Адамян В.М., Сушко М.Я. Introduction to Mathematical Physics

Одеса: Астропринт, 2003. — 162 с.This book covers an introductory minimum of tools and techniques of mathematical physics. The emphasis is on two major concepts: the linear Cauchy problem for partial differential equations on an unbounded space, and the Green’s function, by means of which solving the Cauchy problem reduces to integrating. The relevant elements of the theory of generalized functions and that of Fourier integral transformations are also given. We have restricted our consideration to problems for the unbounded three-dimensional space. As compared to boundary-value problems, they are more transparent and easier to grasp – there is no need to satisfy boundary conditions, which usually break the symmetries intrinsic to problems for an unbounded space. Boundary-value problems, extremely important for description of a wide range of electromagnetic and hydrodynamic phenomena, can be avoided when the fundamentals of theoretical physics are first introduced. We therefore decided to reserve their consideration for the next manual, which we hope to complete in the near future. The book is oriented to Physics majors and is based on the first part of the lecture course in mathematical physics that is usually offered by the Department of Physics at Odessa National University to the sophomore students. This has predetermined some of its features. In particular, the material is represented in a more narrative style than that usually accepted in texts in pure mathematics. We tried – as far as possible – not to overindulge in a great deal of abstract constructions, but to give more attention to the meaning of general statements and the details of their application. Since our potential reader has already taken the three-semester calculus sequence within the limits of the standard university curricula for physicists and engineers, we also took the liberty of not reminding some definitions and concepts of calculus, or even not accentuating which version of these concepts (for instance, the Riemann or the Lebesgue integral) is meant. Contributing to the completeness of some statements and constructions, such notes would not have added much to working out the problems being dealt with in the book. To avoid going deep into pure analysis, we have omitted some of the proofs. Despite some uncertainties in the text, we tried to be precise in all the formulations and proofs. Therefore it seems to us that the book may also be useful for students studying pure or applied mathematics. Almost every section incorporates problems. Some of those are given just to teach the reader to use the concepts introduced, whereas others are integral parts of the main text.Heat conduction in systems with distributed parameters.
The diffusion equation.
The wave equation.
Supplementary facts from the theory of functions.Index. Ukrainian equivalents of the terms.