Equations in Mathematical Physics : A Practical Course

This handbook is addressed to students of technology institutf's where a course on mathematical physics of relatively reduced volume is offered, as well as to engineers and scientists. The aim of the handbook is to treat (demonstrate) the basic methods for solving the simplest problems of classical mathematical physics. The most basic among the methods considered hrre i8 the superposition method. It allows one, based on particular linearly indepmdent HolutionH (solution "atoms"), to obtain the solution of a given problem. To that end the "Hupply" of solution atoms must be complete. This method is a development of the well-known method of particular solutions from the theory of ordinar~' differelltial equations. In contrast to the case of ordinary differential equations, where the number of linearly independent 80lutions is always finite, for a linear partial differrntial equation a complete "supply" of solution atoms is always infinite. This infinite set of Holutions may be discrete (for example, for regular boundary vahlP problems in a bounded domain), or form a continuum (for example, in the case of problems in the whole space). In the first case the superposition method reduces to tlH' construction of a series in the indicated solution atoms with unknown coefficipnts, while in the second case the series is replaced by an integral with respect to the corm:iponding parameters (variables). This first step leads us to the general solution of the associated hOlllogeneous equation under the assumption that the set of solution atoms i;; "complete.

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 Demontstrate 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 Gree&ngrave;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.

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 demontstrate 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 Front Matter....Pages i-viii Introduction....Pages 1-6 Elliptic problems....Pages 7-79 Hyperbolic problems....Pages 81-160 Parabolic problems....Pages 161-204 Back Matter....Pages 205-207 An effective method for solving boundary value problems for the Laplace and Helmoltz equations (in domains possessing a definite symmetry) is the method of separation of variables.