Программирование в системе Mathcad

Лабораторный цикл содержит 5 работ по изучению программирования с использованием математической системы Mathcad. Цикл мо

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2

В 5

Mathcad. :«

220400, « 071900 «

1. 2. 3. 4. "

Mathcad"

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1999

1. 2. 3. 4.

Э. . . . .,

:

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я . .

:

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я

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Mathcad

1.

. ., . ., . . .,

.

MathCAD PLUS 7.0 PRO. .: 345 . Mathcad 6.0 PLUS. , dows 95. .: , 1996, 697 . . . Mathcad 8.0 Pro. .: , 1999, 523 . . ., . . Mathcad: . , 1999, 656 . ч : , , . . .

: -

Mathcad, , , , , , . . .

2. 3.

1999

К 1. 2. 3. 4. 5. 6. 7.

-

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.

Mathcad. "File" "Edit" "View" "Insert" "Format" "Math"

. . . . . .

, 1998, Win-

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.

4

3 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.

"Symbolics" "Window" "Help" .

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XY -

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2,

№ 1 2 3 4 5 6 7

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2

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1. . 2. М 1.

. ч

я 3

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: y=f(x), x,

x, x, ,

XY

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.

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XY

:

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2.

XY

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-

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-

1. Ф 1 y = sin(x) y = cos(x) y = |tg(x)| + 0.1 y = (x2-1)/15 y = (x3-2)/15 y = x2 - 10

y = ∫ sin( x )dx x

8

y=

9

y=

Ф 2 z= exp(x+3)/5000 - 1 z = 0.00025e3-x - 0.6 z = (1+x)6 z = 1+sin(x) z = 5cos(x) z = 0.025e-1.2x z=0.02x3

a -2π -2π -2π -2π -2π -5 -5

b 2π 2π 2π 2π 2π 5 5

h π/20 π/20 π/20 π/20 π/20 1 1

z = 0.05x2

1

10

1

z = 0.01x3

-10

10

1

z = - 0.05(x2 + 10cos(x)) z = 0.01(x2 - 40sin(x)) z = sin(x) + sin(2x) z = sin2(x) + cos(x) z = x(0.5 + x)exp(0.1x) z = 5x - x1.5+sin(x)

-8

8

1

-8 -π -π -π 0

8 π π π 5

1 π/8 π/8 π/8 0.5

−5

d (sin(x ) + 7 ⋅ ln(x )) dx

d 1+ 0.2x ⋅sin(x) (e ) dx

10

y = √2+cos(x)

11 12 13 14 15

y = sin2(x/3) y = cos3(x) y = 0.5x + cos2(x) y = sin(x) + cos2(2x) y = |sin(x)|exp(x/2)

6

5 2. М

1 sin ( x) . exp( x)

f1( x) f2( x) a N n

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f2( a

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. . . . . . . . . .

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3 1.481

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2.

y=sin(x)cos(t) y=sin(x/2)cos(t) y=sin(2x)cos(t) y = sin(x)cos(t/2) y = sin(x/2)cos(2t) y = sin(2x)cos(2t) y = (1+sin(x)/x)(sin(t)/t) y = (sin(x)/x)cos(t) y = (sin(x)/x)|cos(t)| y = (sin(x)/x)t y = (sin(x)/x)|t| y = (sin(x)/x)sin(t) y = (sin(x)/x)|sin(t)| y = (sin(x)/x)(1-t) y = (sin(x)/x)|t+0.5|

y

x -2π -2π -2π -2π -2π -2π -2π -2π -2π -2π -2π -2π -2π -2π -2π

2π 2π 2π 2π 2π 2π 2π 2π 2π 2π 2π 2π 2π 2π 2π

t -2π -2π -2π -2π -2π -2π -2π -2π -2π -2 -2 -2π -2π -2 -2

2π 2π 2π 2π 2π 2π 2π 2π 2π 2 2 2π 2π 2 2

1

2

3

4

5

6

7

0 0

0

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0

0

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0

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0.036

0.041

0.03

0

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3 0

0.022

0.041

0.047

0.034

0

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4 0

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0

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0

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0

0

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0.055

0.118

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0.118

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-0.079 -0.143 -0.164 -0.118 0

0.177

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0.219

0.472

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0.234

0.505

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0.472

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-0.079 -0.143 -0.164 -0.118 0

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0.382

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20

5 10 15 20

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Given

Find. Minerr.

К

10.

.

З

1

.

1. 0 0.5

0.1

0 0

0.1 0 0.2 0.1 0.5

0

0.2 0

0.1 0.2

0.3 0.7 0.6

0.4

0.8 0.2 0.5 0.7 0.1 0.3 0.4

1 0.9 0.8 0.6

0

0 0

0.1

1. 2. 3.

0.1

0.2

0

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f2(x)

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f2(x).

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Find, y=f1(x) y=f2(x).

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Minerr.

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y=f1(x) y=f2(x)

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y:=

,

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x1 .

y1

13 №

3. f1(x)-

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

a3 0 0 0 0 0 .1 .2 .3 .4 .5 -.1 -.2 -.3 -.4 -.5

3a2 -1 2 1 9 -4 -5 -3 -6 -9 -7 -4 -6 -9 7 1

a1 4 -2 4 -8 4 4 2 1 1 5 9 -7 -8 8 4

14

f2(x) a0 -1 -15 -1 -70 50 40 30 50 70 60 60 55 75 -75 -1

333 0.2exp(x)-20 40|cos(x)| 10ln(x+5.5) 100|sin(x)| 70cos(x) 60exp(|0.1*x|)-100 20sin(2x) exp(|x|)sin(2x) exp(|x|)cos(3x) -60|cos(x)| 15log(x+5.1) -50ln(x+5.1) -100|cos(x)| 100sin(x/2) 40cos(x/2)

1 Mathcad a0

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a2

a1 2

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a3 . x

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2

8.4

0

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x

root ( f1 ( x ) , x ) = 2

2

x

1

x

3

root ( f1 ( x ) , x ) = 0.268 root ( f1 ( x ) , x ) = 3.732

2

4

15

16

3

я

4. a

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h .. b

h

1. 2. 3.

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f2 ( x )

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66 x

2.2

y

0

Given y

f1 ( x ) x1 y1

x

y

f2 ( x )

find ( x , y )

x1 y1

=

2.25 3.77

0

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f1 ( x ) x1 y1

x

y

x1 y1

=

5.099 ,

Find

Given f1 ( x ) x1 y1 x

y

x1 y1

=

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x1 y1

y

f2 ( x )

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3.385 5.823 root.

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1. 2.

5.823 ,

f1 ( x )

. Add Line ← if , while for break otherwise return on error continue -

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3.385

3

y

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1. 2.

f2 ( x )

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Mathcad, .

1. 0.555

3

y

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

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В №

1-

1 x 0

1 0 -x 0 1 x x 0 1 -x2 -x2 0 1 x2 x2

0 1 0 -x -x 0 1 x x 0 1 -x2 -x2 0 1

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L 0

for n ∈ 1 .. N

10 8 9 5 6 7 9 12 10 8 6

1. L

L

1. L

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dx

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9

spectum

7 10 8

R

FC ( N , L )

N

1 . 2 .L

FC ( N , L )

A

spectum

B

spectum

К

0.75

0

0.203 A =

2.974 10

4

0.023 2.974 10 8.403 10

0.318 B =

0.159 0.106

4

0.08

3

0.064

: - A, -B

20

19 4

я

5. N p ( x)

A0 n=1

x

L, L

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1

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f( x ) p( x )

Mathcad

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К 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.

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4. f1(x) (1+x)2 (1-x)2 (a+x)2 (a-x)2 (1+x)3 (1-x)3 (a+x)3 (a-x)3 (1+x)4 (1-x)4 (a+x)4 (a-x)4 (1+x)5 (1-x)5 (a+x)5 (a+x)5

1 f2(x) ax3+bx2+cx+d sin(ax) cos(ax) sec(x) exp(ax) x(ln(x)-1) -csc(x) 1/(1+x2) 1/(a+bx) 1/(1-x2) -cos3(x)/3 sin3(x)/3 x2(ln(x)-0.5)/2 -(ln(x)+1)/x ln2(x)/2 ln3(x)/3

Mathcad a

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f1( x)

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