬɨɦɭ ɜɵɛɟɪɟɦ ɦɚɫɫɢɜɵ ɫ 25 ɫɬɪɨɤɚɦɢ. ɏɨɬɹ ɧɭɠɧɨ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɷɬɨ ɜɟɪɧɨ ɞɥɹ 78

2.1. Ɇɚɬɟɦɚɬɢɤɚ

ɢɡɨɛɪɚɠɟɧɢɹ ɨɤɪɭɠɧɨɫɬɢ. Ⱦɥɹ ɢɡɨɛɪɚɠɟɧɢɹ ɦɧɨɝɨɭɝɨɥɶɧɢɤɨɜ ɪɚɡɦɟɪɵ ɦɚɫɫɢɜɨɜ ɡɚɜɢɫɹɬ ɨɬ ɤɨɥɢɱɟɫɬɜɚ ɫɬɨɪɨɧ. Ɉɞɧɚɤɨ ɟɫɥɢ ɤɨɥɢɱɟɫɬɜɨ ɫɬɨɪɨɧ ɛɭɞɟɬ ɦɟɧɶɲɟ 24, ɬɨ ɧɟɤɨɬɨɪɵɟ ɡɧɚɱɟɧɢɹ ɤɨɨɪɞɢɧɚɬ ɛɭɞɭɬ ɩɨɜɬɨɪɹɬɶɫɹ. ɇɨ ɢɫɤɚɠɟɧɢɹ ɢɡɨɛɪɚɠɟɧɢɹ ɧɟ ɛɭɞɟɬ. ȿɫɥɢ ɤɨɥɢɱɟɫɬɜɨ ɫɬɨɪɨɧ ɛɭɞɟɬ ɛɨɥɶɲɟ 24, ɬɨ ɦɧɨɝɨɭɝɨɥɶɧɢɤ ɧɟ ɛɭɞɟɬ ɢɡɨɛɪɚɠɟɧ ɩɨɥɧɨɫɬɶɸ. Ⱦɥɹ ɢɡɨɛɪɚɠɟɧɢɹ ɨɤɪɭɠɧɨɫɬɢ ɢ ɦɧɨɝɨɭɝɨɥɶɧɢɤɨɜ ɧɭɠɧɨ ɪɚɡɞɟɥɢɬɶ ɦɚɫɫɢɜɵ ɩɭɫɬɨɣ ɫɬɪɨɤɨɣ. ȼɵɞɟɥɹɟɦ ɞɥɹ ɜɩɢɫɚɧɧɨɝɨ ɦɧɨɝɨɭɝɨɥɶɧɢɤɚ ɦɚɫɫɢɜ A10:D34, ɨɩɢɫɚɧɧɨɝɨ ɦɧɨɝɨɭɝɨɥɶɧɢɤɚ – A36:D60, ɚ ɞɥɹ ɨɤɪɭɠɧɨɫɬɢ – A62:D86. ɋɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɞɥɹ ɩɨɫɬɪɨɟɧɢɹ ɨɤɪɭɠɧɨɫɬɢ ɲɚɝ ɩɨɥɹɪɧɨɝɨ ɭɝɥɚ ɪɚɜɟɧ ʹߨȀʹͶ. ɉɨɫɥɟ ɨɫɭɳɟɫɬɜɥɟɧɢɹ ɪɚɫɱɟɬɨɜ ɜɵɞɟɥɹɟɦ ɫɬɨɥɛɰɵ ‫ݔ‬௜ ɢ ‫ݕ‬௜ ɢ ɫɬɪɨɢɦ ɞɢɚɝɪɚɦɦɭ Ɍɨɱɟɱɧɚɹ ɫ ɩɪɹɦɵɦɢ ɨɬɪɟɡɤɚɦɢ ɢ ɦɚɪɤɟɪɚɦɢ, ɞɨɛɚɜɥɹɟɦ ɥɢɧɢɢ ɫɟɬɤɢ ɢ ɪɚɫɬɹɝɢɜɚɟɦ ɨɛɥɚɫɬɶ ɩɨɫɬɪɨɟɧɢɹ ɞɥɹ ɩɪɚɜɢɥɶɧɨɝɨ ɢɡɨɛɪɚɠɟɧɢɹ ɨɤɪɭɠɧɨɫɬɢ ɢ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɦɧɨɝɨɭɝɨɥɶɧɢɤɨɜ. ȼ ɧɚɡɜɚɧɢɟ ɞɢɚɝɪɚɦɦɵ ɦɨɠɧɨ ɜɧɟɫɬɢ ɞɚɧɧɵɟ ɨ ɡɚɞɚɧɧɨɦ ɤɨɥɢɱɟɫɬɜɟ ɫɬɨɪɨɧ ɦɧɨɝɨɭɝɨɥɶɧɢɤɨɜ (ɋ2) ɢ ɜɵɱɢɫɥɟɧɧɵɯ ɡɧɚɱɟɧɢɹɯ ɱɢɫɥɚ ߨ (ɋ5 ɢ ɋ6). Ⱦɥɹ ɷɬɨɝɨ ɧɭɠɧɨ ɜɨ ɜɫɩɨɦɨɝɚɬɟɥɶɧɵɯ ɹɱɟɣɤɚɯ Ʉ6:Ʉ8 ɫɮɨɪɦɢɪɨɜɚɬɶ ɧɟɨɛɯɨɞɢɦɭɸ ɢɧɮɨɪɦɚɰɢɸ. əɱɟɣɤɢ ɮɨɪɦɚɬɢɪɭɟɦ ɤɚɤ ɬɟɤɫɬɨɜɵɟ. ɉɭɫɬɶ ɜ ɧɚɡɜɚɧɢɢ ɦɧɨɝɨɭɝɨɥɶɧɢɤɟ ɛɭɞɟɬ ɱɢɫɥɨ ɤɨɥɢɱɟɫɬɜɚ ɫɬɨɪɨɧ, ɞɟɮɢɫ, ɢ ɫɥɨɜɨ «ɭɝɨɥɶɧɢɤ». Ɍɚɤɠɟ ɜɵɱɢɫɥɟɧɧɵɟ ɡɧɚɱɟɧɢɹ ɱɢɫɥɚ ߨ.. Ɉɫɬɚɟɬɫɹ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɮɭɧɤɰɢɢ ɋɐȿɉɂɌɖ ɫɮɨɪɦɢɪɨɜɚɬɶ ɤɨɧɬɟɤɫɬ, ɤɨɬɨɪɵɣ ɛɭɞɟɬ ɜɵɜɟɞɟɧ ɜ ɷɥɟɦɟɧɬɟ ɞɢɚɝɪɚɦɦɵ ɇɚɡɜɚɧɢɟ ɞɢɚɝɪɚɦɦɵ. ȼ ɨɞɧɨɣ ɹɱɟɣɤɟ G3 ɞɥɹ ɩɪɨɫɬɨɬɵ ɫɨɡɞɚɞɢɦ ɧɚɡɜɚɧɢɟ ɦɧɨɝɨɭɝɨɥɶɧɢɤɚ c ɩɨɦɨɳɶɸ ɫɥɟɞɭɸɳɟɝɨ ɜɵɪɚɠɟɧɢɹ =ɋɐȿɉɂɌɖ(C2;K6). ȼ ɹɱɟɣɤɟ G4 ɨɤɨɧɱɚɬɟɥɶɧɨ ɫɨɡɞɚɟɦ ɩɨɥɧɵɣ ɤɨɧɬɟɤɫɬ ɫ ɨɰɟɧɤɚɦɢ ߨ˅˒ ɢ ߨˑ˒ =ɋɐȿɉɂɌɖ(G3;" ";K7;C5;" ";K8;C6). ɑɬɨɛɵ ɪɚɫɩɨɥɨɠɢɬɶ ɡɧɚɱɟɧɢɹ ɱɢɫɥɚ ߨ ɜɨ ɜɬɨɪɨɣ ɢ ɬɪɟɬɶɟɣ ɫɬɪɨɤɟ ɧɚɡɜɚɧɢɹ ɧɟɨɛɯɨɞɢɦɨ ɭɜɟɥɢɱɢɬɶ ɩɟɪɜɵɣ ɩɪɨɛɟɥ. ɓɟɥɤɚɟɦ ɩɨ ɨɛɴɟɤɬɭ ɇɚɡɜɚɧɢɟ ɞɢɚɝɪɚɦɦɵ ɢ ɜ ɋɬɪɨɤɟ ɮɨɪɦɭɥ ɡɚɧɨɫɢɦ ɡɧɚɤ ɪɚɜɟɧɫɬɜɚ ɢ ɚɞɪɟɫ ɹɱɟɣɤɢ ɫ ɤɨɧɬɟɤɫɬɨɦ, ɳɟɥɤɚɟɦ ɩɨ Enter. Ʉɨɧɬɟɤɫɬ ɧɚɡɜɚɧɢɹ ɛɭɞɟɬ ɢɡɦɟɧɹɬɶɫɹ ɩɪɢ ɫɦɟɧɟ ɤɨɥɢɱɟɫɬɜɚ ɫɬɨɪɨɧ ɦɧɨɝɨɭɝɨɥɶɧɢɤɨɜ. ȼ ɯɨɞɟ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɦɨɠɧɨ ɧɟ ɬɨɥɶɤɨ ɭɜɢɞɟɬɶ ɧɢɠɧɸɸ ɢ ɜɟɪɯɧɸɸ ɝɪɚɧɢɰɵ ɱɢɫɥɚ ߨ, ɪɚɫɫɱɢɬɚɧɧɵɯ ɩɨ ɦɟɬɨɞɭ Ⱥɪɯɢɦɟɞɚ, ɧɨ ɢ ɨɩɪɟɞɟɥɢɬɶɫɹ ɫ ɤɨɥɢɱɟɫɬɜɨɦ ɫɬɨɪɨɧ ɦɧɨɝɨɭɝɨɥɶɧɢɤɚ ɞɥɹ ɜɢɡɭɚɥɶɧɨɝɨ ɢɡɨɛɪɚɠɟɧɢɹ ɨɤɪɭɠɧɨɫɬɢ ɩɪɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ. Ⱦɥɹ ɢɡɭɱɟɧɢɹ ɜɨɩɪɨɫɚ ɫɯɨɞɢɦɨɫɬɢ ɨɰɟɧɨɤ ɱɢɫɥɚ ߨ ɨɬ ɱɢɫɥɚ ɫɬɨɪɨɧ ɦɧɨɝɨɭɝɨɥɶɧɢɤɨɜ ɫɨɡɞɚɞɢɦ ɬɚɛɥɢɰɭ ɪɚɫɱɟɬɚ ߨ˅˒ ɢ ߨˑ˒ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ݊. Ɂɚɬɟɦ ɩɨ ɞɚɧɧɵɦ ɬɚɛɥɢɰɵ ɫɬɪɨɢɦ ɝɪɚɮɢɤɢ, ɝɞɟ ɧɚɝɥɹɞɧɨ ɭɜɢɞɢɦ ɫɯɨɞɢɦɨɫɬɶ ɨɰɟɧɨɤ. Ʉɨɥɢɱɟɫɬɜɨ ɫɬɪɨɤ ɜ ɦɚɫɫɢɜɟ ɜɨɡɶɦɟɦ 94. ɗɬɨ ɨɛɟɫɩɟɱɢɬ ɜɵɱɢɫɥɟɧɢɹ ɨɬ ɬɪɟɭɝɨɥɶɧɢɤɨɜ ɞɨ 9679

2. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ MS Excel

ɭɝɨɥɶɧɢɤɨɜ ɫ ɲɚɝɨɦ ɪɚɜɧɵɦ 1. Ⱦɥɹ ɚɜɬɨɦɚɬɢɡɚɰɢɢ ɢɫɫɥɟɞɨɜɚɧɢɣ ɜɵɞɟɥɢɦ ɹɱɟɣɤɭ ɞɥɹ ɧɚɱɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ ɫɬɨɪɨɧ Q3 ɢ ɲɚɝɚ ɢɡɦɟɧɟɧɢɹ ɢɯ ɤɨɥɢɱɟɫɬɜɚ Q4. ȼ ɧɚɱɚɥɶɧɨɣ ɹɱɟɣɤɟ ɦɚɫɫɢɜɚ N10 ɡɚɧɨɫɢɦ ɧɚɱɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ, ɚ ɜ ɩɨɫɥɟɞɭɸɳɢɯ ɹɱɟɣɤɚɯ ɭɜɟɥɢɱɢɜɚɟɦ ɤɨɥɢɱɟɫɬɜɨ ɫɬɨɪɨɧ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɲɚɝɚ ɢ ɡɧɚɱɟɧɢɹ ɜ ɩɪɟɞɵɞɭɳɟɣ ɹɱɟɣɤɟ. Ɋɚɫɱɟɬ ɨɰɟɧɨɤ ɱɢɫɥɚ ߨ ɨɫɭɳɟɫɬɜɥɹɟɦ ɩɨ ɮɨɪɦɭɥɚɦ ɩɪɢɜɟɞɟɧɧɵɦ ɜɵɲɟ. Ɍɚɤɠɟ ɮɨɪɦɢɪɭɟɦ ɫɬɨɥɛɟɰ ɡɧɚɱɟɧɢɹ ɱɢɫɥɚ ߨ. Ɂɚɞɚɞɢɦ ɧɚɱɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɫɬɨɪɨɧ ɦɧɨɝɨɭɝɨɥɶɧɢɤɨɜ ɪɚɜɧɨɟ 6 ɢ ɲɚɝ 1. ȼɵɞɟɥɢɦ ɜɫɟ ɫɬɨɥɛɰɵ ɬɚɛɥɢɰɵ ɞɥɹ ɩɨɫɬɪɨɟɧɢɹ ɞɢɚɝɪɚɦɦɵ Ɍɨɱɟɱɧɚɹ ɫ ɩɪɹɦɵɦɢ ɨɬɪɟɡɤɚɦɢ. Ɇɨɠɧɨ ɩɪɨɢɡɜɟɫɬɢ ɧɟɨɛɯɨɞɢɦɨɟ ɮɨɪɦɚɬɢɪɨɜɚɧɢɟ ɷɥɟɦɟɧɬɨɜ ɞɢɚɝɪɚɦɦɵ ɞɥɹ ɭɥɭɱɲɟɧɢɹ ɧɚɝɥɹɞɧɨɫɬɢ. ɇɚ ɝɪɚɮɢɤɟ ɧɚɛɥɸɞɚɟɦ ɫɯɨɞɢɦɨɫɬɶ ɨɰɟɧɨɤ ɤ ɱɢɫɥɭ ߨ. ɉɨ ɞɚɧɧɵɦ ɜ ɬɚɛɥɢɰɟ ɢ ɧɚ ɝɪɚɮɢɤɚɯ ɜɢɞɢɦ, ɱɬɨ ɜ ɪɚɣɨɧɟ ɤɨɥɢɱɟɫɬɜɚ ɫɬɨɪɨɧ ɪɚɜɧɵɦ 60 ɩɨɥɭɱɚɟɦ ɜɫɟɦ ɩɪɢɜɵɱɧɨɟ ɱɢɫɥɨ ߨ ൌ ͵ǡͳͶ. ɉɨɫɥɟ ɢɡɦɟɧɟɧɢɹ ɮɨɪɦɚɬɚ ɹɱɟɟɤ ɪɚɫɱɟɬɚ ɨɰɟɧɨɤ ɧɚ ɬɢɩ Ⱦɪɨɛɹɦɢ ɞɨ ɞɜɭɯ ɰɢɮɪ ɩɨɥɭɱɚɟɦ ɫɚɦɨɟ ɢɧɬɟɪɟɫɧɨɟ. ȼɢɞɢɦ ɱɢɫɥɚ ɡɧɚɦɟɧɢɬɨɝɨ ɧɟɪɚɜɟɧɫɬɜɚ Ⱥɪɯɢɦɟɞɚ ͵ ൅ ͳͲΤ͹ͳ ൏ ߨ ൏ ͵ ൅ ͳΤ͹. ȼɟɪɯɧɹɹ ɝɪɚɧɢɰɚ ɧɟɪɚɜɟɧɫɬɜɚ ʹʹΤ͹ ɧɨɫɢɬ ɧɚɡɜɚɧɢɟ Ⱥɪɯɢɦɟɞɨɜɨ ɱɢɫɥɨ. ȿɫɥɢ ɩɪɢ ɩɨɞɫɱɟɬɟ ɞɥɢɧɵ ɷɤɜɚɬɨɪɚ Ɂɟɦɥɢ ɢɫɩɨɥɶɡɨɜɚɬɶ ɨɰɟɧɤɢ ߨ˅˒ ɢ ߨˑ˒ , ɩɨɥɭɱɟɧɧɵɟ ɩɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ 96-ɦɧɨɝɨɭɝɨɥɶɧɢɤɨɜ, ɬɨ ɨɲɢɛɤɢ ɛɭɞɭɬ ɫɨɫɬɚɜɥɹɬɶ -7ɤɦ ɢ 14 ɤɦ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɞɥɹ ɧɢɠɧɟɣ ɢ ɜɟɪɯɧɟɣ ɨɰɟɧɤɢ ɱɢɫɥɚ ߨ. Ɉɰɟɧɤɢ ɫɨɜɩɚɞɚɸɬ ɫ ɱɢɫɥɨɦ ߨ ɞɨ 2 ɡɧɚɤɚ ɩɨɫɥɟ ɡɚɩɹɬɨɣ (ߨ˅˒ ൌ ߨˑ˒ ൌ ߨ ൌ ͵ǡͳͶ). ɉɪɢ ɡɚɞɚɧɢɢ ɦɧɨɝɨɭɝɨɥɶɧɢɤɨɜ ɫ ɱɢɫɥɨɦ ɫɬɨɪɨɧ ɛɨɥɟɟ 6000 ɩɨɥɭɱɢɦ ɨɰɟɧɤɢ, ɤɨɬɨɪɵɟ ɛɭɞɭɬ ɫɨɜɩɚɞɚɬɶ ɞɨ 6-7 ɡɧɚɤɨɜ ɩɨɫɥɟ ɡɚɩɹɬɨɣ. ɂɦɟɸɬɫɹ ɞɪɭɝɢɟ ɚɥɝɨɪɢɬɦɵ ɪɚɫɱɟɬɚ ɱɢɫɥɚ ߨ. ɉɪɢ ɠɟɥɚɧɢɢ ɢɯ ɦɨɠɧɨ ɫɪɚɜɧɢɬɶ ɫ ɚɥɝɨɪɢɬɦɨɦ Ⱥɪɯɢɦɟɞɚ. 2.1.15. ȼɵɱɢɫɥɟɧɢɟ ɱɢɫɥɚ ɩɢ ɦɟɬɨɞɨɦ Ɇɨɧɬɟ-Ʉɚɪɥɨ ɉɥɨɳɚɞɶ ɤɪɭɝɚ ܵˍ˓ ɫ ɟɞɢɧɢɱɧɵɦ ɪɚɞɢɭɫɨɦ ɪɚɜɧɚ ɱɢɫɥɭ ߨ. ɉɥɨɳɚɞɶ ɤɜɚɞɪɚɬɚ ܵˍ˅ ɨɩɢɫɚɧɧɨɝɨ ɜɨɤɪɭɝ ɤɪɭɝɚ ɫ ɟɞɢɧɢɱɧɵɦ ɪɚɞɢɭɫɨɦ ɪɚɜɧɚ ɱɟɬɵɪɟɦ. Ɇɟɬɨɞ Ɇɨɧɬɟ-Ʉɚɪɥɨ ɩɨɡɜɨɥɹɟɬ ɨɩɪɟɞɟɥɢɬɶ ɩɥɨɳɚɞɶ ɮɢɝɭɪɵ ɩɨ ɤɨɥɢɱɟɫɬɜɭ ɩɨɩɚɞɚɧɢɣ ɬɨɱɟɤ ɜ ɫɨɨɬɜɟɬɫɬɜɭɸɳɭɸ ɨɛɥɚɫɬɶ. Ʉɨɨɪɞɢɧɚɬɵ ɬɨɱɟɤ ɞɨɥɠɧɵ ɩɨɞɱɢɧɹɬɶɫɹ ɫɥɭɱɚɣɧɨɦɭ ɡɚɤɨɧɭ. ȼ ɧɚɲɟɦ ɫɥɭɱɚɟ – ɪɚɜɧɨɦɟɪɧɨɦɭ ɪɚɫɩɪɟɞɟɥɟɧɢɸ. ȿɫɥɢ ɜ ɤɜɚɞɪɚɬ ɩɨɩɚɥɨ ݊ˍ˅ ɬɨɱɟɤ, ɚ ɜ ɤɪɭɝ - ݊ˍ˓ ɬɨɱɟɤ, ɬɨ ɦɨɠɧɨ ɫɨɫɬɚɜɢɬɶ ɫɥɟɞɭɸɳɢɟ ɫɨɨɬɧɨɲɟɧɢɟ ܵˍ˓ Τܵˍ˅ ൌ ݊ˍ˓ Τ݊ˍ˅ . ɂɡ ɷɬɨɝɨ ɫɨɨɬɧɨɲɟɧɢɹ ɩɨɥɭ80

2.1. Ɇɚɬɟɦɚɬɢɤɚ

ɱɚɟɦ ߨ ൌ Ͷ ݊ˍ˓ Τ݊ˍ˅ . ɑɟɦ ɛɨɥɶɲɟ ɬɨɱɟɤ, ɬɟɦ ɬɨɱɧɟɟ ɛɭɞɟɬ ɪɟɡɭɥɶɬɚɬ ɪɚɫɱɟɬɚ ɱɢɫɥɚ ߨ. ɋɨɡɞɚɞɢɦ ɬɚɛɥɢɰɭ (A3:D1002) ɞɥɹ ɡɚɩɢɫɢ 1000 ɬɨɱɟɤ ɫɨ ɫɥɭɱɚɣɧɵɦɢ ɤɨɨɪɞɢɧɚɬɚɦ ɧɚ ɩɥɨɫɤɨɫɬɢ ɨɝɪɚɧɢɱɟɧɧɨɣ ɤɜɚɞɪɚɬɨɦ, ɤɨɬɨɪɵɣ ɨɩɢɫɚɧ ɜɨɤɪɭɝ ɤɪɭɝɚ ɫ ɟɞɢɧɢɱɧɵɦ ɪɚɞɢɭɫɨɦ. ɐɟɧɬɪ ɤɪɭɝɚ ɪɚɡɦɟɳɚɟɦ ɜ ɧɚɱɚɥɟ ɤɨɨɪɞɢɧɚɬ. Ⱦɥɹ ɮɨɪɦɢɪɨɜɚɧɢɹ ɤɨɨɪɞɢɧɚɬ ɬɨɱɟɤ ɢɫɩɨɥɶɡɭɟɦ ɮɭɧɤɰɢɸ ɋɅɑɂɋ(), ɤɨɬɨɪɚɹ ɝɟɧɟɪɢɪɭɟɬ ɩɨ ɪɚɜɧɨɦɟɪɧɨɦɭ ɡɚɤɨɧɭ ɜ ɞɢɚɩɚɡɨɧɟ ɬɨ 0 ɞɨ 1. Ʉɨɨɪɞɢɧɚɬɵ ɬɨɱɟɤ X ɢ Y ɝɟɧɟɪɢɪɭɸɬɫɹ ɜ ɞɢɚɩɚɡɨɧɟ ɨɬ -1 ɞɨ 1 ɫ ɩɨɦɨɳɶɸ ɜɵɪɚɠɟɧɢɹ (ɋɅɑɂɋ()0,5)*2, ɤɨɬɨɪɨɟ ɡɚɩɢɫɵɜɚɟɦ ɜ ɫɬɨɥɛɰɵ X ɢ Y ɬɚɛɥɢɰɵ. ȼ ɫɬɨɥɛɰɟ ɋ ɜɵɱɢɫɥɹɟɦ ɪɚɞɢɭɫ ɬɨɱɟɤ ܴ ൌ ሺܺ ଶ ൅ ܻ ଶ ሻ଴ǡହ ɨɬɧɨɫɢɬɟɥɶɧɨ ɧɚɱɚɥɚ ɤɨɨɪɞɢɧɚɬ, ɤɨɬɨɪɵɣ ɢɫɩɨɥɶɡɭɟɬɫɹ ɞɥɹ ɮɨɪɦɢɪɨɜɚɧɢɹ ɩɪɢɡɧɚɤɚ ɧɚɯɨɠɞɟɧɢɹ ɬɨɱɟɤ ɜ ɤɪɭɝɟ ɩɨ ɜɵɪɚɠɟɧɢɸ ȿɋɅɂ(R 10 Then MsgBox "Ʉɨɧɟɰ ɦɨɞɟɥɢɪɨɜɚɧɢɹ" ȼɵɞɚɱɚ ɫɨɨɛɳɟɧɢɹ End If End Sub. ɉɪɢ ɳɟɥɱɤɟ ɧɚ ɤɧɨɩɤɟ Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɬɪɚɟɤɬɨɪɢɢ ɲɚɪɢɤɨɜ ɩɪɨɢɡɜɨɞɢɬɶɫɹ ɪɚɫɱɟɬ ɬɟɤɭɳɢɯ ɤɨɨɪɞɢɧɚɬ ɩɪɚɜɨɝɨ ɲɚɪɢɤɚ ɞɨ ݅ ൐ ͳͲ, ɩɨɫɥɟ ɤɨɬɨɪɨɝɨ ɜɵɞɚɟɬɫɹ ɫɨɨɛɳɟɧɢɟ «Ʉɨɧɟɰ ɦɨɞɟɥɢɪɨɜɚɧɢɹ». Ɍɟɤɭɳɢɟ ɤɨɨɪɞɢɧɚɬɵ ɲɚɪɢɤɨɜ ɢ ɬɪɚɟɤɬɨɪɢɢ ɡɚɩɢɫɵɜɚɸɬɫɹ ɜ ɹɱɟɣɤɢ ɦɚɫɫɢɜɚ ɬɪɚɟɤɬɨɪɢɣ D12:E44, ɤɨɬɨɪɵɣ ɡɚɞɚɧ ɞɥɹ ɡɚɩɢɫɢ 11 ɬɨɱɟɤ ɬɪɚɟɤɬɨɪɢɢ. ȼ ɦɚɫɫɢɜɟ ɜɵɞɟɥɟɧɵ ɹɱɟɣɤɢ ɞɥɹ ɢɡɨɛɪɚɠɟɧɢɹ ɧɢɬɟɣ ɢ ɲɚɪɢɤɨɜ. Ɍɚɤ ɤɚɤ ɤɨɨɪɞɢɧɚɬɵ ɧɢɠɧɢɯ ɤɨɧɰɨɜ ɧɢɬɟɣ ɢ ɤɨɨɪɞɢɧɚɬ ɲɚɪɢɤɨɜ ɫɢɦɦɟɬɪɢɱɧɵ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ ɨɪɞɢɧɚɬ, ɬɨ ɜ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɹɱɟɣɤɢ ɤɨɩɢɪɭɸɬɫɹ ɤɨ152

2.2. Ɏɢɡɢɤɚ

ɨɪɞɢɧɚɬɵ ɫ ɨɛɪɚɬɧɵɦ ɡɧɚɤɨɦ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɩɨɥɭɱɚɟɦ ɢɡɨɛɪɚɠɟɧɢɟ ɬɪɚɟɤɬɨɪɢɢ ɡɚɪɹɠɟɧɧɵɯ ɲɚɪɢɤɨɜ, ɤɨɬɨɪɵɟ ɪɚɡɨɲɥɢɫɶ ɢ ɧɚɯɨɞɹɬɫɹ ɜ ɫɨɫɬɨɹɧɢɢ ɩɨɤɨɹ. Ⱦɥɹ ɢɡɨɛɪɚɠɟɧɢɹ ɫɬɪɨɢɦ ɞɢɚɝɪɚɦɦɭ Ɍɨɱɟɱɧɚɹ ɫ ɩɪɹɦɵɦɢ ɥɢɧɢɹɦɢ ɢ ɦɚɪɤɟɪɚɦɢ ɩɨ ɞɚɧɧɵɦ ɦɚɫɫɢɜɚ ɬɪɚɟɤɬɨɪɢɣ. ɉɪɨɢɡɜɨɞɢɦ ɮɨɪɦɚɬɢɪɨɜɚɧɢɟ ɨɬɞɟɥɶɧɵɯ ɷɥɟɦɟɧɬɨɜ ɞɢɚɝɪɚɦɦɵ. Ɉɫɬɚɸɬɫɹ ɢɧɬɟɪɟɫɧɵɟ ɜɨɩɪɨɫɵ, ɫɜɹɡɚɧɧɵɟ ɫ ɜɪɟɦɟɧɟɦ ɪɚɫɯɨɠɞɟɧɢɹ ɲɚɪɢɤɨɜ, ɢɯ ɭɫɤɨɪɟɧɢɟɦ ɢ ɫɤɨɪɨɫɬɶɸ. ɉɨɩɪɨɛɭɟɦ ɪɚɡɪɟɲɢɬɶ ɷɬɢ ɜɨɩɪɨɫɵ. ɉɨɫɬɪɨɢɦ ɝɪɚɮɢɤ ɢɡɦɟɧɟɧɢɹ ɫɢɥɵ Ʉɭɥɨɧɚ ɩɨ ɦɟɪɟ ɨɬɤɥɨɧɟɧɢɹ ɡɚɪɹɠɟɧɧɵɯ ɲɚɪɢɤɨɜ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɭɝɥɚ ɢɯ ɪɚɫɯɨɠɞɟɧɢɹ. Ʌɭɱɲɟ ɜɜɟɫɬɢ ɜɪɟɦɹ, ɧɨ ɨɧɨ ɧɟ ɢɡɜɟɫɬɧɨ. ɇɭɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɧɚɱɚɥɶɧɨɟ ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɲɚɪɢɤɚɦɢ. ȿɫɥɢ ɜɡɹɬɶ ɟɝɨ ɪɚɜɧɨɟ ɧɭɥɸ, ɬɨ ɡɧɚɱɟɧɢɟ ɫɢɥɵ ɛɭɞɟɬ ɪɚɜɧɹɬɶɫɹ ɛɟɫɤɨɧɟɱɧɨɫɬɢ. Ɉɩɪɟɞɟɥɢɦ ɪɚɞɢɭɫɵ ɲɚɪɢɤɨɜ ‫ݎ‬ ɩɨ ɢɯ ɡɚɞɚɧɧɨɣ ɦɚɫɫɟ ݉ ɢ ɩɥɨɬɧɨɫɬɢ ɦɚɬɟɪɢɚɥɚ ߩ˛ , ɢɡ ɤɨɬɨɪɨɝɨ ɨɧɢ ɫɞɟɥɚɧɵ. ɂɫɩɨɥɶɡɭɟɦ ɫɥɟɞɭɸɳɟɟ ɜɵɪɚɠɟɧɢɟ ݉ ൌ ܸߩ˛ , ɝɞɟ య ܸ ൌ Ͷߨ‫ ݎ‬ଷ Τ͵ – ɨɛɴɟɦ ɲɚɪɢɤɚ. Ɋɚɞɢɭɫ ɲɚɪɢɤɚ ‫ ݎ‬ൌ ඥ͵݉ΤͶߨߩ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɰɟɧɬɪɚɦɢ ɲɚɪɢɤɨɜ ɧɟ ɦɨɠɟɬ ɛɵɬɶ ɦɟɧɶɲɟ ʹ‫ݎ‬. ɗɬɨ ɡɧɚɱɟɧɢɟ ɜɨɡɶɦɟɦ ɡɚ ɧɚɱɚɥɶɧɨɟ ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɲɚɪɢɤɚɦɢ. ȼ ɩɪɨɝɪɚɦɦɭ ɤɧɨɩɤɢ ɇɚɱɚɥɶɧɵɟ ɭɫɬɚɧɨɜɤɢ ɜ ɤɨɧɰɟ ɜɫɬɚɜɥɹɟɦ ɫɥɟɞɭɸɳɢɟ ɤɨɞɵ lo = (3 * Cells(4, 4) / (4 * pi * 8000)) ^ 1 / 3 'ɇɚɱɚɥɶɧɨɟ ɪɚɫɫɬɨɹɧɢɟ ɲɚɪɢɤɚ ɨɬ ɜɟɪɬɢɤɚɥɢ dxo = lo / Cells(1, 4) 'ɋɢɧɭɫ ɧɚɱɚɥɶɧɨɝɨ ɭɝɨɥ ɨɬɤɥɨɧɟɧɢɹ ɲɚɪɢɤɨɜ ɨɬ ɜɟɪɬɢɤɚɥɢ. ɋɱɢɬɚɟɦ, ɱɬɨ ɲɚɪɢɤɢ ɫɞɟɥɚɧɵ ɢɡ ɦɟɬɚɥɥɚ ɫ ߩ˛ ൌ ͺͲͲͲ ˍˆΤˏଷ . Ɋɚɫɱɟɬ ɫɢɥɵ Ʉɭɥɨɧɚ ɩɪɨɢɡɜɨɞɢɦ ɩɨ ɜɵɪɚɠɟɧɢɸ ‫ܨ‬௞ ൌ ݇ ‫ݍ‬ଵ ‫ݍ‬ଶ ΤሺͶ‫ܮ‬ଶ ሻ ൌ ݇ ‫ݍ‬ଵ ‫ݍ‬ଶ ȀሺͶܴଶ ‫݊݅ݏ‬ଶ ‫ן‬ሻ. ɉɪɢ ɧɚɯɨɠɞɟɧɢɢ ɭɝɥɚ ɨɤɨɧɱɚɬɟɥɶɧɨɝɨ ɪɚɫɯɨɠɞɟɧɢɹ ɲɚɪɢɤɨɜ ɜɜɟɥɢ ɩɚɪɚɦɟɬɪ ܽ ൌ ݇‫ݍ‬ଵ ‫ݍ‬ଶ ȀሺͶܴଶ ݉݃ሻ. ɉɪɢ ɩɨɞɫɬɚɧɨɜɤɢ ɩɚɪɚɦɟɬɪɚ ɩɨɥɭɱɢɦ ‫ܨ‬௞ ൌ ܽ݉݃Ȁ‫݊݅ݏ‬ଶ ‫ן‬. ɗɬɭ ɮɨɪɦɭɥɭ ɛɭɞɟɦ ɢɫɩɨɥɶɡɨɜɚɬɶ ɞɥɹ ɪɚɫɱɟɬɚ ɫɢɥɵ Ʉɭɥɨɧɚ. Ɋɚɫɱɟɬ ɧɚɱɚɥɶɧɨɝɨ ɭɝɥɚ ߙ଴ ɪɚɫɯɨɠɞɟɧɢɹ ɲɚɪɢɤɨɜ ɩɪɨɢɡɜɨɞɢɦ ɢɡ ɭɫɥɨɜɢɹ ɟɝɨ ɦɚɥɨɫɬɢ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, •‹ ߙ଴ ൌ ‫ݎ‬Ȁܴ ɢ ‫ܨ‬௞ ൌ ܴܽ݉݃ଶ Ȁ‫ ݎ‬ଶ . ȼ ɩɪɨɝɪɚɦɦɭ ɤɧɨɩɤɢ Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɬɪɚɟɤɬɨɪɢɢ ɲɚɪɢɤɨɜ ɜɫɬɚɜɥɹɟɦ ɞɨ ɭɜɟɥɢɱɟɧɢɹ i ɫɥɟɞɭɸɳɢɣ ɤɭɫɨɱɟɤ ɪɚɫɱɟɬɚ ɫɢɥɵ Ʉɭɥɨɧɚ If i = 0 Then Cells(22 + i, 6) = (bf * Cells(4, 4) * Cells(8, 4) * Cells(1, 4) ^ 2) / lo ^ 2 'Ɋɚɫɱɟɬ ɬɟɤɭɳɟɣ Fk Else 153

2. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ MS Excel

Cells(22 + i, 6) = bf * Cells(4, 4) * Cells(8, 4) / Sin(ai) ^ 2 'Ɋɚɫɱɟɬ ɬɟɤɭɳɟɣ Fk End If. ɗɬɚ ɩɪɨɝɪɚɦɦɚ ɡɚɩɢɫɵɜɚɟɬ ɜ ɦɚɫɫɢɜ F22:F32 ɡɧɚɱɟɧɢɟ ɫɢɥɵ ɞɥɹ ɤɚɠɞɨɝɨ ɲɚɝɚ ɦɨɞɟɥɢɪɨɜɚɧɢɹ. ɉɨɫɬɪɨɢɦ ɬɨɱɟɱɧɵɣ ɝɪɚɮɢɤ ɫɢɥɵ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɤɨɨɪɞɢɧɚɬɵ ɲɚɪɢɤɚ ɩɨ ɨɫɢ ɚɛɫɰɢɫɫ (D22:D32). ɑɬɨɛɵ ɨɬɨɛɪɚɡɢɬɶ ɜɫɟ ɡɧɚɱɟɧɢɹ ɋɢɥɵ Ʉɭɥɨɧɚ ɭɫɬɚɧɚɜɥɢɜɚɟɦ ɥɨɝɚɪɢɮɦɢɱɟɫɤɢɣ ɦɚɫɲɬɚɛ ɞɥɹ ɨɫɢ ɨɪɞɢɧɚɬ. ȼɢɞɢɦ, ɱɬɨ ɧɚ ɩɟɪɜɨɦ ɲɚɝɟ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɫɢɥɚ ɢɦɟɟɬ ɨɱɟɧɶ ɛɨɥɶɲɨɟ ɡɧɚɱɟɧɢɟ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɩɨɫɥɟɞɭɸɳɢɦɢ ɲɚɝɚɦɢ (ɭɞɚɥɟɧɢɟɦ ɲɚɪɢɤɨɜ). ɉɟɪɟɣɞɟɦ ɤ ɪɚɫɱɟɬɭ ɭɝɥɨɜɨɝɨ ɭɫɤɨɪɟɧɢɹ ɲɚɪɢɤɨɜ ɩɪɢ ɢɯ ɪɚɫɯɨɠɞɟɧɢɢ. ȼɨɫɩɨɥɶɡɭɟɦɫɹ ɨɫɧɨɜɧɵɦ ɭɪɚɜɧɟɧɢɟɦ ɜɪɚɳɚɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɦɚɬɟɪɢɚɥɶɧɨɣ ɬɨɱɤɢ ‫ ߚܬ‬ൌ σ௝ ‫ܯ‬௝ , ɝɞɟ ‫ – ܬ‬ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɦɚɬɟɪɢɚɥɶɧɨɣ ɬɨɱɤɢ; ‫ܯ‬௝ – ɦɨɦɟɧɬ j-ɨɣ ɜɧɟɲɧɟɣ ɫɢɥɵ, ɜɨɡɞɟɣɫɬɜɭɸɳɟɣ ɧɚ ɦɚɬɟɪɢɚɥɶɧɭɸ ƹ ɬɨɱɤɭ. Ɇɨɦɟɧɬ ɢɧɟɪɰɢɢ ɦɚɬɟɪɢɚɥɶɧɨɣ ɬɨɱɤɢ ‫ ܬ‬ൌ ܴ݉. Į ɋɨɫɬɚɜɢɦ ɭɪɚɜɧɟɧɢɟ ɞɥɹ ɨɞɧɨɝɨ ɢɡ ɲɚɪɢɤɨɜ ܴ݉ଶ ߚ ൌ െܲ •‹ ߙ ܴ ൅ ‫ܨ‬௞ …‘• ߙ ܴ. 900 Ɍ ɍɝɥɨɜɨɟ ɭɫɤɨɪɟɧɢɟ ɜ ɥɸɛɨɣ ɬɨɱɤɟ ɬɪɚɟɤɬɨɪɢɢ ɲɚɪɢĮ Fk ி ௚ ɤɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɜɵɪɚɠɟɧɢɟɦ ߚ ൌ ೖ …‘• ߙ െ •‹ ߙ. Ɉ ோ ௠ோ X Ⱦɥɹ ɜɵɱɢɫɥɟɧɢɹ ɭɝɥɨɜɨɝɨ ɭɫɤɨɪɟɧɢɹ ɜɫɬɚɜɥɹɟɦ Į P ɫɬɪɨɤɢ ɢ ɩɨɥɭɱɚɟɦ ɫɥɟɞɭɸɳɭɸ ɩɪɨɝɪɚɦɦɭ If i = 0 Then Cells(22 + i, 6) = (bf * Cells(4, 4) * Cells(8, 4) * Cells(1, 4) ^ 2) / lo ^ 2 'Ɋɚɫɱɟɬ ɬɟɤɭɳɟɣ Fk Cells(22 + i, 7) = bf / (Sin(dxo) ^ 2 * Cells(4, 4) * Cells(1, 4)) * Cos(dxo) Cells(8, 4) * Sin(dxo) / Cells(1, 4) 'Ɋɚɫɱɟɬ ɬɟɤɭɳɟɝɨ ɭɝɥɨɜɨɝɨ ɭɫɤɨɪɟɧɢɹ ɲɚɪɢɤɨɜ Else Cells(22 + i, 6) = bf * Cells(4, 4) * Cells(8, 4) / Sin(ai) ^ 2 'Ɋɚɫɱɟɬ ɬɟɤɭɳɟɣ Fk Cells(22 + i, 7) = bf / (Sin(ai) ^ 2 * Cells(4, 4) * Cells(1, 4)) * Cos(ai) Cells(8, 4) * Sin(ai) / Cells(1, 4) 'Ɋɚɫɱɟɬ ɬɟɤɭɳɟɝɨ ɭɝɥɨɜɨɝɨ ɭɫɤɨɪɟɧɢɹ ɲɚɪɢɤɨɜ End If. Ɂɧɚɱɟɧɢɹ ɭɝɥɨɜɨɝɨ ɭɫɤɨɪɟɧɢɹ ɡɚɩɢɫɵɜɚɸɬɫɹ ɜ ɦɚɫɫɢɜ G22:G32. Ⱥɧɚɥɨɝɢɱɧɨ ɫɬɪɨɢɦ ɝɪɚɮɢɤ ɭɝɥɨɜɨɝɨ ɭɫɤɨɪɟɧɢɹ ɞɥɹ ɤɚɠɞɨɝɨ ɲɚɝɚ ɦɨɞɟɥɢɪɨɜɚɧɢɹ, ɧɨ ɧɟ ɜɜɨɞɢɦ ɥɨɝɚɪɢɮɦɢɱɟɫɤɭɸ ɲɤɚɥɭ ɢɡ-ɡɚ ɨɬɪɢɰɚɬɟɥɶɧɵɯ ɡɧɚɱɟɧɢɣ ɭɝɥɨɜɵɯ ɭɫɤɨɪɟɧɢɣ ɜ ɪɚɣɨɧɟ ɬɨɱɤɢ ɩɨɤɨɹ. ɗɬɨ ɟɫɬɟɫɬɜɟɧɧɨ ɩɪɢ ɭɱɟɬɟ ɢɧɟɪɰɢɨɧ154

2.2. Ɏɢɡɢɤɚ

ɧɨɫɬɶ ɲɚɪɢɤɨɜ. ȼ ɬɨɱɤɟ ɩɨɤɨɹ ɞɨɥɠɟɧ ɧɚɛɥɸɞɚɬɶɫɹ ɡɚɬɭɯɚɸɳɢɣ ɩɪɨɰɟɫɫ ɞɜɢɠɟɧɢɹ ɲɚɪɢɤɚ ɞɨ ɩɨɥɧɨɝɨ ɩɨɤɨɹ. Ɍɟɩɟɪɶ ɦɨɠɧɨ ɩɟɪɟɣɬɢ ɤ ɨɩɪɟɞɟɥɟɧɢɸ ɜɪɟɦɟɧɢ ɪɚɫɯɨɠɞɟɧɢɹ ɡɚɪɹɠɟɧɧɵɯ ɲɚɪɢɤɨɜ. Ȼɭɞɟɦ ɫɱɢɬɚɬɶ, ɱɬɨ ɧɚ ɭɝɥɨɜɨɦ ɲɚɝɟ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ݀ߙ ɭɝɥɨɜɨɟ ɭɫɤɨɪɟɧɢɟ ɧɟ ɢɡɦɟɧɹɟɬɫɹ. ɑɟɦ ɦɟɧɶɲɟ ɭɝɥɨɜɨɣ ɲɚɝ, ɬɟɦ ɞɨɫɬɨɜɟɪɧɟɟ ɷɬɨ ɭɬɜɟɪɠɞɟɧɢɟ. Ɋɚɫɱɟɬ ɜɪɟɦɟɧɢ ɩɪɨɯɨɠɞɟɧɢɹ ɭɝɥɨɜɨɝɨ ɲɚɝɚ ɬɪɚɟɤɬɨɪɢɢ ɲɚɪɢɤɚ ɛɭɞɟɦ ɩɪɨɢɡɜɨɞɢɬɶ ɩɨ ɮɨɪɦɭɥɟ మ ‫ݐ‬௜ ൌ ඥʹ݀ߙ Τߚ . Ʉɚɤ ɜɢɞɢɦ ɩɨ ɝɪɚɮɢɤɭ ɭɫɤɨɪɟɧɢɹ ɜ ɧɚɱɚɥɟ ɭɱɚɫɬɤɚ ɭɫɤɨɪɟɧɢɟ ɛɨɥɶɲɟ, ɚ ɜ ɤɨɧɰɟ ɭɦɟɧɶɲɚɟɬɫɹ. ɍɦɟɧɶɲɟɧɢɟ ɫɜɹɡɚɧɨ ɫ ɭɦɟɧɶɲɟɧɢɟɦ ɫɢɥɵ Ʉɭɥɨɧɚ. ɉɪɢ ɪɚɫɱɟɬɟ ɜɪɟɦɟɧɢ ɛɭɞɟɦ ɢɫɩɨɥɶɡɨɜɚɬɶ ɧɚɱɚɥɶɧɵɟ ɡɧɚɱɟɧɢɹ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɢ. ɋɨɡɞɚɞɢɦ ɬɪɟɬɶɸ ɭɩɪɚɜɥɹɸɳɭɸ ɤɧɨɩɤɭ ɢ ɫɨɡɞɚɞɢɦ ɩɪɨɝɪɚɦɦɭ ɪɚɫɱɟɬɚ ɜɪɟɦɟɧɢ. Ɂɚɩɢɫɶ ɜɪɟɦɟɧɢ ɛɭɞɟɦ ɩɪɨɢɡɜɨɞɢɬɶ ɜ ɦɚɫɫɢɜ ɇ22:ɇ31. ɉɪɨɝɪɚɦɦɚ ɨɛɟɫɩɟɱɢɜɚɟɬ ɪɚɫɱɟɬ ɜɪɟɦɟɧɢ ɩɨ 10 ɧɚɱɚɥɶɧɵɦ ɬɨɱɤɚɦ ɭɝɥɨɜɵɯ ɢɧɬɟɪɜɚɥɨɜ. Private Sub CommandButton3_Click() For i = 0 To 9 Step 1 uck = Cells(22 + i, 7) Cells(22 + i, 8) = (2 * grvrad * Cells(3, 8) / uck) ^ 0.5 'Ɋɚɫɱɟɬ ɢ ɡɚɩɢɫɶ ɜɪɟɦɟɧɢ Next i End Sub. ɋɭɦɦɚɪɧɨɟ ɜɪɟɦɹ ɪɚɫɯɨɠɞɟɧɢɹ ɲɚɪɢɤɨɜ ɪɚɜɧɨ 0,467 ɫɟɤɭɧɞ. ɉɟɪɜɵɣ ɭɱɚɫɬɨɤ ɲɚɪɢɤɢ ɩɪɨɯɨɞɹɬ ɩɪɚɤɬɢɱɟɫɤɢ ɡɚ ɧɭɥɶ ɫɟɤɭɧɞ. ɉɨɫɥɟɞɧɢɣ ɭɱɚɫɬɨɤ ɩɪɟɨɞɨɥɟɜɚɟɬɫɹ ɡɚ ɛɨɥɟɟ ɞɥɢɬɟɥɶɧɨɟ ɜɪɟɦɹ. Ɇɨɞɟɥɶ ɪɚɫɯɨɠɞɟɧɢɹ ɡɚɪɹɠɟɧɧɵɯ ɲɚɪɢɤɨɜ ɞɚɟɬ ɩɪɟɞɫɬɚɜɥɟɧɢɟ ɨ ɜɟɥɢɱɢɧɟ ɪɹɞɚ ɩɚɪɚɦɟɬɪɨɜ. Ɇɨɠɧɨ ɬɟɩɟɪɶ ɦɨɠɧɨ ɫɨɡɞɚɬɶ ɦɨɞɟɥɶ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɜɪɟɦɟɧɢ ɜ ɤɚɱɟɫɬɜɟ ɨɫɧɨɜɧɨɝɨ ɲɚɝɚ ɩɨɫɬɪɨɟɧɢɹ ɬɪɚɟɤɬɨɪɢɢ ɪɚɫɯɨɠɞɟɧɢɹ ɲɚɪɢɤɨɜ. ɇɨ ɡɞɟɫɶ ɟɫɬɶ ɩɪɨɛɥɟɦɚ ɜɪɟɦɟɧɧɨɝɨ ɜɵɛɨɪɚ ɢɧɬɟɪɜɚɥɚ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɜ ɧɚɱɚɥɟ ɩɪɨɰɟɫɫɚ ɪɚɫɯɨɠɞɟɧɢɹ. Ʉɚɤ ɜɢɞɢɦ, ɜɧɚɱɚɥɟ ɲɚɪɢɤɢ ɪɚɡɥɟɬɚɸɬɫɹ ɦɝɧɨɜɟɧɧɨ. ɇɚɜɟɪɧɨɟ, ɰɟɥɟɫɨɨɛɪɚɡɧɨ ɜɪɟɦɟɧɧɨɣ ɢɧɬɟɪɜɚɥ ɫɞɟɥɚɬɶ ɪɚɡɧɨɣ ɜɟɥɢɱɢɧɵ ɞɥɹ ɷɬɚɩɨɜ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɬɪɚɟɤɬɨɪɢɢ ɲɚɪɢɤɨɜ. 2.2.17. Ɂɚɛɟɣ ɝɨɥ ɫ 11 ɦɟɬɪɨɜ ɋɨɡɞɚɞɢɦ ɦɨɞɟɥɶ ɩɨɥɟɬɚ ɮɭɬɛɨɥɶɧɨɝɨ ɦɹɱɚ ɩɪɢ ɧɚɡɧɚɱɟɧɢɢ ɲɬɪɚɮɧɨɝɨ ɭɞɚɪɚ ɫ 11-ɦɟɬɪɨɜɨɣ ɨɬɦɟɬɤɢ ɩɨ ɜɨɪɨɬɚɦ. ɉɨɥɟɬ ɦɹɱɚ ɛɭɞɟɦ ɦɨɞɟɥɢɪɨɜɚɬɶ ɜ 155

2. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ MS Excel

ɩɥɨɫɤɨɫɬɢ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɣ ɤ ɜɨɪɨɬɚɦ. ȼ ɤɚɱɟɫɬɜɟ ɢɫɯɨɞɧɵɯ ɩɚɪɚɦɟɬɪɨɜ ɦɨɞɟɥɢ ɛɭɞɟɦ ɢɫɩɨɥɶɡɨɜɚɬɶ ɜɟɫ ɢ ɪɚɡɦɟɪɵ ɦɹɱɚ, ɚ ɬɚɤɠɟ ɜɟɫ ɢ ɫɤɨɪɨɫɬɶ ɞɜɢɠɟɧɢɹ ɧɨɝɢ ɮɭɬɛɨɥɢɫɬɚ, ɩɨɥɨɠɟɧɢɟ ɮɭɬɛɨɥɢɫɬɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɦɹɱɚ. Ȼɭɞɟɦ ɫɱɢɬɚɬɶ, ɱɬɨ ɧɨɝɚ ɮɭɬɛɨɥɢɫɬɚ ɧɟ ɫɝɢɛɚɟɬɫɹ ɜ ɤɨɥɟɧɤɟ ɢ ɦɹɱ ɥɟɬɢɬ ɜ ɛɟɡɜɨɡɞɭɲɧɨɦ ɩɪɨɫɬɪɚɧɫɬɜɟ. ɉɚɪɚɦɟɬɪɵ, ɫɜɹɡɚɧɧɵɟ ɫ ɮɭɬɛɨɥɢɫɬɨɦ ɦɨɠɧɨ ɢɡɦɟɧɹɬɶ. Ɋɚɡɦɟɪɵ ɜɨɪɨɬ ɫɬɚɧɞɚɪɬɧɵɟ. ɉɨɥɟɬ ɦɹɱɚ ɛɭɞɟɬ ɡɚɜɢɫɟɬɶ ɨɬ ɜɟɤɬɨɪɚ ɫɤɨɪɨɫɬɢ, ɤɨɬɨɪɵɣ ɜɵɱɢɫɥɹɟɬɫɹ ɜ ɦɨɦɟɧɬ ɭɞɚɪɚ ɧɨɝɨɣ ɩɨ ɦɹɱɭ. ɉɪɢ ɷɬɨɦ ɦɨɠɟɬ ɢɡɦɟɧɹɬɶɫɹ ɤɚɤ ɫɤɨɪɨɫɬɶ ɩɨɥɟɬɚ, ɬɚɤ ɢ ɭɝɨɥ ɜɟɤɬɨɪɚ ɫɤɨɪɨɫɬɢ ɤ ɝɨɪɢɡɨɧɬɭ (ɩɥɨɫɤɨɫɬɢ ɩɨɥɹ). Ɏɚɤɬ ɩɨɩɚɞɚɧɢɹ ɦɹɱɚ ɜ ɜɨɪɨɬɚ ɛɭɞɟɦ ɨɩɪɟɞɟɥɹɬɶ ɩɨ ɤɨɨɪɞɢɧɚɬɚɦ ɦɹɱɚ ɜ ɫɬɜɨɪɟ ɜɨɪɨɬ. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɛɭɞɟɦ ɨɫɭɳɟɫɬɜɥɹɬɶ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɩɨ ɫɥɟɞɭɸɳɢɦ ɷɬɚɩɚɦ: 1. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɩɨɥɨɠɟɧɢɹ ɜɨɪɨɬ ɢ ɦɹɱɚ ɜ ɬɪɟɯɦɟɪɧɨɦ ɩɪɨɫɬɪɚɧɫɬɜɟ. 2. Ɇɨɞɟɥɢɪɨɜɚɧɢɹ ɭɞɚɪɚ ɧɨɝɨɣ ɮɭɬɛɨɥɢɫɬɨɦ ɩɨ ɦɹɱɭ. 3. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɩɨɥɟɬɚ ɦɹɱɚ ɢ ɨɩɪɟɞɟYɷɤɪ ɥɟɧɢɟ ɮɚɤɬɚ ɩɨɩɚɞɚɧɢɹ. Z Ȼɟɪɟɦ ɫɥɟɞɭɸɳɢɟ ɪɚɡɦɟɪɵ ɮɭɬɛɨɥɶɧɵɯ ɜɨ(X,Y,Z) ɪɨɬ: ɜɵɫɨɬɚ 2,44ɦ (8ɮɭɬɨɜ), ɲɢɪɢɧɚ 7,32ɦ (8ɹɪɞɨɜ). Ⱦɥɹ ɧɚɝɥɹɞɧɨɫɬɢ ɜɨɡɶɦɟɦ ɮɪɨɧɬɚɥɶɧɭɸ Y Xɷɤɪ ɞɢɦɟɬɪɢɱɟɫɤɭɸ ɩɪɨɟɤɰɢɸ (ɫɦ. ɡɚɞɚɱɭ ɉɨɫɬɪɨɟɧɢɟ 450 450 ɩɪɨɫɬɟɣɲɢɯ ɨɛɴɟɦɧɵɯ ɮɢɝɭɪ). ȼ ɩɟɪɜɭɸ ɨɱɟɪɟɞɶ (X,Y) ɧɟɨɛɯɨɞɢɦɨ ɨɛɟɫɩɟɱɢɬɶ ɩɟɪɟɫɱɟɬ ɤɨɨɪɞɢɧɚɬ ɢɡ ɫɨ- X ɨɬɜɟɬɫɬɜɭɸɳɟɣ ɩɪɨɟɤɰɢɢ XYZ ɧɚ ɩɥɨɫɤɭɸ ɩɨɜɟɪɯɧɨɫɬɶ, ɤɨɬɨɪɭɸ ɧɚɡɨɜɟɦ ɷɤɪɚɧɧɨɣ ɫɢɫɬɟɦɨɣ ɤɨɨɪɞɢɧɚɬ ɏɷɤɪYɷɤɪ. Ɇɚɫɲɬɚɛɧɵɟ ɤɨɷɮɮɢɰɢɟɧɬɵ ɩɨ ɨɫɹɦ ɩɪɨɟɤɰɢɣ ɭɱɢɬɵɜɚɬɶ ɧɟ ɛɭɞɟɦ. ɉɟɪɟɫɱɟɬ ɤɨɨɪɞɢɧɚɬ ɢɡ ɮɪɨɧɬɚɥɶɧɨɣ ɞɢɦɟɬɪɢɱɟɫɤɨɣ ɩɪɨɟɤɰɢɢ ɜ ɷɤɪɚɧɧɭɸ ɫɢɫɬɟɦɭ ɤɨɨɪɞɢɧɚɬ ɨɫɭɳɟɫɬɜɥɹɟɦ ɩɨ ɮɨɪɦɭɥɚɦ (ɫɦ. ɪɢɫɭɧɨɤ) ܺˠˍ˓ ൌ ܻ െ ܺ ‫ ‹• כ‬Ͷͷ଴ , ܻˠˍ˓ ൌ ܼ െ ܺ ‫ •‘… כ‬Ͷͷ଴ . ȼ ɹɱɟɣɤɢ D14, D15 ɡɚɩɢɫɵɜɚɟɦ ɩɚɪɚɦɟɬɪɵ ɮɭɬɛɨɥɶɧɵɯ ɜɨɪɨɬ. Ⱦɚɥɟɟ ɜ ɦɚɫɫɢɜɟ D18:E25 ɮɨɪɦɢɪɭɟɦ ɤɨɨɪɞɢɧɚɬɵ ɨɬɪɟɡɤɨɜ ɨɫɟɣ ɤɨɨɪɞɢɧɚɬ ɜ ɷɤɪɚɧɧɨɣ ɫɢɫɬɟɦɟ. Ⱦɥɢɧɭ ɨɬɪɟɡɤɨɜ ɡɚɞɚɟɦ ɫ ɭɱɟɬɨɦ ɪɚɡɦɟɪɨɜ ɜɨɪɨɬ ɢ ɜɨɡɦɨɠɧɨɝɨ ɧɚɯɨɠɞɟɧɢɹ ɮɭɬɛɨɥɢɫɬɚ ɨɬɧɨɫɢɬɟɥɶɧɨ 11-ɦɟɬɪɨɜɨɣ ɨɬɦɟɬɤɢ. ɇɚɱɚɥɶɧɵɟ ɤɨɨɪɞɢɧɚɬɵ ɨɬɪɟɡɤɨɜ ɪɚɜɧɵ ɧɭɥɸ. Ɍɚɤ ɤɚɤ ɨɫɢ ɷɤɪɚɧɧɨɣ ɫɢɫɬɟɦɵ ɤɨɨɪɞɢɧɚɬ ɫɨɜɩɚɞɚɸɬ ɫ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦɢ ɨɫɹɦɢ Z ɢ Y, ɬɨ ɩɪɨɫɬɨ ɡɚɞɚɟɦ ɢɯ ɡɧɚɱɟɧɢɹ ɛɟɡ ɩɟɪɟɫɱɟɬɚ (D21:E25). Ʉɨɨɪɞɢɧɚɬɵ ɨɬɪɟɡɤɨɜ ɩɟɪɟɤɥɚɞɢɧ ɜɨɪɨɬ ɜɵɱɢɫɥɹɟɦ ɜ ɦɚɫɫɢɜɟ D27:E34. ȼ ɩɟɪɜɵɯ ɹɱɟɣɤɚɯ ɡɚɞɚɟɦ ɤɨɨɪɞɢɧɚɬɵ ɥɟɜɨɣ ɲɬɚɧɝɢ, ɜɨ ɜɬɨɪɨɣ ɝɪɭɩɩɟ ɹɱɟɟɤ – ɤɨɨɪɞɢɧɚɬɵ ɩɪɚɜɨ ɲɬɚɧɝɢ, ɚ ɜ ɩɨɫɥɟɞɧɢɯ ɹɱɟɣɤɚɯ - ɤɨɨɪɞɢɧɚɬɵ ɩɟɪɟɤɥɚɞɢɧɵ ɜɨɪɨɬ. 156

2.2. Ɏɢɡɢɤɚ

ɉɨɫɥɟ ɡɚɞɚɧɢɹ ɤɨɨɪɞɢɧɚɬ ɦɨɠɧɨ ɨɛɪɚɬɢɬɶɫɹ ɤ ɦɚɫɬɟɪɭ ɩɨɫɬɪɨɟɧɢɹ ɞɢɚɝɪɚɦɦ, ɜɵɛɪɚɬɶ Ɍɨɱɟɱɧɚɹ ɫ ɩɪɹɦɵɦɢ, ɚ ɡɚɬɟɦ, ɩɨɥɭɱɢɜ ɢɡɨɛɪɚɠɟɧɢɟ ɨɬɮɨɪɦɚɬɢɪɨɜɚɬɶ ɨɬɞɟɥɶɧɵɟ ɷɥɟɦɟɧɬɵ ɞɢɚɝɪɚɦɦɵ. Ⱦɥɹ ɩɨɫɬɪɨɟɧɢɹ ɞɢɚɝɪɚɦɦɵ ɢɫɩɨɥɶɡɭɟɦ ɦɚɫɫɢɜ ɹɱɟɟɤ D18:E69. ȼ ɷɬɨɬ ɦɚɫɫɢɜ ɜɤɥɸɱɟɧɵ ɤɨɨɪɞɢɧɚɬɵ ɦɹɱɚ ɢ ɬɪɚɟɤɬɨɪɢɢ ɟɝɨ ɩɨɥɟɬɚ. Ɉɬɪɟɡɤɚɦ ɜɨɪɨɬ ɡɚɞɚɟɦ ɛɨɥɶɲɭɸ ɲɢɪɢɧɭ ɢ ɱɟɪɧɵɣ ɰɜɟɬ. Ɏɨɪɦɢɪɭɟɦ ɧɚɞɩɢɫɢ ɤ ɨɫɹɦ ɤɨɨɪɞɢɧɚɬ. ɉɪɟɞɜɚɪɢɬɟɥɶɧɨ ɜ ɹɱɟɣɤɚɯ R1:R3 ɞɟɥɚɟɦ ɡɚɝɨɬɨɜɤɢ ɧɚɞɩɢɫɟɣ. Ⱦɚɥɟɟ ɧɚ ɝɪɚɮɢɤɟ ɜɵɛɢɪɚɟɦ ɤɨɧɟɱɧɭɸ ɬɨɱɤɭ ɨɫɢ ɢ ɞɜɚɠɞɵ ɩɨ ɧɟɣ ɳɟɥɤɚɟɦ. ȼɵɡɵɜɚɟɦ ɤɨɧɬɟɤɫɬɧɨɟ ɦɟɧɸ ɢ ɜɵɛɢɪɚɟɦ ɩɭɧɤɬ Ⱦɨɛɚɜɢɬɶ ɩɨɞɩɢɫɶ ɞɚɧɧɵɯ. ɉɨɹɜɥɹɟɬɫɹ ɧɚɞɩɢɫɶ. Ɉɛɵɱɧɨ ɷɬɨ ɤɚɤɨɟ-ɬɨ ɡɧɚɱɟɧɢɟ ɬɨɱɤɢ. ȼ ɫɬɪɨɤɟ ɮɨɪɦɭɥ ɫɬɚɜɢɦ ɡɧɚɤ ɪɚɜɟɧɫɬɜɚ ɢ ɳɟɥɤɚɟɦ ɩɨ ɹɱɟɣɤɟ ɫ ɧɭɠɧɵɦ ɫɨɞɟɪɠɚɧɢɟɦ. ɑɟɪɟɡ ɤɨɧɬɟɤɫɬɧɨɟ ɦɟɧɸ ɤɨɧɟɱɧɨɣ ɬɨɱɤɢ ɨɫɢ ɫɨɡɞɚɟɦ ɫɬɪɟɥɤɢ. ɇɚ ɞɢɚɝɪɚɦɦɟ ɧɚ 11-ɦɟɬɪɨɜɨɣ ɨɬɦɟɬɤɢ ɪɚɫɩɨɥɚɝɚɟɬɫɹ ɢɡɨɛɪɚɠɟɧɢɹ ɦɹɱɚ ɞɨ ɧɚɧɟɫɟɧɢɹ ɩɨ ɧɟɦɭ ɭɞɚɪɚ. ȼɟɫ ɦɹɱɚ ɧɚ ɨɮɢɰɢɚɥɶɧɵɯ ɫɨɪɟɜɧɨɜɚɧɢɹɯ ɧɟ ɞɨɥɠɟɧ ɩɪɟɜɵɲɚɬɶ 450 ɝɪɚɦɦ, ɚ ɨɤɪɭɠɧɨɫɬɶ ɫɨɫɬɚɜɥɹɬɶ 68-70 ɫɦ. ɉɨɷɬɨɦɭ ɛɟɪɟɦ ɪɚɞɢɭɫ ɦɹɱɚ ɪɚɜɧɵɦ 11 ɫɦ.

Ʉɨɨɪɞɢɧɚɬɵ ɦɹɱɚ ɡɚɧɨɫɢɦ ɜ ɹɱɟɣɤɢ D36 ɢ E36. Ⱦɥɹ ɬɨɱɤɢ ɦɹɱɚ ɜɵɡɵɜɚɟɦ ɤɨɧɬɟɤɫɬɧɨɟ ɦɟɧɸ ɢ ɭɫɬɚɧɚɜɥɢɜɚɟɦ ɪɚɡɦɟɪɵ ɦɚɪɤɟɪɚ, ɤɨɬɨɪɵɟ ɢɦɢɬɢɪɭɸɬ ɦɹɱ. Ɇɹɱ ɭɫɬɚɧɚɜɥɢɜɚɟɬɫɹ ɧɚ 11ɦɟɬɪɨɜɨɣ ɨɬɦɟɬɤɢ. Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɧɚɱɚɥɶɧɨɝɨ ɜɟɤɬɨɪɚ ɩɨɥɟɬɚ ɢɡɨɛɪɚɡɢɦ ɟɝɨ ɜ ɜɢɞɟ ɨɤɪɭɠɧɨɫɬɢ ɢɡ 12 ɨɬɪɟɡɤɨɜ. Ʉɨɨɪɞɢɧɚɬɵ ɨɬɪɟɡɤɨɜ ɜɵɱɢɫɥɹɟɦ ɫ ɭɱɟɬɨɦ ɰɟɧɬɪɚ ɦɹɱɚ ɩɨ ɜɵɪɚɠɟɧɢɹɦ ܺˠˍ˓௜ ൌ ܴˏ ‫߮ •‘… כ‬௜ ൅ ‫ ˏܮ‬, ܻˠˍ˓௜ ൌ ܴˏ ‫߮ ‹• כ‬௜ ൅ ܴˏ , ߮௜ ൌ ݅ ‫ߨ כ‬Τͳʹ, 157

2. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ MS Excel

ɝɞɟ ‫ – ˏܮ‬ɞɚɥɶɧɨɫɬɶ 11-ɦɟɬɪɨɜɨɣ ɨɬɦɟɬɤɢ, ܴˏ – ɪɚɞɢɭɫ ɦɹɱɚ. Ɋɟɡɭɥɶɬɚɬɵ ɜɵɱɢɫɥɟɧɢɣ ɧɚɯɨɞɹɬɫɹ ɜ ɦɚɫɫɢɜɟ D83:E97. Ɍɟɩɟɪɶ ɦɨɠɧɨ ɩɪɢɫɬɭɩɢɬɶ ɤ ɦɨɞɟɥɢɪɨɜɚɧɢɸ ɧɨɝ ɮɭɬɛɨɥɢɫɬɚ ɩɪɢ ɭɞɚɪɟ ɩɨ ɦɹɱɭ. Ɉɞɧɚ ɧɨɝɚ ɞɨɥɠɧɚ ɨɫɬɚɜɚɬɶɫɹ ɧɟɩɨɞɜɢɠɧɨɣ, ɚ ɞɪɭɝɚɹ ɞɜɢɝɚɬɶɫɹ ɫ ɨɩɪɟɞɟɥɟɧɧɨɣ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɶɸ. Ⱦɥɹ ɤɚɠɞɨɣ ɧɨɝɢ ɜɵɞɟɥɹɟɦ ɦɚɫɫɢɜɵ ɹɱɟɟɤ. Ɏɨɪɦɢɪɭɟɦ ɤɨɨɪɞɢɧɚɬɵ ɨɬɪɟɡɤɨɜ ɦɨɞɟɥɢ ɧɨɝ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɡɚɞɚɧɧɵɯ ɨɫɧɨɜɧɵɯ ɩɚɪɚɦɟɬɪɨɜ (D7:D10). ɋɥɟɞɭɟɬ ɨɫɬɚɧɨɜɢɬɶɫɹ ɧɚ ɩɚɪɚɦɟɬɪɚɯ ɧɨɝɢ. ɋɪɟɞɧɢɣ ɜɟɫ ɧɨɝɢ ɫɨɫɬɚɜɥɹɟɬ 20-25% ɨɬ ɨɛɳɟɝɨ ɜɟɫɚ. Ⱦɥɢɧɚ ɧɨɝɢ – 50-54% ɨɬ ɪɨɫɬɚ. ɉɪɢ 42 ɪɚɡɦɟɪɟ ɨɛɭɜɢ ɞɥɢɧɚ ɫɬɭɩɧɢ ɫɨɫɬɚɜɥɹɟɬ 28 ɫɦ. ɗɬɢ ɞɚɧɧɵɟ ɦɨɠɧɨ ɭɬɨɱɧɢɬɶ ɜ ɢɧɬɟɪɧɟɬɟ ɢɥɢ ɡɚɧɟɫɬɢ ɜ ɦɨɞɟɥɶ ɧɭɠɧɵɟ ɡɧɚɱɟɧɢɹ. Ɍɚɤ ɤɚɤ ɬɪɚɟɤɬɨɪɢɹ ɩɨɥɟɬɚ ɦɹɱɚ ɥɟɠɢɬ ɜ ɩɥɨɫɤɨɫɬɢ ܺˠˍ˓ ǡ ܱǡ ܻˠˍ˓ , ɬɨ ɧɟ ɬɪɟɛɭɟɬɫɹ ɩɟɪɟɫɱɟɬɚ ɤɨɨɪɞɢɧɚɬ. ɗɬɨ ɬɚɤɠɟ ɭɩɪɨɳɚɟɬ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɭɞɚɪɚ ɩɨ ɦɹɱɭ. Ɇɨɞɟɥɶ ɧɨɝɢ ɫɨɫɬɨɢɬ ɢɡ 2-ɯ Yɷɤɪ ɨɬɪɟɡɤɨɜ. ɗɬɨ ɫɬɨɩɚ ɢ ɧɨɝɚ ɞɨ ɛɟɞɪɚ. Ⱦɥɹ ɧɟɩɨɞɜɢɠɧɨɣ ɧɨɝɢ ɜɵɞɟɥɹɟɦ ɹɱɟɣɤɢ D77:E81, ɚ ɞɥɹ ɩɨɞɜɢɠɧɨɣ (ɭɞɚɪɧɨɣ) ɧɨɝɢ D71:E85. ȼ ɹɱɟɣɤɚɯ D77:E78 ɮɨɪɦɢɪɭɟɦ ɤɨɨɪɞɢɧɚɬɵ ɧɨɝɢ, ɚ ɜ ɹɱɟɣɤɚɯ D80:E81- ɫɬɭɩɧɢ. Ʉɨɨɪɞɢɧɚɬɵ ɜɟɪɯɚ ɧɨɝɢ ɜɵRɦ (Xɦ ,Yɦ) ɱɢɫɥɹɸɬɫɹ ɩɨ ɜɵɪɚɠɟɧɢɸ Xɷɤɪ SS ܺ଴ ൌ ‫ ˏܮ‬൅ ‫ˏܮ‬ː ǡ ܻ଴ ൌ ܰǡ ɚ ɤɨLɦɧ Lɦ ɨɪɞɢɧɚɬɵ ɧɢɡɚ - ܺ ൌ ‫ ˏܮ‬൅ ‫ˏܮ‬ː ǡ ܻ ൌ ͲǤ Ⱥɧɚɥɨɝɢɱɧɨ ɨɩɪɟɞɟɥɹɸɬɫɹ ɤɨɨɪɞɢɧɚɬɵ ɨɬɪɟɡɤɚ ɫɬɭɩɧɢ, ɭ ɤɨɬɨɪɵɯ ɤɨɨɪɞɢɧɚɬɵ ɩɨ ܻ ൌ ͲǤ Ɍɟɩɟɪɶ ɦɨɠɧɨ ɩɟɪɟɣɬɢ ɤ ɡɚɞɚɧɢɸ ɤɨɨɪɞɢɧɚɬ ɭɞɚɪɧɨɣ ɧɨɝɢ ɮɭɬɛɨɥɢɫɬɚ. ɉɟɪɟɫɱɟɬ ɤɨɨɪɞɢɧɚɬ ɜ ɹɱɟɣɤɚɯ ɩɪɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ ɡɚɧɢɦɚɟɬ ɦɧɨɝɨ ɜɪɟɦɟɧɢ. Ⱦɥɹ ɫɨɤɪɚɳɟɧɢɹ ɜɪɟɦɟɧɢ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɪɚɫɱɟɬɵ ɩɨ ɭɞɚɪɧɨɣ ɧɨɝɟ ɛɭɞɟɦ ɩɪɨɢɡɜɨɞɢɬɶ ɜ ɩɪɨɰɟɞɭɪɚɯ ɭɩɪɚɜɥɹɸɳɢɯ ɤɧɨɩɨɤ. 158

2.2. Ɏɢɡɢɤɚ

ɋɨɡɞɚɞɢɦ ɭɩɪɚɜɥɹɸɳɭɸ ɤɧɨɩɤɭ «ɇɚɱɚɥɶɧɵɟ ɭɫɬɚɧɨɜɤɢ». ɇɚ ɜɤɥɚɞɤɟ Ɋɚɡɪɚɛɨɬɱɢɤ ɜ ɝɪɭɩɩɟ ɗɥɟɦɟɧɬɵ ɭɩɪɚɜɥɟɧɢɹ ɪɚɫɤɪɵɜɚɟɦ ɫɩɢɫɨɤ ȼɫɬɚɜɢɬɶ. Ɂɚɬɟɦ ɜɵɛɢɪɚɟɦ Ʉɧɨɩɤɭ ɜ ɗɥɟɦɟɧɬ ActiveX ɢ ɩɪɨɬɹɠɤɨɣ ɮɨɪɦɢɪɭɟɦ ɤɧɨɩɤɭ ɧɭɠɧɨɝɨ ɪɚɡɦɟɪɚ. ȼɵɡɵɜɚɟɦ ɤɨɧɬɟɤɫɬɧɨɟ ɦɟɧɸ ɤɧɨɩɤɢ ɢ ɜɵɯɨɞɢɦ ɧɚ ɟɟ ɫɜɨɣɫɬɜɚ. ȼ ɨɤɧɟ Properties ɜ ɩɭɧɤɬɟ Caption ɡɚɩɢɫɵɜɚɟɦ ɧɭɠɧɨɟ ɧɚɡɜɚɧɢɟ ɤɧɨɩɤɢ. Ⱦɚɥɟɟ ɞɜɚɠɞɵ ɳɟɥɤɧɭɜ ɩɨ ɤɧɨɩɤɟ «ɇɚɱɚɥɶɧɵɟ ɭɫɬɚɧɨɜɤɢ» ɜ ɨɤɧɟ Code ɫɨɡɞɚɟɦ ɩɪɨɝɪɚɦɦɭ (ɩɪɨɰɟɞɭɪɭ). ɋɧɚɱɚɥɚ ɨɛɧɭɥɹɟɦ ɦɚɫɫɢɜ ɬɟɤɭɳɢɯ ɩɚɪɚɦɟɬɪɨɜ ɦɨɞɟɥɢ (I2:I9), ɚ ɡɚɬɟɦ ɨɛɧɭɥɹɟɦ ɦɚɫɫɢɜ ɬɪɚɟɤɬɨɪɢɢ ɩɨɥɟɬɚ ɦɹɱɚ (D38:E70), ɟɝɨ ɰɟɧɬɪɚ ɦɚɫɫɵ (D36:E36) ɢ ɦɚɫɫɢɜ ɭɞɚɪɧɨɣ ɧɨɝɢ (D71:E75). Ɂɚɩɢɫɵɜɚɟɦ ɤɨɨɪ(X0,Y0) ɞɢɧɚɬɵ ɭɫɬɚɧɨɜɤɢ ɦɹɱɚ ɞɥɹ ɨɬɨɛɪɚɠɟɧɢɹ ɟɝɨ ɩɨɥɟɬɚ ɜ ɨɛɳɟɣ ɞɢɚɝɪɚɦɦɟ. Ɉɛɧɭɥɹɟɦ ɩɪɢɡɧɚɤ ƶȀDZ ɭɞɚɪɚ ɩɨ ɦɹɱɭ, ɤɨɬɨɪɵɣ ɛɭɞɟɦ ɢɫɩɨɥɶɡɨɜɚɬɶ ɞɥɹ N ɨɩɪɟɞɟɥɟɧɢɹ ɪɚɡɥɢɱɧɵɯ ɫɢɬɭɚɰɢɣ ɜ ɦɨɞɟɥɢ. hɦ S N Ɉɩɪɟɞɟɥɢɦ ɭɝɥɨɜɭɸ ɫɤɨɪɨɫɬɶ ɞɜɢɠɟɧɢɹ ɧɨɝɢ ɢ ɲɚɝ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɭɞɚɪɚ ɩɨ ɦɹɱɭ. ɉɪɢ ɷɬɨɦ ɛɭɞɟɦ ɢɫɩɨɥɶɡɨɜɚɬɶ ɡɚɞɚɧɧɵɟ ɩɚɪɚɦɟɬɪɵ ɦɹɱɚ, ɧɨɝɢ ɢ ɫɤɨɪɨɫɬɢ ɭɞɚɪɚ. Ȼɭɞɟɦ ɫɱɢɬɚɬɶ, ɱɬɨ Xɷɤɪ S ɩɪɢ ɭɞɚɪɟ ɩɨ ɦɹɱɭ ɜɵɫɨɬɚ ɩɹɬɤɢ ɧɨɝɢ ɧɟ ɞɨɥɠɧɚ ɩɪɟɜɵɲɚɬɶ ɪɚɡɦɟɪɵ ɦɹɱɚ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɜɵɫɨɬɚ ɩɨɞɴɟɦɚ ɩɹɬɤɢ ɧɨɝɢ ɛɭɞɟɬ ɨɩɪɟɞɟɥɹɬɶɫɹ ɜɵɫɨɬɨɣ ɦɹɱɚ ʹ ‫ ˏܴ כ‬Ǥ ɉɪɢ ɷɬɨɦ ɦɚɤɫɢɦɚɥɶɧɵɣ ɭɝɨɥ ɩɨɜɨɪɨɬɚ ɧɨɝɢ ɜɵɱɢɫɥɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ మ

߮˖ˇ ൌ ܽ‫݃ݐܿݎ‬ሺ ටܰ ଶ െ ݄ˏ ଶ Ȁ݄ˏ ሻ, ɝɞɟ ݄ˏ ൌ ܰ െ ʹ ‫ ˏܴ כ‬Ǥ ɍɝɥɨɜɚɹ ɫɤɨɪɨɫɬɶ ɞɜɢɠɟɧɢɹ ɧɨɝɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɜɵɪɚɠɟɧɢɟɦ ߱˖ˇ ൌ ܸ˖ˇ Ȁܰǡ ɝɞɟ ܸ˖ˇ - ɥɢɧɟɣɧɚɹ ɫɤɨɪɨɫɬɶ ɞɜɢɠɟɧɢɹ ɧɨɝɢ, ɤɨɬɨɪɚɹ ɡɚɞɚɟɬɫɹ (D11). ȼɵɱɢɫɥɹɟɦ ɦɚɤɫɢɦɚɥɶɧɨ ɜɨɡɦɨɠɧɨɟ ɜɪɟɦɹ ɭɞɚɪɚ ɩɨ ɦɹɱɭ ɩɨ ɮɨɪɦɭɥɟ ‫ ˇ˖ݐ‬ൌ ߮˖ˇ Ȁ߱˖ˇ Ǥ Ʉɚɤ ɩɨɤɚɡɚɥɨ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ 20 ɜɪɟɦɟɧɧɵɯ ɢɧɬɟɪɜɚɥɨɜ ɞɨɫɬɚɬɨɱɧɨ ɞɥɹ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɭɞɚɪɚ ɩɨ ɦɹɱɭ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜɪɟɦɟɧɧɨɣ ɲɚɝ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɭɞɚɪɚ ɨɩɪɟɞɟɥɹɟɦ ɩɨ ɜɵɪɚɠɟɧɢɸ ο‫ ˇ˖ݐ‬ൌ ‫ ˇ˖ݐ‬/20. ɍɝɥɨɜɭɸ ɫɤɨɪɨɫɬɶ ɢ ɜɪɟɦɟɧɧɨɣ ɢɧɬɟɪɜɚɥ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɡɚɩɢɫɵɜɚɟɦ ɜ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɹɱɟɣɤɢ ɦɚɫɫɢɜɨɜ. ɉɪɢ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɦɨɠɧɨ ɫɞɟɥɚɬɶ ɡɚɩɢɫɢ ɢ ɞɪɭɝɢɯ ɜɵɱɢɫɥɹɟɦɵɯ ɩɚɪɚɦɟɬɪɨɜ. Ⱦɥɹ ɨɪɝɚɧɢɡɚɰɢɢ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɨɛɧɭɥɹɟɦ ɫɱɟɬɱɢɤɢ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɭɞɚɪɚ ɢ ɩɨɥɟɬɚ ɦɹɱɚ. Ɍɟɤɫɬ ɩɪɨɝɪɚɦɦɵ ɤɧɨɩɤɢ «ɇɚɱɚɥɶɧɵɟ ɭɫɬɚɧɨɜɤɢ» ɩɪɢɜɟɞɟɧ ɧɢɠɟ. Private Sub CommandButton1_Click() 159

2. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ MS Excel

Range(Cells(2, 9), Cells(10, 9)) = Null 'Ɉɛɧɭɥɟɧɢɟ ɬɟɤɭɳɢɯ ɩɚɪɚɦɟɬɪɨɜ ɦɨɞɟɥɢ Range(Cells(36, 4), Cells(75, 5)) = Null 'Ɉɛɧɭɥɟɧɢɟ ɦɚɫɫɢɜɚ ɬɪɚɟɤɬɨɪɢɢ, ɰɟɬɪɚ ɦɚɫɫɵ ɦɹɱɚ ɢ ɭɞɚɪɧɨɣ ɧɨɝɢ Cells(36, 4) = Cells(5, 4) 'Ɂɚɩɢɫɶ ɤɨɨɪɞɢɧɚɬ ɭɫɬɚɧɨɜɤɢ ɦɹɱɚ Cells(36, 5) = Cells(3, 4) Prydara = 0 'Ɉɛɧɭɥɟɧɢɟ ɩɪɢɡɧɚɤɚ ɭɞɚɪɚ ɩɨ ɦɹɱɭ bcp = Cells(8, 4) - 2 * Cells(3, 4) fyd = Atn((Cells(8, 4) ^ 2 - bcp ^ 2) ^ 0.5 / bcp) 'ȼɵɱɢɫɥɟɧɢɟ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɭɝɥɚ ɩɨɜɨɪɨɬɚ ɧɨɝɢ ɫ ɭɱɟɬɨɦ ɜɵɫɨɬɵ ɦɹɱɚ wyd = Cells(11, 4) / Cells(8, 4) 'ɍɝɥɨɜɚɹ ɫɤɨɪɨɫɬɶ ɭɞɚɪɚ Cells(12, 4) = wyd 'Ɂɚɩɢɫɶ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɢ ɭɞɚɪɚ ɜ ɦɚɫɫɢɜ tyd = fyd / wyd 'ȼɪɟɦɹ ɭɞɚɪɚ dtyd = tyd / 20 'ȼɪɟɦɟɧɧɨɣ ɲɚɝ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɭɞɚɪɚ Cells(3, 9) = dtyd 'Ɂɚɩɢɫɶ ɜɪɟɦɟɧɧɨɝɨ ɲɚɝɚ ɜ ɦɚɫɫɢɜ i = 0 'ɇɚɱɚɥɶɧɵɟ ɡɧɚɱɟɧɢɹ ɫɱɟɬɱɢɤɚ ɲɚɝɨɜ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɭɞɚɪɚ ɩɨ ɦɹɱɭ j = 0 'ɇɚɱɚɥɶɧɵɟ ɡɧɚɱɟɧɢɹ ɫɱɟɬɱɢɤɚ ɲɚɝɨɜ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɬɪɚɟɤɬɨɪɢɢ ɩɨɥɟɬɚ ɦɹɱɚ End Sub ȼ ɪɟɡɭɥɶɬɚɬɟ ɳɟɥɱɤɚ ɩɨ ɤɧɨɩɤɟ ɩɨɥɭɱɚɟɦ ɜɬɨɪɭɸ ɞɢɚɝɪɚɦɦɭ ɫ ɤɪɭɩɧɵɦ ɩɥɚɧɨɦ ɧɨɝɢ ɢ ɦɹɱɚ (ɩɪɟɞɜɚɪɢɬɟɥɶɧɨ ɧɭɠɧɨ ɡɚɧɟɫɬɢ ɜɫɟ ɧɟɨɛɯɨɞɢɦɵɟ ɢɫɯɨɞɧɵɟ ɞɚɧɧɵɟ).

Ⱥɧɚɥɨɝɢɱɧɨ ɫɨɡɞɚɟɦ ɜɬɨɪɭɸ ɤɧɨɩɤɭ «Ɇɨɞɟɥɢɪɨɜɚɧɢɟ» ɢ ɩɪɨɝɪɚɦɦɭ, ɤɨɬɨɪɚɹ ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɢɠɟ. ȼ ɷɬɨɣ ɩɪɨɝɪɚɦɦɟ ɨɫɭɳɟɫɬɜɥɹɟɦ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɭɞɚɪɚ ɩɨ ɦɹɱɭ, ɩɨɥɟɬ ɦɹɱɚ ɢ ɨɩɪɟɞɟɥɟɧɢɟ ɩɨɩɚɞɚɧɢɹ ɜ ɫɬɜɨɪ ɜɨɪɨɬ. ɉɪɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ ɭɞɚɪɚ ɩɨ ɦɹɱɭ ɧɭɠɧɨ ɩɨɥɭɱɢɬɶ ɧɚɱɚɥɶɧɵɟ ɩɚɪɚɦɟɬɪɵ ɬɪɚɟɤɬɨɪɢɢ ɩɨɥɟɬɚ, ɚ ɬɚɤɠɟ ɜɵɹɫɧɢɬɶ ɮɚɤɬ ɭɞɚɪɚ ɩɨ ɦɹɱɭ ɢ ɞɨɥɟɬɢɬ ɥɢ ɦɹɱ ɞɨ ɜɨɪɨɬ. ɉɨ ɢɫɯɨɞɧɵɦ ɩɚɪɚɦɟɬɪɚɦ ɜɵɱɢɫɥɹɟɦ ɤɨɨɪɞɢɧɚɬɵ ɜɟɪɯɚ ɩɨɞɜɢɠɧɨɣ ɧɨɝɢ ሺܺ଴ ǡ ܻ଴ ሻ ɜ ɷɤɪɚɧɧɨɣ ɩɥɨɫɤɨɫɬɢ. Ʉɨɨɪɞɢɧɚɬɵ ɡɚɩɢɫɵɜɚɟɦ ɜ ɦɚɫɫɢɜ ɭɞɚɪɧɨɣ ɧɨɝɢ ɞɥɹ ɢɡɨɛɪɚɠɟɧɢɹ ɟɟ ɞɜɢɠɟɧɢɹ ɧɚ ɞɢɚɝɪɚɦɦɟ. Ɉɧɢ ɨɩɪɟɞɟɥɹɸɬ ɰɟɧɬɪ ɜɪɚɳɟɧɢɹ ɭɞɚɪɧɨɣ ɧɨɝɢ. 160

2.2. Ɏɢɡɢɤɚ

Ⱦɚɥɟɟ ɩɪɨɜɟɪɹɟɦ ɪɚɜɟɧɫɬɜɨ ɧɭɥɸ ɩɪɢɡɧɚɤɚ Prydara ɢ ɧɚɱɢɧɚɟɦ ɦɨɞɟɥɢɪɨɜɚɬɶ ɞɜɢɠɟɧɢɟ ɧɨɝɢ ɩɨ ɜɪɟɦɟɧɧɵɦ ɬɚɤɬɚɦ. ȿɫɥɢ ɫɱɟɬɱɢɤ ɲɚɝɨɜ i ɪɚɜɟɧ ɧɭɥɸ, ɬɨ ɩɨɥɨɠɟɧɢɟ ɭɞɚɪɧɨɣ ɧɨɝɢ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɧɚɱɚɥɶɧɨɦɭ ɩɨɥɨɠɟɧɢɸ. Ɏɨɪɦɢɪɭɟɦ ɤɨɨɪɞɢɧɚɬɵ, ɤɨɬɨɪɵɟ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɧɟɩɨɞɜɢɠɧɨɣ ɧɨɝɟ ɢ ɡɚɩɢɫɵɜɚɟɦ ɜ ɦɚɫɫɢɜ ɞɥɹ ɨɬɨɛɪɚɠɟɧɢɹ. Ʉɚɠɞɵɣ ɬɚɤɬ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɳɟɥɱɤɨɦ ɩɨ ɤɧɨɩɤɟ «Ɇɨɞɟɥɢɪɨɜɚɧɢɟ». ɉɪɢ ɷɬɨɦ ɧɚɱɢɫɥɹɟɬɫɹ ɫɱɟɬɱɢɤ i. ɇɚ ɜɬɨɪɨɦ ɬɚɤɬɟ ɫɱɟɬɱɢɤ ɫɬɚɧɨɜɢɬɫɹ ɛɨɥɶɲɟ ɧɭɥɹ ɢ ɧɚɱɢɧɚɟɬɫɹ ɪɚɫɱɟɬ ɤɨɨɪɞɢɧɚɬ ɨɬɪɟɡɤɨɜ ɧɨɝɢ ɩɪɢ ɟɟ ɞɜɢɠɟɧɢɢ, ɤɨɬɨɪɵɟ (X0,Y0) ɡɚɩɢɫɵɜɚɟɦ ɜ ɦɚɫɫɢɜ ɞɢɚɝɪɚɦɦɵ. ɋɱɢɬɚɟɦ, ɱɬɨ ɭɞɚɪ ɩɨ ɦɹɱɭ ɧɚɧɨɫɢɬɫɹ ɧɨɫɤɨɦ ɧɨɝɢ. ɇɚɱɢɧɚɟɦ ɜɵɱɢɫɥɹɬɶ ɤɨɨɪɞɢɧɚɬɵ N ƶi N ɩɹɬɤɢ ɧɨɝɢ ɩɨ ɮɨɪɦɭɥɚɦ (xɫi,yɫi) ‫˒ݔ‬௜ ൌ ܺ଴ െ ܰ ‫߮ ‹• כ‬௜ ǡ S మ ƶ ଶ i ‫˒ݕ‬௜ ൌ ܻ଴ െ ඥܰ െ ‫˒ݔ‬௜ , (xɩi,yɩi) ɝɞɟ ߮௜ ൌ ߱˖ˇ ‫ כ‬ο‫ – ݅ כ ˇ˖ݐ‬ɭɝɨɥ ɩɨɜɨɪɨɬɚ ɧɨS Xɷɤɪ ɝɢ ɧɚ ݅-ɦ ɲɚɝɟ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɭɞɚɪɚ. ɗɬɢ ɤɨɨɪɞɢɧɚɬɵ ɡɚɩɢɫɵɜɚɟɦ ɜ ɦɚɫɫɢɜ ɞɥɹ ɢɡɨɛɪɚɠɟɧɢɹ ɫɚɦɨɣ ɧɨɝɢ, ɚ ɬɚɤɠɟ ɤɚɤ ɤɨɨɪɞɢɧɚɬɵ ɩɹɬɤɢ ɞɥɹ ɢɡɨɛɪɚɠɟɧɢɹ ɫɬɨɩɵ. Ʉɨɨɪɞɢɧɚɬɵ ɧɨɫɤɚ ɧɨɝɢ ɨɩɪɟɞɟɥɹɟɦ ɩɨ ɮɨɪɦɭɥɚɦ ‫˔ݔ‬௜ ൌ ‫˒ݔ‬௜ െ ܵ ‫߮ •‘… כ‬௜ , ‫˔ݕ‬௜ ൌ ‫˒ݕ‬௜ ൅ ܵ ‫߮ ‹• כ‬௜ . ɂɦɟɹ ɤɨɨɪɞɢɧɚɬɵ ɫɬɨɩɵ, ɨɩɪɟɞɟɥɹɟɦ ɜɨɡɦɨɠɧɵɣ ɩɪɨɦɚɯ ɩɪɢ ɭɞɚɪɟ ɩɨ ɦɹɱɭ ɧɚ ɤɚɠɞɨɦ ɬɚɤɬɟ ɦɨɞɟɥɢɪɨɜɚɧɢɹ. ɋɧɚɱɚɥɚ ɜɵɱɢɫɥɹɟɦ ɤɜɚɞɪɚɬ ɪɚɫɫɬɨɹɧɢɹ ɨɬ ɰɟɧɬɪɚ ɦɹɱɚ ɞɨ ɧɨɫɤɚ ɫɬɨɩɵ ɩɨ ɜɵɪɚɠɟɧɢɸ ଶ ܴˏ˔ ൌ ሺ‫˔ݕ‬௜ െ ‫ ˏݕ‬ሻଶ ൅ ሺ‫˔ݔ‬௜ െ ‫ ˏݕ‬ሻଶ , ɚ ɡɚɬɟɦ ɜɵɩɨɥɧɟɧɢɟ ɭɫɥɨɜɢɹ: ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɰɟɧɬɪɨɦ ɦɹɱɚ ɢ ɧɨɫɤɨɦ ɫɬɨɩɵ ɛɨɥɶɲɟ ɪɚɞɢɭɫɚ ɦɹɱɚ ɢ ɜɵɫɨɬɚ ɫɬɨɩɵ ɛɨɥɶɲɟ ɜɵɫɨɬɵ ɦɹɱɚ ɢ ɲɚɝ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɛɨɥɶɲɟ ɦɚɤɫɢɦɚɥɶɧɨɝɨ. ɉɪɢ ɜɵɩɨɥɧɟɧɢɢ ɷɬɨɝɨ ɭɫɥɨɜɢɹ ɜɵɞɚɟɬɫɹ ɫɨɨɛɳɟɧɢɟ «ɍɞɚɪ ɦɢɦɨ ɦɹɱɚ». ȼ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ ɞɨɩɨɥɧɢɬɟɥɶɧɨ ɩɪɨɜɟɪɹɟɬɫɹ ɭɫɥɨɜɢɟ: Yɷɤɪ ɪɚɫɫɬɨɹɧɢɟ ɦɟɠV ɞɭ ɰɟɧɬɪɨɦ ɦɹɱɚ ƶi ɢ ɧɨɫɤɨɦ ɫɬɨɩɵ (xɦ ,yɦ) Vɦ ɦɟɧɶɲɟ ɪɚɞɢɭɫɚ ơȀDZ (xɫi,yɫi) ɦɹɱɚ. ƶi ȼ ɩɨɥɨɠɢɬɟɥɶɧɨɦ ɫɥɭɱɚɟ ɜɵXɷɤɪ (xɩi,yɩi) ɱɢɫɥɹɸɬɫɹ ɧɚɱɚɥɶɧɵɟ ɩɚɪɚɦɟɬɪɵ 161

2. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ MS Excel

ɬɪɚɟɤɬɨɪɢɢ ɩɨɥɟɬɚ ɦɹɱɚ: ɧɚɱɚɥɶɧɚɹ ɫɤɨɪɨɫɬɶ ɢ ɭɝɨɥ ɧɚɤɥɨɧɚ ɜɟɤɬɨɪɚ ɫɤɨɪɨɫɬɢ ɤ ɝɨɪɢɡɨɧɬɭ. ɇɚɱɚɥɶɧɵɣ ɭɝɨɥ ɧɚɤɥɨɧɚ ɜɟɤɬɨɪɚ ɫɤɨɪɨɫɬɢ ɦɹɱɚ ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ ߙ˖ˇ ൌ ܽ‫݃ݐܿݎ‬ሺሺ‫ ˏݕ‬െ ‫˕˔ݕ‬௜ ሻΤሺ‫˕˔ݔ‬௜ െ ‫ ˏݔ‬ሻሻ. ɋɱɢɬɚɟɦ, ɱɬɨ ɭɞɚɪ ɩɨ ɦɹɱɭ ɩɪɨɢɡɜɨɞɢɬɫɹ ɦɝɧɨɜɟɧɧɨ. ɋ ɭɱɟɬɨɦ ɦɚɫɫ ɦɹɱɚ ɢ ɧɨɝɢ ɜɵɱɢɫɥɹɟɦ ɧɚɱɚɥɶɧɭɸ ɫɤɨɪɨɫɬɶ ɩɨɥɟɬɚ ɦɹɱɚ ܸˏ ൌ ݉ː Τ݉ˏ ‫•‘… כ ܸ כ‬൫߮௜ െ ߙ˖ˇ ൯ǡ ɝɞɟ ݉ː - ɦɚɫɫɚ ɧɨɝɢ, ݉ˏ – ɦɚɫɫɚ ɦɹɱɚ, ܸ- ɫɤɨɪɨɫɬɶ ɭɞɚɪɧɨɣ ɧɨɝɢ. ɉɨɫɥɟ ɷɬɨɝɨ ɩɪɨɜɟɪɹɟɬɫɹ ɡɧɚɤ ɧɚɱɚɥɶɧɨɝɨ ɭɝɥɚ ɧɚɤɥɨɧɚ ɫɤɨɪɨɫɬɢ ɩɨɥɟɬɚ ɦɹɱɚ. ɉɪɢ ɡɧɚɱɟɧɢɢ ɛɨɥɶɲɟ ɧɭɥɹ ɜɵɞɚɟɬɫɹ ɫɨɨɛɳɟɧɢɟ «ɍɞɚɪ ɩɨ ɦɹɱɭ ɢ ɦɹɱ ɩɨɥɟɬɢɬ!!!» ɢ ɮɨɪɦɢɪɭɟɬɫɹ ɩɪɢɡɧɚɤ ɩɨɥɟɬɚ ɦɹɱɚ Prydara = 3, ɚ ɜ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ – «ɍɞɚɪ ɩɨ ɦɹɱɭ, ɧɨ ɦɹɱ ɩɨɤɚɬɢɬɫɹ ɩɨ ɡɟɦɥɟ!!!"». ɇɚ ɫɥɟɞɭɸɳɟɦ ɬɚɤɬɟ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɩɪɢ Prydara = 3 ɩɪɨɢɡɜɨɞɢɬɫɹ ɪɚɫɱɟɬ ɞɚɥɶɧɨɫɬɢ ɩɨɥɟɬɚ ɦɹɱɚ ɩɨ ɪɚɫɱɟɬɧɵɦ ɧɚɱɚɥɶɧɵɦ ɭɫɥɨɜɢɹɦ ɩɨ ɮɨɪɦɭɥɟ ܴ˒ˑˎ ൌ ܸˏଶ ‫‹• כ‬ሺʹ ‫ ˇ˖ߙ כ‬ሻ ‫݃ כ‬଴ , ଶ ɝɞɟ ݃଴ ൌ ͻǡͺͳ ˏΤ˔ – ɭɫɤɨɪɟɧɢɟ ɫɜɨɛɨɞɧɨɝɨ ɩɚɞɟɧɢɹ. ȼɫɟ ɪɚɫɱɟɬɵ ɞɟɥɚɸɬɫɹ ɩɪɢ ɩɪɟɞɩɨɥɨɠɟɧɢɢ ɩɨɥɟɬɚ ɦɹɱɚ ɜ ɨɞɧɨɪɨɞɧɨɦ ɩɨɥɟ ɫɢɥɵ ɬɹɠɟɫɬɢ (ɫɦ. ɡɚɞɚɱɭ Ɍɪɚɟɤɬɨɪɢɹ ɩɨɥɟɬɚ ɛɪɨɲɟɧɧɨɝɨ ɬɟɥɚ). ȿɫɥɢ ɞɚɥɶɧɨɫɬɶ ɩɨɥɟɬɚ ɦɟɧɶɲɟ 11ɦɟɬɪɨɜ, ɬɨ ɜɵɞɚɟɬɫɹ ɫɨɨɛɳɟɧɢɟ «Ɇɹɱ ɧɟ ɞɨɥɟɬɢɬ ɞɨ ɜɨɪɨɬ!!!». ȼ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ ɜɵɱɢɫɥɹɟɬɫɹ ɜɪɟɦɹ ɩɨɥɟɬɚ ɦɹɱɚ ɩɨ ɮɨɪɦɭɥɟ ܶ˒ˑˎ ൌ ܸˏ ‫‹• כ‬ሺ ߙ˖ˇ ሻȀ݃଴ , ɚ ɡɚɬɟɦ ɜɪɟɦɟɧɧɨɣ ɲɚɝ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɬɪɚɟɤɬɨɪɢɢ ο‫ ݐ‬ൌ ܶ˒ˑˎ ȀʹͲ. Ⱦɚɥɟɟ ɩɪɨɜɨɞɢɬɫɹ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɩɨɥɟɬɚ ɦɹɱɚ, ɩɪɨɜɟɪɤɚ ɩɨɩɚɞɚɧɢɹ ɟɝɨ ɜ ɜɨɪɨɬɚ ɢ ɜɵɜɨɞ ɫɨɨɛɳɟɧɢɹ ɨɛ ɨɤɨɧɱɚɧɢɢ ɦɨɞɟɥɢɪɨɜɚɧɢɹ. ɉɪɢ ɨɤɨɧɱɚɧɢɢ ɬɚɤɬɚ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɧɚɱɢɫɥɹɟɬɫɹ ɫɱɟɬɱɢɤ j, ɚ ɤɚɠɞɵɣ ɬɚɤɬ ɧɚɱɢɧɚɟɬɫɹ ɫ ɳɟɥɱɤɚ ɧɚ ɤɧɨɩɤɟ «Ɇɨɞɟɥɢɪɨɜɚɧɢɟ». ɇɚ ɤɚɠɞɨɦ ɬɚɤɬɟ ɜɵɱɢɫɥɹɸɬɫɹ ɬɟɤɭɳɢɟ ɤɨɨɪɞɢɧɚɬɵ ɬɪɚɟɤɬɨɪɢɢ ɩɨɥɟɬɚ ɦɹɱɚ (ɟɝɨ ɰɟɧɬɪɚ ɬɹɠɟɫɬɢ) ɩɨ ɮɨɪɦɭɥɚɦ ‫ˏݔ‬௝ ൌ ‫ ˏܮ‬െ ሺܸˏ௝ ‫ ˇ˖ߙ •‘… כ‬ሻ ‫ כ‬ο‫݆ כ ݐ‬, ‫ˏݕ‬௝ ൌ ሺܸˏ௝ ‫ ˇ˖ߙ ‹• כ‬ሻ ‫ כ‬ο‫ ݆ כ ݐ‬െ ݃଴ ‫ כ‬ሺο‫݆ כ ݐ‬ሻଶ Ȁʹ. Ɍɚɤɠɟ ɪɚɫɫɱɢɬɵɜɚɟɦ ɩɨɥɧɭɸ ɫɤɨɪɨɫɬɶ ɦɹɱɚ ɧɚ j-ɦ ɬɚɤɬɟ ଶ ଶ ൅ ܸ˅ˈ˓௝ ሻ଴ǡହ , ܸˏ௝ ൌ ሺܸˆˑ˓ ɝɞɟ ܸˆˑ˓ ൌ ܸˏ ‫ ˇ˖ߙ •‘… כ‬- ɝɨɪɢɡɨɧɬɚɥɶɧɚɹ ɫɤɨɪɨɫɬɶ ɦɹɱɚ (ɩɨɫɬɨɹɧɧɚɹ), 162

2.2. Ɏɢɡɢɤɚ

ܸ˅ˈ˓௝ ൌ ܸˏ ‫ ˇ˖ߙ ‹• כ‬െ ݃଴ ‫ כ‬ο‫݆ כ ݐ‬- ɜɟɪɬɢɤɚɥɶɧɚɹ ɫɤɨɪɨɫɬɶ ɦɹɱɚ. ȼɫɟ ɪɚɫɱɟɬɧɵɟ ɩɚɪɚɦɟɬɪɵ ɡɚɩɢɫɵɜɚɟɦ ɜ ɦɚɫɫɢɜ I2:I10. Ɇɨɠɧɨ ɦɚɫɫɢɜ ɞɨɩɨɥɧɢɬɶ ɩɪɢ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɞɪɭɝɢɦɢ ɩɚɪɚɦɟɬɪɚɦɢ. Ɍɚɤɠɟ ɨɞɧɨɜɪɟɦɟɧɧɨ ɢɞɟɬ ɡɚɩɢɫɶ ɤɨɨɪɞɢɧɚɬ ɬɪɚɟɤɬɨɪɢɢ ɦɹɱɚ ɜ ɦɚɫɫɢɜ D38:E69 (ɜɢɞɢɦ 4-ɟ ɬɨɱɤɢ ɤɨɨɪɞɢɧɚɬ ɦɹɱɚ). Ⱦɚɥɟɟ ɩɪɨɜɨɞɢɦ ɩɪɨɜɟɪɤɭ ɩɨɩɚɞɚɧɢɹ ɜ ɫɬɜɨɪ ɜɨɪɨɬ. ȿɫɥɢ ɤɨɨɪɞɢɧɚɬɚ ɩɨ ɞɚɥɶɧɨɫɬɢ ɰɟɧɬɪɚ ɬɹɠɟɫɬɢ ɦɹɱɚ ɦɟɧɶɲɟ ɧɭɥɹ, ɚ ɜɵɫɨɬɚ ɦɹɱɚ ɦɟɧɶɲɟ ɜɵɫɨɬɵ ɜɨɪɨɬ, ɬɨ ɩɨɩɚɥɢ ɜ ɜɨɪɨɬɚ ɢ ɜɵɞɚɟɬɫɹ ɫɨɨɛɳɟɧɢɟ «ȽɈɅ ȽɈɅ ȽɈɅ!!!».

ȿɫɥɢ ɜɵɫɨɬɚ ɦɹɱɚ ɛɨɥɶɲɟ ɜɵɫɨɬɵ ɜɨɪɨɬ, ɬɨ ɜɵɞɚɟɬɫɹ ɫɨɨɛɳɟɧɢɟ «ȼɵɲɟ ɜɨɪɨɬ!!!». ȼ ɨɛɨɢɯ ɫɥɭɱɚɹɯ ɩɪɢɡɧɚɤ Prydara = 4 ɢ ɧɚ ɫɥɟɞɭɸɳɟɦ ɬɚɤɬɟ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɜɵɞɚɟɬɫɹ ɫɨɨɛɳɟɧɢɟ «Ʉɨɧɟɰ ɦɨɞɟɥɢɪɨɜɚɧɢɹ». ɉɪɨɝɪɚɦɦɚ ɤɧɨɩɤɢ «Ɇɨɞɟɥɢɪɨɜɚɧɢɟ» ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɢɠɟ. Private Sub CommandButton2_Click() Cells(71, 4) = Cells(5, 4) + Cells(10, 4) 'Ʉɨɨɪɞɢɧɚɬɚ ɯɷɤɪ ɜɟɪɯɚ ɧɨɝɢ Cells(71, 5) = Cells(8, 4) 'Ʉɨɨɪɞɢɧɚɬɚ yɷɤɪ ɜɟɪɯɚ ɧɨɝɢ If Prydara = 0 Then 'Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɭɞɚɪɚ ɩɨ ɦɹɱɭ If i = 0 Then 'ɇɚɱɚɥɶɧɨɟ ɩɨɥɨɠɟɧɢɟ ɧɨɝɢ Cells(72, 4) = Cells(5, 4) + Cells(10, 4) 'Ʉɨɨɪɞɢɧɚɬɚ ɯɷɤɪ ɧɢɡɚ ɧɨɝɢ Cells(72, 5) = 0 'Ʉɨɨɪɞɢɧɚɬɚ yɷɤɪ ɧɢɡɚ ɧɨɝɢ Cells(74, 4) = Cells(5, 4) + Cells(10, 4) 'Ʉɨɨɪɞɢɧɚɬɚ ɯɷɤɪ ɩɹɬɤɢ Cells(74, 5) = 0 'Ʉɨɨɪɞɢɧɚɬɚ yɷɤɪ ɩɹɬɤɢ Cells(75, 4) = Cells(5, 4) + Cells(10, 4) - Cells(9, 4) 'Ʉɨɨɪɞɢɧɚɬɚ ɯɷɤɪ ɫɬɨɩɵ ɛɟɡ ɩɹɬɤɢ Cells(75, 5) = 0 'Ʉɨɨɪɞɢɧɚɬɚ yɷɤɪ ɫɬɨɩɵ ɛɟɡ ɩɹɬɤɢ End If If i > 0 Then 'Ⱦɜɢɠɟɧɢɟ ɧɨɝɢ ɩɪɢ ɭɞɚɪɟ 163

2. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ MS Excel

t = dtyd * i 'Ɍɟɤɭɳɢɟ ɜɪɟɦɟɧɹ ɭɞɚɪɚ Cells(2, 9) = t 'Ɂɚɩɢɫɶ ɬɟɤɭɳɟɝɨ ɜɪɟɦɟɧɢ ɭɞɚɪɚ fi = wyd * t 'ɍɝɨɥ ɩɨɜɨɪɨɬɚ ɧɨɝɢ ɩɪɢ ɭɞɚɪɟ xs = Cells(5, 4) + Cells(10, 4) - Cells(8, 4) * Sin(fi) ys= Cells(8, 4) - (Cells(8, 4) ^ 2 - (Cells(8, 4) * Sin(fi)) ^ 2) ^ 0.5 Cells(72, 4) = xs 'Ɍɟɤɭɳɢɟ ɷɤɪɚɧɧɵɟ ɤɨɨɪɞɢɧɚɬɵ ɧɢɡɚ ɧɨɝɢ Cells(72, 5) = ys Cells(74, 4) = xs 'Ɍɟɤɭɳɢɟ ɷɤɪɚɧɧɵɟ ɤɨɨɪɞɢɧɚɬɵ ɩɹɬɤɢ Cells(74, 5) = ys Cells(75, 4) = xs - Cells(9, 4) * Cos(fi) 'Ɍɟɤɭɳɢɟ ɷɤɪɚɧɧɵɟ ɤɨɨɪɞɢɧɚɬɵ ɧɨɫɤɚ ɫɬɨɩɵ Cells(75, 5) = ys + Cells(9, 4) * Sin(fi) rdom = (Cells(75, 4) - Cells(5, 4)) ^ 2 + (Cells(75, 5) - Cells(3, 4)) ^ 2 If rdom > Cells(3, 4) ^ 2 And ys > 2 * Cells(3, 4) And i > 20 Then MsgBox "ɍɞɚɪ ɦɢɦɨ ɦɹɱɚ" 'ȼɵɞɚɱɚ ɫɨɨɛɳɟɧɢɹ Else If rdom 26 Then MsgBox "Ʉɨɧɟɰ ɦɨɞɟɥɢɪɨɜɚɧɢɸ" 'ȼɵɞɚɱɚ ɫɨɨɛɳɟɧɢɹ End If End Sub. ȼ ɩɪɨɜɟɪɤɟ ɨɤɨɧɱɚɧɢɹ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɫɱɟɬɱɢɤ j ɫɪɚɜɧɢɜɚɟɬɫɹ ɫ ɱɢɫɥɨɦ 26, ɤɨɬɨɪɨɟ ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɨɥɢɱɟɫɬɜɨɦ ɫɬɨɥɛɰɨɜ ɜ ɦɚɫɫɢɜɟ ɞɢɚɝɪɚɦɦɵ. ɉɪɢ ɢɯ ɭɜɟɥɢɱɟɧɢɢ ɢɥɢ ɭɦɟɧɶɲɟɧɢɢ ɧɭɠɧɨ ɢɡɦɟɧɢɬɶ ɱɢɫɥɨ. ȼ ɩɪɨɰɟɞɭɪɟ ɤɧɨɩɤɢ «ɇɚɱɚɥɶɧɵɟ ɭɫɬɚɧɨɜɤɢ» ɨɱɢɳɚɟɦ ɧɚɡɜɚɧɢɟ ɢ ɡɚɞɚɟɦ ɩɭɫɬɵɟ ɞɢɚɩɚɡɨɧɵ ɞɥɹ ɭɞɚɥɟɧɢɹ ɤɪɢɜɨɣ. Private Sub CommandButton1_Click() j = 0 'Ɉɛɧɭɥɟɧɢɟ ɫɱɟɬɱɢɤɚ ɩɨ ɞɚɥɶɧɨɫɬɢ 169

2. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ MS Excel

ActiveSheet.ChartObjects(2).Chart.HasTitle = False 'ɍɞɚɥɟɧɢɟ ɧɚɡɜɚɧɢɹ ɝɪɚɮɢɤɚ ActiveSheet.ChartObjects(2).Chart.HasTitle = True ' Ɏɨɪɦɢɪɨɜɚɧɢɟ ɧɚɡɜɚɧɢɹ ɞɢɚɝɪɚɦɦɵ ActiveSheet.ChartObjects(2).Chart.ChartTitle.Text = " " ActiveSheet.ChartObjects(2).Chart.SeriesCollection(1).XValues = Range("$AM$10:$AM$11") 'Ɂɚɞɚɧɢɟ ɩɭɫɬɨɝɨ ɞɢɚɩɚɡɨɧɚ ɞɚɧɧɵɯ ɞɥɹ ɨɫɢ ɚɛɫɰɢɫɫ ActiveSheet.ChartObjects(2).Chart.SeriesCollection(1).Values = Range("$AN$10:$AN$11") 'Ɂɚɞɚɧɢɟ ɩɭɫɬɨɝɨ ɞɢɚɩɚɡɨɧɚ ɞɚɧɧɵɯ ɞɥɹ ɨɫɢ ɨɪɞɢɧɚɬ End Sub. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɫɧɚɱɚɥɚ ɳɟɥɤɚɟɦ ɧɚ ɤɧɨɩɤɟ «ɇɚɱɚɥɶɧɵɟ ɭɫɬɚɧɨɜɤɢ», ɚ ɡɚɬɟɦ ɳɟɥɤɚɟɦ ɧɚ ɤɧɨɩɤɟ «ȼɵɛɨɪ ɩɨ ɩɚɪɚɦɟɬɪɭ ɞɚɥɶɧɨɫɬɶ» ɞɥɹ ɩɟɪɟɛɨɪɚ ɫɪɟɡɨɜ ɩɨ ɞɚɥɶɧɨɫɬɢ ɢ ɧɚɛɥɸɞɚɟɦ ɞɜɢɠɟɧɢɟ ɜɨɥɧɵ.

Ⱥɧɚɥɨɝɢɱɧɨ ɫɨɡɞɚɟɦ ɞɢɚɝɪɚɦɦɭ ɞɥɹ ɫɪɟɡɨɜ ɩɨ ɜɪɟɦɟɧɢ, ɧɨ ɜɵɞɟɥɹɟɦ ɞɢɚɩɚɡɨɧ ɹɱɟɟɤ ɋ9:Ⱥɋ10. ɉɪɨɝɪɚɦɦɚ ɤɧɨɩɤɢ «ȼɵɛɨɪ ɩɨ ɩɚɪɚɦɟɬɪɭ ɜɪɟɦɹ» ɜɵɝɥɹɞɢɬ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ: Private Sub CommandButton3_Click() k = Round(i * Cells(5, 2), 3) 'ȼɵɱɢɫɥɟɧɢɟ ɬɟɤɭɳɟɝɨ ɜɪɟɦɟɧɢ ɫ ɨɤɪɭɝɥɟɧɢɟɦ ActiveSheet.ChartObjects(3).Chart.HasTitle = False 'ɍɞɚɥɟɧɢɟ ɧɚɡɜɚɧɢɹ ɝɪɚɮɢɤɚ ActiveSheet.ChartObjects(3).Chart.HasTitle = True ' Ɏɨɪɦɢɪɨɜɚɧɢɟ ɧɚɡɜɚɧɢɹ ɞɢɚɝɪɚɦɦɵ ActiveSheet.ChartObjects(3).Chart.ChartTitle.Text = "T" & i & "=" & k & ", ɫɟɤ" ActiveSheet.ChartObjects(3).Chart.SeriesCollection(1).XValues = Range("$c$9:$ac$9") 'Ɂɚɞɚɧɢɟ ɞɢɚɩɚɡɨɧɚ ɞɚɧɧɵɯ ɞɥɹ ɨɫɢ ɚɛɫɰɢɫɫ

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2.2. Ɏɢɡɢɤɚ

ActiveSheet.ChartObjects(3).Chart.SeriesCollection(1).Values = Range(Cells(10 + i, 3), Cells(10 + i, 29)) 'Ɂɚɞɚɧɢɟ ɞɢɚɩɚɡɨɧɚ ɞɚɧɧɵɯ ɞɥɹ ɨɫɢ ɨɪɞɢɧɚɬ i = i + 1 'ɇɚɱɢɫɥɟɧɢɟ ɫɱɟɬɱɢɤɚ ɩɨ ɞɚɥɶɧɨɫɬɢ If i > 91 Then MsgBox "Ʉɨɧɟɰ ɦɨɞɟɥɢɪɨɜɚɧɢɸ" 'ȼɵɞɚɱɚ ɫɨɨɛɳɟɧɢɹ End If End Sub. ɉɪɨɰɟɞɭɪɚ ɤɧɨɩɤɢ «ɇɚɱɚɥɶɧɵɟ ɭɫɬɚɧɨɜɤɢ» ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɢɠɟ Private Sub CommandButton4_Click() i = 0 'Ɉɛɧɭɥɟɧɢɟ ɫɱɟɬɱɢɤɚ ɩɨ ɜɪɟɦɟɧɢ ActiveSheet.ChartObjects(3).Chart.HasTitle = False 'ɍɞɚɥɟɧɢɟ ɧɚɡɜɚɧɢɹ ɝɪɚɮɢɤɚ ActiveSheet.ChartObjects(3).Chart.HasTitle = True ' Ɏɨɪɦɢɪɨɜɚɧɢɟ ɧɚɡɜɚɧɢɹ ɞɢɚɝɪɚɦɦɵ ActiveSheet.ChartObjects(3).Chart.ChartTitle.Text = " " ActiveSheet.ChartObjects(3).Chart.SeriesCollection(1).XValues = Range("$AM$9:$AN$9") 'Ɂɚɞɚɧɢɟ ɩɭɫɬɨɝɨ ɞɢɚɩɚɡɨɧɚ ɞɚɧɧɵɯ ɞɥɹ ɨɫɢ ɚɛɫɰɢɫɫ ActiveSheet.ChartObjects(3).Chart.SeriesCollection(1).Values = Range("$AM$10:$An$10") 'Ɂɚɞɚɧɢɟ ɩɭɫɬɨɝɨ ɞɢɚɩɚɡɨɧɚ ɞɚɧɧɵɯ ɞɥɹ ɨɫɢ ɨɪɞɢɧɚɬ End Sub. Ɍɟɩɟɪɶ ɦɨɠɧɨ ɩɪɟɫɬɭɩɢɬɶ ɤ ɫɨɡɞɚɧɢɸ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨɣ ɢɧɬɟɪɮɟɪɟɧɰɢɨɧɧɨɣ ɤɚɪɬɢɧɵ ɞɜɭɯ ɜɨɥɧ. Ⱦɥɹ ɢɧɬɟɪɮɟɪɟɧɰɢɢ ɜɨɥɧ ɞɨɥɠɧɵ ɫɨɛɥɸɞɚɬɶɫɹ ɫɥɟɞɭɸɳɢɟ ɭɫɥɨɜɢɹ: x ȼɨɥɧɵ ɞɨɥɠɧɵ ɢɦɟɬɶ ɨɞɢɧɚɤɨɜɵɟ ɭɝɥɨɜɵɟ ɱɚɫɬɨɬɵ. x ȼɨɥɧɵ ɞɨɥɠɧɵ ɪɚɫɩɪɨɫɬɪɚɧɹɬɶɫɹ ɜ «ɨɞɢɧɚɤɨɜɵɯ» ɧɚɩɪɚɜɥɟɧɢɹɯ. ɂɦɟɟɦ ɞɜɟ ɜɨɥɧɵ: ‫ͳݕ‬ሺ‫ݐ‬ǡ ‫ͳݔ‬ሻ ൌ ܽ ‫‹• כ‬ሺ߱ ‫ ݐ כ‬െ ݇ ‫ͳݔ כ‬ሻ, ‫ʹݕ‬ሺ‫ݐ‬ǡ ‫ʹݔ‬ሻ ൌ ܽ ‫‹• כ‬ሺ߱ ‫ ݐ כ‬െ ݇ ‫ʹݔ כ‬ሻ, ɝɞɟ ‫ ͳݔ‬ɢ ‫ ʹݔ‬- ɪɚɫɫɬɨɹɧɢɹ ɨɬ ɢɫɬɨɱɧɢɤɨɜ ɜɨɥɧ ɞɨ ɬɨɱɤɢ ɫɥɨɠɟɧɢɹ ɜɨɥɧ. ȼ ɬɨɱɤɟ ɫɥɨɠɟɧɢɹ ɢɦɟɟɦ ‫ݕ‬ሺ‫ݐ‬ǡ ‫ͳݔ‬ǡ ‫ʹݔ‬ሻ ൌ ‫ݕ‬ሺ‫ݐ‬ǡ ‫ͳݔ‬ሻ ൅ ‫ݕ‬ሺ‫ݐ‬ǡ ‫ʹݔ‬ሻ ൌ ‫‹• כ ܣ‬ሺȰሻ, మ ଶ ɝɞɟ ‫ ܣ‬ൌ ඥܽ ൅ ܽଶ ൅ ʹܽ ‫•‘… כ ܽ כ‬ሺȰଶ െ Ȱଵ ሻ ൌ ܽ ‫ כ‬మඥʹ ൅ ʹ ‫•‘… כ‬ሺȰଶ െ Ȱଵ ሻ – ɚɦɩɥɢɬɭɞɚ ɪɟɡɭɥɶɬɢɪɭɸɳɟɣ ɜɨɥɧɵ, Ȱଶ ൌ െ݇ ‫ – ʹݔ כ‬ɧɚɛɟɝ ɮɚɡɚ ɜɬɨɪɨɣ ɜɨɥɧɵ ɜ ɬɨɱɤɟ ɫɥɨɠɟɧɢɹ ɜɨɥɧ, Ȱଵ ൌ െ݇ ‫ – ͳݔ כ‬ɧɚɛɟɝ ɮɚɡɚ ɩɟɪɜɨɣ ɜɨɥɧɵ ɜ ɬɨɱɤɟ ɫɥɨɠɟɧɢɹ ɜɨɥɧ, ୱ୧୬ሺ஍భ ሻାୱ୧୬ሺ஍మ ሻ Ȱ ൌ ƒ”…–‰ሺ ሻ - ɮɚɡɚ ɪɟɡɭɥɶɬɢɪɭɸɳɟɝɨ ɤɨɥɟɛɚɧɢɹ ɩɪɢ ɪɚɜɟɧୡ୭ୱሺ஍భ ሻାୡ୭ୱሺ஍మ ሻ

ɫɬɜɟ ɚɦɩɥɢɬɭɞ ɜɨɥɧ.

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2. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ MS Excel

ȼ ɩɟɪɜɭɸ ɨɱɟɪɟɞɶ ɪɚɫɫɱɢɬɚɟɦ 0 j ɪɚɫɫɬɨɹɧɢɹ ɞɨ ɤɚɠɞɨɣ ɬɨɱɤɢ ɫɥɨɠɟɧɢɹ xj ɜɨɥɧ ɧɚ ɩɥɨɫɤɨɫɬɢ. Ɋɚɡɨɛɶɟɦ ɜɫɸ 0 X1 i, j ɩɥɨɫɤɨɫɬɶ ɧɚ ɷɥɟɦɟɧɬɚɪɧɵɟ ɤɜɚɞɪɚɬɵ. ɑɟɦ ɦɟɧɶɲɟ ɫɬɨɪɨɧɚ ɤɜɚɞɪɚɬɚ, ɬɟɦ ɛɨi1 ɥɟɟ ɞɟɬɚɥɶɧɭɸ ɩɨɥɭɱɢɦ ɤɚɪɬɢɧɭ ɢɧX2 ɬɟɪɮɟɪɟɧɰɢɢ ɜɨɥɧ. ɋɬɨɪɨɧɚ ɞɨɥɠɧɚ ɛɵɬɶ ɦɟɧɶɲɟ ɞɥɢɧɵ ɜɨɥɧɵ. Ⱦɚɥɶɧɨɫɬɶ i2 ɨɬ ɢɫɬɨɱɧɢɤɨɜ ɜɨɥɧ ɞɨ ɜɵɛɪɚɧɧɨɣ ɬɨɱɤɢሺ݅ǡ ݆ሻ ɢɯ ɫɥɨɠɟɧɢɹ ɜɵɱɢɫɥɹɸɬɫɹ i ɤɚɤ xi మ ଶ ଶ ‫ ͳݔ‬ൌ ο‫ כ ݔ‬ඥሺ݅ െ ݅ͳሻ ൅ ݆ , మ ‫ ʹݔ‬ൌ ο‫ כ ݔ‬ඥሺ݅ െ ݅ʹሻଶ ൅ ݆ ଶ , ɝɞɟ ο‫ ݔ‬- ɫɬɨɪɨɧɚ ɤɜɚɞɪɚɬɚ, ݅ͳ ɢ ݅ʹ - ɤɨɨɪɞɢɧɚɬɵ ɢɫɬɨɱɧɢɤɨɜ ɜɨɥɧ ɧɚ ɨɫɢ ‫݅ݔ‬. Ɇɨɞɟɥɶ ɢɧɬɟɪɮɟɪɟɧɰɢɢ ɜɨɥɧ ɫɨɡɞɚɟɦ ɧɚ 3-ɟɦ ɥɢɫɬɟ. Ɏɨɪɦɢɪɭɟɦ ɹɱɟɣɤɢ ɞɥɹ ɩɚɪɚɦɟɬɪɨɜ ɜɨɥɧ, ɤɨɨɪɞɢɧɚɬ ɢɯ ɢɫɬɨɱɧɢɤɨɜ ɢ ɪɚɫɫɱɢɬɵɜɚɟɦ ɧɟɨɛɯɨɞɢɦɵɟ ɜɟɥɢɱɢɧɵ ɞɥɹ ɞɚɥɶɧɟɣɲɢɯ ɪɚɫɱɟɬɨɜ. Ɂɚɞɚɟɦ ɢɡɦɟɧɟɧɢɹ ɢɧɞɟɤɫɨɜ ɤɨɨɪɞɢɧɚɬ ɭɡɥɨɜ ɧɚ ɩɥɨɫɤɨɫɬɢ (‫݅ݔ‬ǡ ‫݆ݔ‬ሻ: ݅ ൌ Ͳ ǥ ͸ͷ, ݆ ൌ Ͳ ǥ ͵Ͷ. ɉɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɞɟɥɚɟɦ ɪɚɫɱɟɬɵ Ȱଵ ,Ȱଶ , Ȱଶ െ Ȱଵ , ‫ܣ‬, Ȱ ɢ ‫ݕ‬ሺ‫ݐ‬ǡ ‫ͳݔ‬ǡ ‫ʹݔ‬ሻ. Ⱦɥɹ ɤɚɠɞɨɝɨ ɩɚɪɚɦɟɬɪɚ ɜɵɞɟɥɹɟɦ ɫɜɨɣ ɦɚɫɫɢɜ. Ⱦɥɹ ɪɚɫɱɟɬɚ Ȱଵ ɜɵɞɟɥɹɟɦ ɦɚɫɫɢɜ E6:AN72. ȼ ɫɬɨɥɛɰɟ ȿ ɮɨɪɦɢɪɭɟɦ ɡɧɚɱɟɧɢɹ ɞɚɥɶɧɨɫɬɢ, ɤɨɬɨɪɵɟ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɢɧɞɟɤɫɭ ݅ (ɫɬɨɥɛɟɰ D). Ⱥɧɚɥɨɝɢɱɧɨ ɮɨɪɦɢɪɭɟɦ ɡɧɚɱɟɧɢɹ ɞɚɥɶɧɨɫɬɢ ɩɨ ɢɧɞɟɤɫɭ ݆. ȼ ɹɱɟɣɤɟ F7 ɫɨɡɞɚɟɦ ɪɚɫɱɟɬɧɨɟ ɜɵɪɚɠɟɧɢɟ =-$B$11*$B$10*(($D7-$B$12)^2+F$5^2)^0,5, ɜ ɤɨɬɨɪɨɦ ɭɫɬɚɧɚɜɥɢɜɚɟɦ ɚɛɫɨɥɸɬɧɵɟ ɡɧɚɱɟɧɢɹ ɜ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɷɥɟɦɟɧɬɚɯ ɚɞɪɟɫɨɜ ɞɚɧɧɵɯ. Ɂɚɬɟɦ, ɢɫɩɨɥɶɡɭɹ ɦɟɯɚɧɢɡɦ ɚɜɬɨɡɚɩɨɥɧɟɧɢɹ, ɡɚɩɨɥɧɹɟɦ ɜɟɫɶ ɦɚɫɫɢɜ ɪɚɫɱɟɬɚ Ȱଵ . Ⱦɚɥɟɟ ɬɚɤɠɟ ɜɵɱɢɫɥɹɟɦ ɡɧɚɱɟɧɢɹ Ȱଶ . Ɂɚɬɟɦ – ɡɧɚɱɟɧɢɹ Ȱଶ െ Ȱଵ . ɋɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɜ MS Excel ɩɟɪɟɫɱɟɬ ɞɚɧɧɵɯ ɜ ɛɨɥɶɲɢɯ ɦɚɫɫɢɜɚɯ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɫ ɡɚɦɟɬɧɨɣ ɡɚɞɟɪɠɤɨɣ. ɉɨɷɬɨɦɭ ɞɥɹ ɩɨɫɬɪɨɟɧɢɹ 172

2.2. Ɏɢɡɢɤɚ

ɞɢɚɝɪɚɦɦ ɛɨɥɶɲɢɯ ɦɚɫɫɢɜɨɜ ɰɟɥɟɫɨɨɛɪɚɡɧɨ ɫɨɤɪɚɳɚɬɶ ɜɪɟɦɹ ɪɚɫɱɟɬɚ. ȼ ɦɨɞɟɥɢ ɩɨɫɬɟɩɟɧɧɨ ɜɵɱɢɫɥɹɟɦ ɩɚɪɚɦɟɬɪɵ ɫ ɜɵɞɟɥɟɧɢɟɦ ɞɥɹ ɧɢɯ ɨɬɞɟɥɶɧɵɯ ɦɚɫɫɢɜɨɜ. ɉɪɢ ɷɬɨɦ ɦɨɠɧɨ ɭɜɢɞɟɬɶ ɨɬɞɟɥɶɧɵɟ ɯɚɪɚɤɬɟɪɧɵɟ ɡɚɜɢɫɢɦɨɫɬɢ ɧɚ ɪɚɡɥɢɱɧɵɯ ɷɬɚɩɚɯ ɜɵɱɢɫɥɟɧɢɣ. ɇɚ ɜɵɞɟɥɟɧɧɨɦ ɮɪɚɝɦɟɧɬɟ ɦɚɫɫɢɜɚ ɪɚɫɱɟɬɚ Ȱଶ െ Ȱଵ ɜ ɪɚɣɨɧɟ ɫɟɪɟɞɢɧɵ ɦɟɠɞɭ ɢɫɬɨɱɧɢɤɚɦɢ ɜɨɥɧ ɧɚɛɥɸɞɚɟɦ ɪɚɡɧɨɫɬɶ ɮɚɡ ɪɚɜɧɭɸ ɧɭɥɸ, ɚ ɬɚɤɠɟ ɫɢɦɦɟɬɪɢɱɧɨɫɬɶ ɡɧɚɱɟɧɢɣ ɨɬɧɨɫɢɬɟɥɶɧɨ ɧɭɥɟɜɵɯ ɡɧɚɱɟɧɢɣ. ȼɫɟ ɝɨɬɨɜɨ ɞɥɹ ɪɚɫɱɟɬɚ ɚɦɩɥɢɬɭɞɵ ɢɧɬɟɪɮɟɪɟɧɰɢɨɧɧɨɣ ɜɨɥɧɵ ‫ܣ‬. ȼ ɦɚɫɫɢɜɟ ɚɦɩɥɢɬɭɞɵ ɦɨɠɧɨ ɜ ɹɱɟɣɤɚɯ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɫɟɪɟɞɢɧɟ ɪɚɫɫɬɨɹɧɢɹ ɦɟɠɞɭ ɢɫɬɨɱɧɢɤɚɦɢ, ɭɜɢɞɟɬɶ ɦɚɤɫɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɞɥɹ ɜɫɟɯ ɡɧɚɱɟɧɢɣ ɢɧɞɟɤɫɚ ݆. ȼɵɱɢɫɥɟɧɢɟ ɮɚɡɵ ɢɧɬɟɪɮɟɪɟɧɰɢɨɧɧɨɣ ɜɨɥɧɵ ɩɪɨɢɡɜɨɞɢɦ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɮɭɧɤɰɢɢ ATAN2, ɤɨɬɨɪɚɹ ɨɛɟɫɩɟɱɢɜɚɟɬ ɪɚɫɱɟɬ ɮɚɡɵ ɨɬ –ư ɞɨ ư. Ɉɫɬɚɥɨɫɶ ɜɵɱɢɫɥɢɬɶ ɡɧɚɱɟɧɢɹ ɢɧɬɟɪɮɟɪɟɧɰɢɨɧɧɨɣ ɜɨɥɧɵ ɜ ɭɡɥɚɯ ɩɥɨɫɤɨɫɬɢ (‫݅ݔ‬ǡ ‫݆ݔ‬ሻ ɢ ɩɨɫɬɪɨɢɬɶ ɞɢɚɝɪɚɦɦɭ ɢɧɬɟɪɮɟɪɟɧɰɢɨɧɧɨɣ ɤɚɪɬɢɧɵ. ȼɵɞɟɥɹɟɦ ɦɚɫɫɢɜ E356:AN422 ɢ ɨɛɪɚɳɚɟɦɫɹ ɤ ɞɢɚɝɪɚɦɦɟ ɉɪɨɜɨɥɨɱɧɚɹ ɩɨɜɟɪɯɧɨɫɬɶ. ɗɬɨɬ ɬɢɩ ɞɢɚɝɪɚɦɦɵ ɞɚɟɬ ɜɢɞ ɫɜɟɪɯɭ ɢɧɬɟɪɮɟɪɟɧɰɢɨɧɧɨɣ ɤɚɪɬɢɧɵ ɫɥɨɠɟɧɢɹ ɞɜɭɯ ɤɨɝɟɪɟɧɬɧɵɯ ɜɨɥɧ. ɉɪɢ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɞɨɛɚɜɥɹɟɦ ɢ ɮɨɪɦɚɬɢɪɭɟɦ ɷɥɟɦɟɧɬɵ ɞɢɚɝɪɚɦɦɵ. ȼ ɤɚɱɟɫɬɜɟ ɩɪɢɦɟɪɚ ɩɪɟɞɫɬɚɜɥɟɧɚ ɞɢɚɝɪɚɦɦɚ ɫ ɞɜɭɦɹ ɢɫɬɨɱɧɢɤɚɦɢ ɤɨɝɟɪɟɧɬɧɵɯ ɜɨɥɧ, ɤɨɬɨɪɵɟ ɢɦɟɸɬ ɤɨɨɪɞɢɧɚɬɵ ݅ͳ ൌ ͳͲ ɢ ݅ʹ ൌ ͷͲ. ɇɚ ɧɟɣ ɜɢɞɧɵ ɯɚɪɚɤɬɟɪɧɵɟ ɥɢɧɢɢ, ɤɨɬɨɪɵɟ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɥɢɧɢɹɦ ɝɢɩɟɪɛɨɥɵ ɫ ɮɨɤɭɫɚɦɢ, ɫɨɜɩɚɞɚɸɳɢɦɢ ɫ ɢɫɬɨɱɧɢɤɚɦɢ ɜɨɥɧ. ɋɨɜɦɟɫɬɢɦ ɤɨɨɪɞɢɧɚɬɵ ɢɫɬɨɱɧɢɤɨɜ ɜɨɥɧ ݅ͳ ൌ ݅ʹ ൌ ʹͲ ɢ ɩɨɥɭɱɢɦ

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2. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ MS Excel

ɢɧɬɟɪɮɟɪɟɧɰɢɨɧɧɭɸ ɞɢɚɝɪɚɦɦɭ ɫ ɤɨɧɰɟɧɬɪɢɱɟɫɤɢɦɢ ɤɪɭɝɚɦɢ, ɝɞɟ ɦɨɠɧɨ ɩɪɢɛɥɢɡɢɬɟɥɶɧɨ ɨɩɪɟɞɟɥɢɬɶ ɞɥɢɧɭ ɜɨɥɧɵ. ɂɡɦɟɧɹɹ ɢɫɯɨɞɧɵɟ ɞɚɧɧɵɟ, ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɪɚɡɧɨɨɛɪɚɡɧɵɟ ɢɧɬɟɪɮɟɪɟɧɰɢɨɧɧɵɟ ɤɚɪɬɢɧɵ ɫɥɨɠɟɧɢɹ ɞɜɭɯ ɜɨɥɧ. Ʉɚɤ ɭɠɟ ɨɬɦɟɱɚɥɨɫɶ ɜɵɲɟ, ɭɪɨɜɧɢ ɚɦɩɥɢɬɭɞ ɧɟ ɜɫɟɝɞɚ ɨɤɪɚɲɟɧɵ «ɭɞɨɛɧɵɦɢ» ɰɜɟɬɚɦɢ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɦɨɠɧɨ ɨɛɪɚɬɢɬɶɫɹ ɤ ɫɩɢɫɤɭ ɐɜɟɬɚ ɢ ɜɵɛɪɚɬɶ ɩɨɞɯɨɞɹɳɭɸ ɩɚɥɢɬɪɭ ɰɜɟɬɨɜ. ȿɫɥɢ ɩɨɞɯɨɞɹɳɚɹ ɩɚɥɢɬɪɚ ɨɬɫɭɬɫɬɜɭɟɬ, ɬɨ ɦɨɠɧɨ ɫɨɡɞɚɬɶ ɧɨɜɵɟ ɰɜɟɬɚ ɬɟɦɵ. Ɉɫɬɚɟɬɫɹ ɨɬɤɪɵɬɵɦ ɜɨɩɪɨɫ ɡɚɞɚɧɢɹ ɤɨɥɢɱɟɫɬɜɚ ɭɪɨɜɧɟɣ ɨɬɨɛɪɚɠɟɧɢɹ ɚɦɩɥɢɬɭɞɵ ɢɧɬɟɪɮɟɪɟɧɰɢɨɧɧɨɣ ɜɨɥɧɵ. Ⱦɥɹ ɷɬɨɝɨ ɧɭɠɧɨ ɪɚɫɤɪɵɬɶ ɫɩɢɫɨɤ Ɉɫɢ ɢ ɜɵɛɪɚɬɶ Ɉɫɧɨɜɧɚɹ ɜɟɪɬɢɤɚɥɶɧɚɹ ɨɫɶ. Ɂɚɬɟɦ ɜɵɛɪɚɬɶ Ⱦɨɩɨɥɧɢɬɟɥɶɧɵɟ ɩɚɪɚɦɟɬɪɵ ɨɫɧɨɜɧɨɣ ɜɟɪɬɢɤɚɥɶɧɨɣ ɨɫɢ ɢ ɜ ɩɨɹɜɢɜɲɟɦɫɹ ɨɤɧɟ Ɏɨɪɦɚɬ ɨɫɢ ɭɫɬɚɧɨɜɢɬɶ ɮɢɤɫɢɪɨɜɚɧɧɭɸ ɰɟɧɭ ɨɫɧɨɜɧɵɯ ɞɟɥɟɧɢɣ. ɗɬɨ ɩɨɡɜɨɥɢɬ ɭɫɬɚɧɨɜɢɬɶ ɧɭɠɧɭɸ ɞɟɬɚɥɢɡɚɰɢɸ ɩɨ ɭɪɨɜɧɹɦ ɢɧɬɟɪɮɟɪɟɧɰɢɨɧɧɨɣ ɤɚɪɬɢɧɵ ɫɥɨɠɟɧɢɹ ɜɨɥɧ ɩɪɢ ɦɨɞɟɥɢɪɨɜɚɧɢɢ.

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2.2. Ɏɢɡɢɤɚ

2.2.19. Ȼɨɦɛɨɦɟɬɚɧɢɟ ɩɨ ɧɚɡɟɦɧɨɣ ɰɟɥɢ ɫ ɫɚɦɨɥɟɬɚ ɋɨɡɞɚɞɢɦ ɦɨɞɟɥɶ ɫɛɪɨɫɚ ɛɨɦɛɵ ɫ ɫɚɦɨɥɟɬɚ ɩɨ ɧɚɡɟɦɧɨɣ ɰɟɥɢ. ɋɱɢɬɚɟɦ, ɱɬɨ ɫɚɦɨɥɟɬ ɥɟɬɢɬ ɧɚ ɡɚɞɚɧɧɨɣ ɜɵɫɨɬɟ ɫ ɩɨɫɬɨɹɧɧɨɣ ɫɤɨɪɨɫɬɶɸ. ɉɪɢ ɩɨɞɥɟɬɟ ɤ ɰɟɥɢ ɫɛɪɚɫɵɜɚɟɬ ɛɨɦɛɭ, ɤɨɬɨɪɚɹ ɥɟɬɢɬ ɩɨ ɬɪɚɟɤɬɨɪɢɢ ɤ ɧɚɡɟɦɧɨɣ ɰɟɥɢ. ɉɨɥɟɬ ɛɨɦɛɵ ɩɪɨɢɫɯɨɞɢɬ ɜ ɨɞɧɨɪɨɞɧɨɦ ɩɨɥɟ ɬɹɠɟɫɬɢ ɢ ɜ ɛɟɡɜɨɡɞɭɲɧɨɦ ɩɪɨɫɬɪɚɧɫɬɜɟ. ȿɫɥɢ ɬɨɱɤɚ Y ɩɚɞɟɧɢɹ ɛɨɦɛɵ ɧɚɯɨɞɢɬɫɹ ɛɥɢɠɟ ɪɚɞɢɭɫɚ ɩɨɪɚɠɟɧɢɹ ɨɬ ɰɟɥɢ, ɬɨ ɰɟɥɶ ɫɱɢ(Xcɛ, Ycɛ) (ܺ˔˕ ǡ ܻ˔˕ ሻ ɬɚɟɬɫɹ ɭɧɢɱɬɨɠɟɧɧɨɣ. Vɫ ɇɚɡɟɦɧɚɹ ɰɟɥɶ ɧɚɯɨɞɢɬɫɹ ɧɚ Vɫ (ܺ˄ ǡ ܻ˄ ሻ ɨɩɪɟɞɟɥɟɧɧɨɦ ɪɚɫɫɬɨɹɧɢɢ ɨɬ ɧɚɱɚɥɚ Vɜ ɫɢɫɬɟɦɵ ɤɨɨɪɞɢɧɚɬ. ɋɚɦɨɥɟɬ ɢɦɟɟɬ ɡɚVɛ ɞɚɧɧɵɟ ɤɨɨɪɞɢɧɚɬɵ ɩɨ ɞɚɥɶɧɨɫɬɢ, ɜɵܺ˙ X ɫɨɬɟ ɩɨɥɟɬɚ ɢ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɫɤɨɪɨɫɬɢ. Ɇɨɞɟɥɢɪɨɜɚɬɶ ɫɛɪɨɫ ɛɨɦɛɵ ɛɭɞɟɦ ɜ ɜɟɪɬɢɤɚɥɶɧɨɣ ɩɥɨɫɤɨɫɬɢ. Ɍɪɚɟɤɬɨɪɢɹ ɫɚɦɨɥɟɬɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɨɨɪɞɢɧɚɬɚɦɢ ܺ˔ ɢ ܻ˔ . Ʉɨɨɪɞɢɧɚɬɵ ɬɪɚɟɤɬɨɪɢɢ ɛɭɞɟɦ ɪɚɫɫɱɢɬɵɜɚɬɶ ɩɨ ɮɨɪɦɭɥɚɦ ܺ˔ ൌ ܺ˔˕ െ ܸ˔ ‫ݐ כ‬௖ , ܻ˔ ൌ ܻ˔˕ ൌ ‫ܪ‬௖ , ɝɞɟ ‫ݐ‬௖ - ɬɟɤɭɳɟɟ ɜɪɟɦɹ ɨɬ ɬɨɱɤɢ ɫɬɚɪɬɚ ɫɚɦɨɥɟɬɚ, ܺ˔˕ - ɞɚɥɶɧɨɫɬɶ ɫɬɚɪɬɚ ɨɬ ɧɚɱɚɥɚ ɤɨɨɪɞɢɧɚɬ, ܻ˔˕ - ɜɵɫɨɬɚ ɫɚɦɨɥɟɬɚ ɜ ɬɨɱɤɟ ɫɬɚɪɬɚ (ɪɚɜɧɚ ɜɵɫɨɬɟ ɩɨɥɟɬɚ). Ɍɨɱɤɚ ɫɬɚɪɬɚ ɹɜɥɹɟɬɫɹ ɭɫɥɨɜɧɨɣ ɬɨɱɤɨɣ ɩɨɥɟɬɚ ɫɚɦɨɥɟɬɚ, ɜ ɤɨɬɨɪɨɣ ɧɚɱɢɧɚɟɬɫɹ ɪɟɲɚɬɶɫɹ ɡɚɞɚɱɚ ɩɨ ɩɨɪɚɠɟɧɢɸ ɰɟɥɢ. ɉɪɢ ɫɛɪɨɫɟ ɛɨɦɛɵ ɜ ɬɨɱɤɟ (ܺ˔˄ ,ܻ˔˄ ሻ ɧɚɱɢɧɚɟɬɫɹ ɪɚɫɱɟɬ ɬɪɚɟɤɬɨɪɢɢ ɩɨɥɟɬɚ ɛɨɦɛɵ. Ʉɨɨɪɞɢɧɚɬɵ ɬɪɚɟɤɬɨɪɢɢ ɜɵɱɢɫɥɹɟɦ ɩɨ ɮɨɪɦɭɥɚɦ ܺ˄ ൌ ܺ˔˄ െ ܸ˔ ‫ ˄ݐ כ‬, ܻ˄ ൌ ܻ˔˄ െ ݃଴ ‫˄ݐ כ‬ଶ Ȁʹ, ɝɞɟ ‫ ˄ݐ‬- ɬɟɤɭɳɟɟ ɜɪɟɦɹ ɨɬ ɦɨɦɟɧɬɚ ɫɛɪɨɫɚ ɛɨɦɛɵ. ɉɪɢ ɞɨɫɬɢɠɟɧɢɢ ɛɨɦɛɵ ɜɵɫɨɬɵ ɪɚɜɧɨɣ ɧɭɥɹ ɨɩɪɟɞɟɥɹɟɦ ɨɬɤɥɨɧɟɧɢɟ ɟɟ ɩɨ ɞɚɥɶɧɨɫɬɢ ɨɬ ɧɚɡɟɦɧɨɣ ɰɟɥɢ οܴ ൌ ܺ˙ െ ܺ˄ . ȿɫɥɢ ȁοܴȁ ൑ ܴ˒ˑ˓˃ˉ , ɬɨ ɰɟɥɶ ɭɧɢɱɬɨɠɟɧɚ (ܴ˒ˑ˓˃ˉ - ɪɚɞɢɭɫ ɩɨɪɚɠɟɧɢɹ). ȼ ɷɬɨɣ ɦɨɞɟɥɢ ɫɨɡɞɚɞɢɦ ɮɨɪɦɭ, ɧɚ ɤɨɬɨɪɨɣ ɪɚɫɩɨɥɨɠɢɦ ɭɩɪɚɜɥɹɸɳɢɟ ɷɥɟɦɟɧɬɵ. Ⱦɥɹ ɜɵɡɨɜɚ ɮɨɪɦɵ ɫɨɡɞɚɞɢɦ ɭɩɪɚɜɥɹɸɳɭɸ ɤɧɨɩɤɭ «ȼɵɡɨɜ ɮɨɪɦɵ ɞɥɹ ɦɨɞɟɥɢɪɨɜɚɧɢɹ» ɧɚ ɥɢɫɬɟ. Ʉɧɨɩɤɭ ɰɟɥɟɫɨɨɛɪɚɡɧɨ ɫɨɡɞɚɜɚɬɶ ɩɨɫɥɟ ɫɨɡɞɚɧɢɹ ɮɨɪɦɵ. ɇɚ ɜɤɥɚɞɤɟ Ɋɚɡɪɚɛɨɬɱɢɤ ɳɟɥɤɚɟɦ ɧɚ ɤɧɨɩɤɟ Visual Basic ɞɥɹ ɜɵɡɨɜɚ ɪɟɞɚɤɬɨɪɚ. 175 Powered by TCPDF (www.tcpdf.org)

2. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ MS Excel

Ɋɚɫɤɪɵɜɚɟɦ ɦɟɧɸ Insert ɢ ɳɟɥɤɚɟɦ ɧɚ ɩɭɧɤɬɟ Userform. ɉɨɹɜɥɹɟɬɫɹ ɨɤɧɨ Userform ɫ ɫɨɡɞɚɧɧɨɣ ɮɨɪɦɨɣ ɢ ɩɚɧɟɥɶ ɫ ɭɩɪɚɜɥɹɸɳɢɦɢ ɷɥɟɦɟɧɬɚɦɢ ToolBox. ȿɫɥɢ ɫɨɡɞɚɥɢ ɥɢɲɧɸɸ ɮɨɪɦɭ, ɬɨ ɞɥɹ ɟɟ ɭɞɚɥɟɧɢɹ ɧɟɨɛɯɨɞɢɦɨ ɜɵɡɜɚɬɶ ɤɨɧɬɟɤɫɬɧɨɟ ɦɟɧɸ ɷɬɨɣ ɮɨɪɦɵ ɢ ɜɵɛɪɚɬɶ ɜ ɧɟɦ ɩɭɧɤɬ Remove. ȼ ɩɨɹɜɢɜɲɟɦɫɹ ɨɤɧɟ ɳɟɥɤɧɭɬɶ ɧɚ ɤɧɨɩɤɟ ɇɟɬ. ȼ ɩɟɪɜɭɸ ɨɱɟɪɟɞɶ ɪɚɡɦɟɳɚɟɦ ɧɚ ɮɨɪɦɟ ɷɥɟɦɟɧɬɵ ɭɩɪɚɜɥɟɧɢɹ. ɓɟɥɱɤɨɦ ɜɵɛɢɪɚɟɦ ɧɭɠɧɵɣ ɷɥɟɦɟɧɬ ɢ ɩɪɨɬɹɠɤɨɣ ɪɚɡɦɟɳɚɟɦ ɟɝɨ ɧɚ ɮɨɪɦɟ. Ⱦɥɹ ɢɡɦɟɧɟɧɢɹ ɪɚɡɦɟɪɨɜ ɷɥɟɦɟɧɬɚ ɦɨɠɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɦɚɪɤɟɪɵ ɢɥɢ ɡɚɞɚɬɶ ɪɚɡɦɟɪɵ ɜ ɟɝɨ ɫɜɨɣɫɬɜɚɯ. Ɇɟɫɬɨ ɪɚɫɩɨɥɨɠɟɧɢɹ ɷɥɟɦɟɧɬɚ ɨɩɪɟɞɟɥɹɟɦ ɩɟɪɟɦɟɳɟɧɢɟɦ. ɇɚ ɮɨɪɦɟ ɪɚɡɦɟɳɚɟɦ Label (Ɇɟɬɤɚ), TextBox (Ɍɟɤɫɬɨɜɨɟ ɩɨɥɟ) ɢ CommandButton (Ʉɨɦɚɧɞɧɚɹ ɤɧɨɩɤɚ). ɋ ɩɨɦɨɳɶɸ ɷɥɟɦɟɧɬɨɜ Label ɫɨɡɞɚɟɦ ɩɨɹɫɧɹɸɳɢɟ ɧɚɞɩɢɫɢ ɞɥɹ TextBox. ɉɨɫɥɟ ɫɨɡɞɚɧɢɹ ɷɥɟɦɟɧɬɚ ɜɵɡɵɜɚɟɦ ɤɨɧɬɟɤɫɬɧɨɟ ɦɟɧɸ ɢ ɜɵɛɢɪɚɟɦ ɩɭɧɤɬ Properties (ɋɜɨɣɫɬɜɚ). ȼ ɩɨɹɜɢɜɲɟɦɫɹ ɨɤɧɟ ɜ ɩɭɧɤɬɟ Caption (Ɂɚɝɨɥɨɜɨɤ) ɫɨɡɞɚɟɦ ɧɭɠɧɭɸ ɧɚɞɩɢɫɶ. ɗɥɟɦɟɧɬɵ TextBox ɢɫɩɨɥɶɡɭɟɦ ɞɥɹ ɜɜɨɞɚ ɢ ɜɵɜɨɞɚ ɞɚɧɧɵɯ. ɋɨɡɞɚɟɦ ɢɯ ɚɧɚɥɨɝɢɱɧɵɦ ɫɩɨɫɨɛɨɦ. ɉɪɢ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɦɨɠɧɨ ɨɛɪɚɬɢɬɶɫɹ ɤ ɫɜɨɣɫɬɜɚɦ ɷɥɟɦɟɧɬɚ ɢ ɨɩɪɟɞɟɥɢɬɶ ɧɭɠɧɵɟ ɩɚɪɚɦɟɬɪɵ. ȼ ɧɚɲɟɦ ɫɥɭɱɚɟ ɰɟɥɟɫɨɨɛɪɚɡɧɨ ɜ ɫɜɨɣɫɬɜɟ Font (ɒɪɢɮɬ) ɭɫɬɚɧɨɜɢɬɶ ɪɚɡɦɟɪ ɲɪɢɮɬɚ. ɋɨɡɞɚɟɦ ɧɚ ɮɨɪɦɟ ɤɧɨɩɤɢ «ɉɟɪɜɢɱɧɵɟ ɪɚɫɱɟɬɵ», «ɉɨɫɬɪɨɟɧɢɟ ɞɢɚɝɪɚɦɦɵ» ɢ «Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɩɨ ɪɚɫɱɟɬɚɦ» ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ CommandButton. ȼ ɫɜɨɣɫɬɜɚɯ ɤɧɨɩɨɤ ɜ ɩɭɧɤɬɟ Caption ɮɨɪɦɢɪɭɟɦ ɧɚɞɩɢɫɢ, ɚ ɜ ɩɭɧɤɬɟ BackColor (ɐɜɟɬ ɮɨɧɚ) ɜɵɛɢɪɚɟɦ ɰɜɟɬ ɮɨɧɚ ɞɥɹ ɜɵɞɟɥɟɧɢɹ ɤɧɨɩɨɤ ɧɚ ɮɨɪɦɟ. ɉɪɢ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɦɨɠɧɨ ɢɡɦɟɧɢɬɶ ɪɚɡɦɟɪɵ ɢ ɪɚɫɩɨɥɨɠɟɧɢɟ ɷɥɟɦɟɧɬɨɜ ɧɚ ɮɨɪɦɟ. ɉɨɫɥɟ ɜɵɡɨɜɚ ɮɨɪɦɵ ɜ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɬɟɤɫɬɨɜɵɟ ɩɨɥɹ ɜɜɨɞɢɦ ɫ ɤɥɚɜɢɚɬɭɪɵ ɧɚɱɚɥɶɧɵɟ ɤɨɨɪɞɢɧɚɬɵ ɢ ɫɤɨɪɨɫɬɶ ɫɚɦɨɥɟɬɚ, ɚ ɬɚɤɠɟ ɤɨɨɪɞɢɧɚɬɭ ɰɟ176

2.2. Ɏɢɡɢɤɚ

ɥɢ. ɉɪɢ ɷɬɨɦ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨ ɭɫɬɚɧɚɜɥɢɜɚɟɦ ɤɭɪɫɨɪ ɜ ɧɭɠɧɨɦ ɬɟɤɫɬɨɜɨɦ ɩɨɥɟ. Ⱦɚɥɟɟ ɞɟɥɚɟɦ ɩɪɟɞɜɚɪɢɬɟɥɶɧɵɟ ɪɚɫɱɟɬɵ. Ⱦɥɹ ɷɬɨɝɨ ɪɚɫɩɨɥɚɝɚɟɦ ɧɚ ɮɨɪɦɟ ɤɧɨɩɤɭ «ɉɟɪɜɢɱɧɵɟ ɪɚɫɱɟɬɵ». Ⱦɜɚɠɞɵ ɳɟɥɤɚɟɦ ɧɚ ɤɧɨɩɤɟ ɢ ɫɨɡɞɚɟɦ ɩɪɨɝɪɚɦɦɭ. ȼ ɧɟɣ ɮɨɪɦɢɪɭɟɦ ɩɟɪɟɦɟɧɧɵɟ ɞɥɹ ɡɚɩɢɫɢ ɜɧɟɫɟɧɧɵɯ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ. Ⱦɟɥɚɟɦ ɩɪɨɫɬɟɣɲɭɸ ɩɪɨɜɟɪɤɭ ɢɫɯɨɞɧɨɝɨ ɩɨɥɨɠɟɧɢɹ ɫɚɦɨɥɟɬɚ. ɋɚɦɨɥɟɬ ɞɨɥɠɟɧ ɧɚɯɨɞɢɬɶɫɹ ɧɚ ɛɨɥɟɟ ɞɚɥɶɧɟɦ ɪɚɫɫɬɨɹɧɢɢ ɨɬ ɧɚɱɚɥɚ ɤɨɨɪɞɢɧɚɬ, ɱɟɦ ɰɟɥɶ. ɂɧɚɱɟ ɜɵɞɚɟɬɫɹ ɫɨɨɛɳɟɧɢɟ ɢ ɧɟɨɛɯɨɞɢɦɨ ɨɬɤɨɪɪɟɤɬɢɪɨɜɚɬɶ ɤɨɨɪɞɢɧɚɬɭ ɫɚɦɨɥɟɬɚ ɩɨ ɨɫɢ ɚɛɫɰɢɫɫ. మ ɉɪɨɢɡɜɨɞɢɦ ɪɚɫɱɟɬ ɩɚɞɟɧɢɹ ɛɨɦɛɵ ɩɨ ɮɨɪɦɭɥɟ ‫ ˄ݐ‬ൌ ඥʹ ‫ ˄˔ܻ כ‬Τ݃଴ . ɋɥɟɞɭɟɬ ɨɛɪɚɬɢɬɶ ɜɧɢɦɚɧɢɟ ɧɚ ɪɚɡɦɟɪɧɨɫɬɢ ɜɟɥɢɱɢɧ, ɜɯɨɞɹɳɢɯ ɜ ɮɨɪɦɭɥɭ, ɢ ɜɜɟɫɬɢ ɤɨɪɪɟɤɬɢɪɨɜɨɱɧɵɟ ɤɨɷɮɮɢɰɢɟɧɬɵ ɞɥɹ ɫɨɝɥɚɫɨɜɚɧɢɹ ɪɚɡɦɟɪɧɨɫɬɟɣ. ȼ ɷɬɨɣ ɮɨɪɦɭɥɟ ɩɟɪɟɜɟɥɢ ɜɵɫɨɬɭ ɢɡ ɤɢɥɨɦɟɬɪɨɜ ɜ ɦɟɬɪɵ ɩɭɬɟɦ ɜɜɟɞɟɧɢɹ ɜɟɥɢɱɢɧɵ 1000. ȼɪɟɦɹ ɩɚɞɟɧɢɹ ɛɨɦɛɵ ɨɤɪɭɝɥɢɥɢ ɞɨ 2-ɝɨ ɡɧɚɤɚ ɩɨɫɥɟ ɡɚɩɹɬɨɣ ɢ ɜɵɜɟɥɢ ɜ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɬɟɤɫɬɨɜɨɟ ɩɨɥɟ. ɉɪɨɢɡɜɨɞɢɦ ɞɚɥɶɧɨɫɬɶ ɩɨɥɟɬɚ ɛɨɦɛɵ ɩɨ ɜɵɪɚɠɟɧɢɸ ܺ˔˄ ൌ ܸ௖ ‫ ˄ݐ כ‬ɫ ɭɱɟɬɨɦ ɫɨɝɥɚɫɨɜɚɧɢɹ ɪɚɡɦɟɪɧɨɫɬɟɣ. Ɋɚɫɱɟɬɧɨɟ ɡɧɚɱɟɧɢɟ ɜɵɜɨɞɢɦ ɧɚ ɮɨɪɦɭ. ȼɵɱɢɫɥɹɟɦ ɜɪɟɦɹ ɫɛɪɨɫɚ ɛɨɦɛɵ ɨɬ ɧɚɱɚɥɶɧɨɣ ɬɨɱɤɢ ɫɚɦɨɥɟɬɚ ɩɨ ɮɨɪɦɭɥɟ ‫ ˄˔ݐ‬ൌ ሺܺ˔˕ െ ܺ˙ െ ܺ˔˄ ሻȀܸ௖ . ɇɟ ɡɚɛɵɜɚɟɦ ɨ ɫɨɝɥɚɫɨɜɚɧɢɢ ɪɚɡɦɟɪɧɨɫɬɟɣ. ȿɫɥɢ ɷɬɨ ɜɪɟɦɹ ɦɟɧɶɲɟ ɧɭɥɹ, ɬɨ ɬɨɱɤɭ ɫɛɪɨɫɚ ɩɪɨɥɟɬɟɥɢ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɮɨɪɦɢɪɭɟɦ ɫɨɨɛɳɟɧɢɟ. ɉɨɫɥɟ ɤɨɪɪɟɤɬɢɪɨɜɤɢ ɢɫɯɨɞɧɵɯ ɞɚɧɧɵɯ ɟɳɟ ɪɚɡ ɩɪɨɢɡɜɨɞɢɦ ɪɚɫɱɟɬɵ. ȼ ɤɨɧɰɟ ɡɚɩɢɫɵɜɚɟɦ ɢɫɯɨɞɧɵɟ ɞɚɧɧɵɟ ɩɨ ɫɚɦɨɥɟɬɭ ɢ ɰɟɥɢ ɜ ɦɚɫɫɢɜ ɞɚɧɧɵɯ ɞɢɚɝɪɚɦɦɵ. ɗɬɨ ɩɨɡɜɨɥɢɬ ɫɨɡɞɚɜɚɬɶ ɞɢɚɝɪɚɦɦɭ ɜ ɡɚɞɚɧɧɨɦ ɞɢɚɩɚɡɨɧɟ ɞɚɧɧɵɯ. ɉɪɨɝɪɚɦɦɚ ɤɧɨɩɤɢ ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɢɠɟ. ɋɥɟɞɭɟɬ ɧɚɩɨɦɧɢɬɶ ɨɛ ɨɛɴɹɜɥɟɧɢɢ ɩɟɪɟɦɟɧɧɵɯ ɩɪɢ ɫɨɡɞɚɧɢɢ ɩɪɨɝɪɚɦɦɵ ɤɧɨɩɤɢ (ɜɫɟ ɨɛɴɹɜɥɟɧɧɵɟ ɩɟɪɟɦɟɧɧɵɟ ɩɪɟɞɫɬɚɜɢɦ ɩɨɡɠɟ). Private Sub CommandButton1_Click() 'ɉɟɪɜɢɱɧɵɟ ɪɚɫɱɟɬɵ Xct = Val(TextBox1) 'ɇɚɱɚɥɶɧɵɟ ɤɨɨɪɞɢɧɚɬɵ ɫɚɦɨɥɟɬɚ Yct = Val(TextBox2) 'ɇɚɱɚɥɶɧɵɟ ɤɨɨɪɞɢɧɚɬɵ ɫɚɦɨɥɟɬɚ Xɰ = Val(TextBox4) 'Ʉɨɨɪɞɢɧɚɬɵ ɰɟɥɢ If Xct