Methods of Theoretical Physics part2

Description

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