In this post, we will see the book Basic Equations And Special Functions Of Mathematical Physics by V. Ya. Arsenin.
About the book
This book consists of two parts. Part 1 gives an account of the methods for solving typical problems in mathematical physics and an introduction to integral equations. Part 2 deals with the applications of these methods to problems requiring the use of special functions. Extensive use is made in this book of the Dirac (𝛿-function. Generalised functions are introduced and their applications are described. Each chapter concludes with a number of problems illustrating the main text (altogether 150 problems with answers are given). This text was designed for students of physics and engineering and was based on a course given at the Department of Theoretical and Experimental Physics of the Moscow Engineering-Physics Institute.
The book was translated from the Russian by S. Chomet was published in 1968.
Credits to original uploader.
You can get the book here.
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Chapter 1 Linear Equations with Two Independent Variables 3
Chapter 2 Partial Differential Equations in Physics. Boundary-value Problems 13
Chapter 3 The Method of Characteristics 32
Chapter 4 Separation of Variables (Fourier Method) 59
Chapter 5 The Method of Green’s Functions for Parabolic Equations 107
Chapter 6 The Method of Green’s Functions for Elliptical Equations 124
Chapter 7 Potentials 146
Chapter 8 Integral Equations 168
Chapter 9 Integral Equations with Symmetric Kernels 188
Chapter 10 Gamma Function 215
Chapter 11 Cylindrical Functions 223
Chapter 12 Spherical Harmonics 268
Chapter 13 Chebyshev-Hermite and Chebyshev—Laguerre Polynomials 291
Appendix Definition of Generalised Functions. The 𝛿 Function 303
Answers and Solutions 321