Equations of Mathematical Physics. A. N. Tikhonov

Аннотация:

Mathematical physics plays an important role in the study of many physical processes — hydrodynamics, elasticity, and electrodynamics, to name just a few. Because of the enormous range and variety of problems dealt with by mathematical physics, this thorough advanced undergraduate- or graduate-level text considers only those problems leading to partial differential equations. Contents:I. Classification of Partial Differential EquationsII. Evaluations of the Hyperbolic TypeIII. Equations of the Parabolic TypeIV. Equations of Elliptic TypeV. Wave Propagation in SpaceVI. Heat Conduction in SpaceVII. Equations of Elliptic Type (Continuation)The authors — two well-known Russian mathematicians — have focused on typical physical processes and the principal types of equations dealing with them. Special attention is paid throughout to mathematical formulation, rigorous solutions, and physical interpretation of the results obtained. Carefully chosen problems designed to promote technical skills are contained in each chapter, along with extremely useful appendixes that supply applications of solution methods described in the main text. At the end of the book, a helpful supplement discusses special functions, including spherical and cylindrical functions.