Equations of Mathematical Physics (Dover Books on Physics) by A. N. Tikhonov (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Excellent book for those interested in differential equations, especially in the fields gravitation, electricity, heat transfer, acoustics and hydrodynamics. However, anything related to differential equations will benefit from the pages of this wonderful work.The book is deep, yet its very good didactics really helps the reader, making things easier.My studies focus is on hydrodynamics, potential hydrodynamics, and this book fits perfectly well all my mathematical needs.One of the best math books ever written!

⭐This is a very important book. The authors put Rayleigh’s potential theorem on a rigorous foundation. Had it been available earlier, it would have altered some of the standard acoustical literature. For example, the Helmholtz integral equation has been widely used to treat certain acoustic diffraction and scattering problems. This is because it has a 30 year head start in the English language literature. Potential theory was put on a rigorous basis by Russian mathematicians, but the translations did not become widely available until the 1960’s.

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⭐The book arrived even earlier than planned, in excellent condition.Also, the customer service replies promptly and is helpful.I am very happy with this purchase.

⭐This is an outstanding and massive treatise (765 pages) on mathematical physics in which the authors give clear exposition of the theory where all types (linear hyperbolic, parabolic and elliptic) of partial differential equation are very well covered. This book has its companion book (A Collection of Problems in Mathematical Physics by B.M. Budak, A.A. Samarskii and A.N. Tikhonov) in the gain massive compendium (768 pages) of problems with solutions which makes this book set very well suited for self-study. Although these books are “old” i.e. originally published in the early 60s by Pergamon Press as translation of books published in the former Soviet Union in the early 50s, they present fundamental theory that as not changed since then.

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