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.

Follow us on The Internet Archive: https://archive.org/details/@mirtitles

Follow Us On Twitter: https://twitter.com/MirTitles

Write to us: mirtitles@gmail.com

Fork us at GitLab: https://gitlab.com/mirtitles/

Add new entries to the detailed book catalog here.

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