In this post, we will see the book A Collection Of Problems On Mathematical Physics by B. M. Budak; A. A. Samarskii; A. N. Tikhonov.

About the book

THE PRESENT book is based on the practical work with equations of mathematical physics done in the Physics Faculty and the external section of Moscow State University. The problems set forth were used in the course “Equations of Mathematical Physics” by A. N. Tikhonov and A. A. Samarskii, and in “A Collection of Problems on Mathematical Physics” by B. M. Budak.

However, in compiling the present work the range of problems examined has been considerably enlarged and the number of problems sev­eral times increased. Much attention has been given to problems on the derivation of equations and boundary conditions. A con­siderable number of problems are given with detailed instructions and solutions. Other problems of similar character are given only with the answers. The chapters are divided into paragraphs accord­ing to the method of solution. This has been done in order to give students the opportunity, by means of independent work, of gain­ing elementary technical skill in solving problems in the principal classes of the equations of mathematical physics.

Therefore this book of problems does not claim to include all methods used in mathematical physics. For example, the opera­tional method, variational and differential methods and the appli­cation of integral equations are not considered.

It is hoped, however, that this book will be useful not only to students but also to engineers and workers in research institutions.

The book was translated from Russian by A.R.M. Robson and translation was edited by D.M. Brink. The book was published in  1964.

Credits to original uploader.

Note: You might notice the page numbering in pdf is weird and not matching the original page numbers. In the original design of the book there is a section on problems first which is followed by the solutions part which deals with chapters as they are in the first part. In this copy, the problem chapters are immediately followed by solutions chapter. For example, Chapter 1 problems are originally with page numbers 1-3 and solutions of this chapter are in pages numbered 163-170. In this version pages 1-3 are followed by 163-170 for continuity in reading. Similarly for other chapters. The book is complete though. We will post a more coherent version later.

You can get the book here.

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Contents

Chapter I Classification and Reduction to Canonical Form of Second Order Partial Differential Equations

Chapter II Equations of Hyperbolic Type

Chapter III Equations of Parabolic Type

Chapter IV Equations of Elliptic Type

Supplement

I. Different Orthogonal System of Coordinates 741

II. Some Formulae of Vector Analysis 748

III. Special Functions 749

IV. Tables 755