Equations in mathematical physics等式在数理物理学

书籍目录

Chapter 1. Elliptic problems  1.1  The Dirichlet problem for the Laplace equation in an annulus　1.2  Examples of Dirichlet problems in an annlus　1.3  The interior and exterior Dirichlet problems　1.4  The Poisson integral for the disc. Complex form Solution of the Diriehlet problem when the boundary conditionis a rational function R(sinψ, cosψ)　1.5  The interior and exterior Diriehlet problems　1.6  Boundary value problems for the Poisson equation in a disc and in an annulus　1.7  Boundary value problems for the Laplace and Poisson equations in a rectangle　1.8  Boundary value problems for the Laplace and Poisson equations in a bounded cylinder　1.9  Boundary value problems for the Laplace and Poisson equations in a ball　1.10 Boundary value problems for the Hehnholtz equations　1.11 Boundary value problem for the Helmoltz equation in a cylinder　1.12 Boundary value problems for the Hehnoltz equation in a disc　1.13 Boundary value problems for the Hehnoltz equation in a ball　1.14 Guided electromagnetic waves　1.15 The method of eonformal mappings (for the solution of boundary value problems in the plane)　1.16 The Green function method　1.17 Other methods　1.18 Problems for independent study　1.19 AnswersChapter 2. Hyperbolic problems　2.1  The travelling-wave method　2.2  The method of selection of particular solutions　2.3  The Fourier integral transform method　2.4  The Laplace integral transform method　2.5  The Hankel integral transform method　2.6  The method of standing waves. Oscillations of a bounded string  2.7  Some examples of mixed problems for the equation of oscillations of a string　2.8  The Fourier method. Oscillations of a rectangular membrae　2.9  The Fourier method. Oscillations of a circular membrane　2.10 The Fourier method. Oscillations of a beam　2.11 The perturbation method　2.12 Problems for independent study　2.13 AnswersChaper 3. Parabolic problems　3.1  The Fourier integral transform method　3.2  The Lapalce integral transform method　3.3  The Fourier method (method of separation of variables)　3.4  A modification of the method of separation of variables for solving the Cauchy problem　3.5  Problems for independent study　3.6  AnswersReferencesIndex

作者简介

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 Greens 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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