Equations of Mathematical Physics

Description

This book consists of three parts: (i) the theory of the equations of mathematical physics; (ii) applications to physical problems; and (iii) special functions. The first part comprises the body of the text. Each of the chapters (except the first) has an appendix which discusses applications to physical problems of the material just presented. The theory of special functions is taken up separately in a special lengthy (about 100 pages) appendix.
The first chapter gives a brief discussion of the classification of second order partial differential equations. Chapters 2, 3, and 4 treat the simplest problems for equations of hyperbolic, parabolic, and elliptic type. The appendices to these chapters take up such topics as the vibrating string and rod, radioactive decomposition, electrostatics, and hydrodynamics.
Chapter 5 is a continuation of chapter 2 and discusses wave propagation in space. The sixth chapter treats heat diffusion in space while chapter 7 continues the discussion of chapter 4 on elliptic equations. Some of the topics considered in the appendices to these chapters are: elasticity, electromagnetic waves, radio waves on the earth's surface, and hollow resonators. Each of the chapters has a set of exercises at the end. The section on special functions develops the theory of Bessel functions, Legendre, Hermite and Laguerre polynomials. A few applications are given.
This book has a wealth of applications, many to topics not usually treated. For example, two applications which the reviewer has not seen elsewhere concern the diffusion of clouds and the influence of radioactivity on the temperature of the earth's core.

Reviewed by M. H. Protter

Ibragimov's Practical Course cites this.