This volume demonstrates the basic methods for solving the classical linear problems in mathematical physics of elliptic, parabolic and hyperbolic nature. The methods of conformal mappings, Fourier analysis and Green`s functions are considered, as well as the perturbation and integral transformation methods.
Many physical processes in fields such as mechanics, thermodynamics, electricity, magnetism or optics are described by means of partial differential equations. The aim of the present book is to demonstrate the basic methods for solving the classical linear problems in mathematical physics of elliptic, parabolic and hyperbolic type. In particular, the methods of conformal mappings, Fourier analysis and Green`s functions are considered, as well as the perturbation method and integral transformation method, among others. Every chapter contains concrete examples with a detailed analysis of their solution.
The book is intended as a textbook for students in mathematical physics, but will also serve as a handbook for scientists and engineers.
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[A] manual for future engineers must strongly differ from the textbook for pure mathematicians, and the book by Pikulin and Pohozaev is the good example. ( ) The purpose ( ) is to offer quick access to the principal facts ( ) This well written book is a reader-friendly and good-organized textbook in the field of PDE. It can be highly recommended for students of technology universities and institutes as well as for engineers.
(Zentralblatt MATH)
Each chapter contains concrete examples with a detailed analysis of their solution and ends with problems for independent study and answers to them.
(EMS Newsletter) Preface.- Introduction.- Chapter 1. Elliptic problems.- Chapter 2. Hyperbolic problems.- Chapter 3. Parabolic problems.- References.- Index.
Victor P. Pikulin was Professor at the Moscow Power Engineering Institute.
Stanislav I. Pohozaev is Professor at the Steklov Institute of Mathematics in Moscow.
