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.

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You can get the book here.

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# Contents

# PART I.

## 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

# PART II

## 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

Bibliography 355

Index 357

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