Problems On The Equations Of Mathematical Physics | M. M. Smirnov

The aim of the present collection of problems is to illustrate the theory of partial differential equations as it is given in various textbooks.
The problems of this collection are divided in three paragraphs. The first paragraph contains introductory excercizes on the reduction of partial differential equations to canonical form. The second paragraph deals mainly with problems, the general solution of which can be formed by means of the method of characteristics e.g. Cauchy’s (or also Goursat’s) and mixed problems.

In the third paragraph the most important method is presented, namely the separation of variables. This is done for mixed problems (for hyperbolic and parabolic equations) and for boundary value problems (elliptic equations).

The solutions of all excercizes are given. Most of the problems are accompanied by an explanation of the solution method used: so that this problem book can also be used for self study.

 CONTENTS
Part I. Problems........................................................................ 7
1. Reduction of partial differential equations with two independent variables to canonical form........................... 7

1. Equations of hyperbolic t y p e ...................................... 7

2. Equations of parabolic t y p e ...................................... 8

3. Equations of elliptic type .......................................... 8
2. The method of characteristics.............................................. 9
3. Separation of variables......................................................... 23
1. Equations of hyperbolic type ...................................... 26
2. Equations of parabolic type.......................................... 33
3. Equations of elliptic type.............................................. 38
Part.II. Solutions and hints.................................................. 43