Methods of Theoretical Physics part2

Table of contents :
Contents......Page 5
9 Approximate Methods ......Page 19
9.1 Perturbation Methods ......Page 21
9.2 Boundary Perturbations ......Page 58
9.3 Perturbation Methods for Scattering and Diffraction......Page 84
9.4 Variational Methods......Page 126
Problems ......Page 178
Tabulation of Approximate Methods ......Page 182
Bibliography ......Page 190
10 Solutions of Laplace’s and Poisson’s Equations ......Page 193
10.1 Solutions in Tivo Dimensions ......Page 195
10.2 Complex Variables and the Two-dimensional Laplace Equation......Page 235
10.3 Solutions for Three Dimensions......Page 272
Problems ......Page 329
Trigonometric and Hyperbolic Functions ......Page 340
Bessel Functions ......Page 341
Legendre Functions ......Page 345
Bibliography ......Page 350
11 The Wave Equation ......Page 351
11.1 Wave Motion on One Space Dimension......Page 352
11.2 Waves in Two Dimensions ......Page 380
11.3 Waves in Three Space Dimensions ......Page 452
11.4 Integral and Variational Techniques ......Page 533
Problems ......Page 575
Cylindrical Bessel Functions ......Page 583
Weber Functions......Page 585
Mathieu Functions ......Page 588
Spherical Bessel Functions ......Page 593
Spheroidal Functions ......Page 596
Short Table of Laplace Transforms ......Page 599
Bibliography ......Page 602
12.1 Solutions of the Diffusion Fquation ......Page 604
12.2 Distribution Functions for Diffusion Problems ......Page 626
12.3 Solutions of Schroedinger's Equation ......Page 658
Problems ......Page 765
Jacobi Polynomials ......Page 774
Semi-cylindrical Functions ......Page 776
Bibliography ......Page 777
13 Vector Fields ......Page 779
13.1 Vector Boundary Conditions, Figenfunctions and Green’s Functions ......Page 782
13.2 Static and Steady-state Solutions ......Page 811
13.3 Vector Wave Solutions ......Page 832
Problems ......Page 911
Table of Spherical Vector Harmonics......Page 918
Bibliography ......Page 921
Appendix ......Page 923
GLOSSARY OF SYMBOLS USED ......Page 924
I. Trigonometric and Hyperbolic Functions.......Page 933
II. Trigonometric and Hyperbolic Functions.......Page 934
III. Hyperbolic Tangent of Complex Quantity.......Page 935
IV. Inverse Hyperbolic Tangent of Complex Quantity.......Page 938
V. Logarithmic and Inverse Hyperbolic Functions. ......Page 939
VI. Spherical Harmonic Functions. ......Page 940
VII. Legendre Functions for Large Arguments.......Page 941
Yin. Legendre Functions for Imaginary Arguments.......Page 942
IX. Legendre Functions of Half-integral Degree.......Page 943
X. Bessel Functions for Cylindrical Coordinates. ......Page 944
XI. Hyperbolic Bessel Functions. ......Page 945
XII. Bessel Functions for Spherical Coordinates.......Page 946
XIII. Legendre Functions for Spherical Coordinates. ......Page 947
XIV. Amplitudes and Phases for Cylindrical Bessel Functions.......Page 948
XV. Amplitudes and Phases for Spherical Bessel Functions. ......Page 950
XVI. Periodic Mathieu Functions.......Page 954
XVII. Normalizing Constants for Periodic Mathieu Functions and Limiting Values of Radial Mathieu Functions. ......Page 957
BIBLIOGRAPHY ......Page 958
Index......Page 959