9783764365011

Equations in Mathematical Physics : A Practical Course

by ;
  • ISBN13:

    9783764365011

  • ISBN10:

    3764365013

  • Format: Hardcover
  • Copyright: 2001-10-01
  • Publisher: Springer Verlag

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Supplemental Materials

What is included with this book?

Summary

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.

Table of Contents

Preface vii
Introduction 1(6)
Elliptic problems
7(74)
The Dirichlet problem for the Laplace equation in an annulus
7(3)
Examples of Dirichlet problems in an annulus
10(1)
The interior and exterior Dirichlet problems
11(3)
The Poisson integral for the disc. Complex form. Solution of the Dirichlet problem when the boundary condition is a rational function R (sin ϕ, cos ϕ)
14(4)
The interior and exterior Dirichlet problems
18(2)
Boundary value problems for the Poisson equation in a disc and in an annulus
20
Boundary value problems for the Laplace and Poisson equations in a rectangle
19(8)
Boundary value problems for the Laplace and Poisson equations in a bounded cylinder
27(6)
Boundary value problems for the Laplace and Poisson equations in a ball
33(10)
Boundary value problems for the Helmholtz equations
43(1)
Boundary value problem for the Helmoltz equation in a cylinder
44(2)
Boundary value problems for the Helmoltz equation in a disc
46(3)
Boundary value problems for the Helmoltz equation in a ball
49(5)
Guided electromagnetic waves
54(1)
The method of conformal mappings (for the solution of boundary value problems in the plane)
55(5)
The Green function method
60(8)
Other methods
68(5)
Problems for independent study
73(3)
Answers
76(5)
Hyperbolic problems
81(80)
The travelling-wave method
81(12)
The method of selection of particular solutions
93(3)
The Fourier integral transform method
96(15)
The Laplace integral transform method
111(4)
The Hankel integral transform method
115(6)
The method of standing waves. Oscillations of a bounded string
121(3)
Some examples of mixed problems for the equation of oscillations of a string
124(6)
The Fourier method. Oscillations of a rectangular membrane
130(6)
The Fourier method. Oscillations of a circular membrane
136(5)
The Fourier method. Oscillations of a beam
141(4)
The perturbation method
145(4)
Problems for independent study
149(6)
Answers
155(6)
Parabolic problems
161(44)
The Fourier integral transform method
161(9)
The Lapalce integral transform method
170(4)
The Fourier method (method of separation of variables)
174(16)
A modification of the method of separation of variables for solving the Cauchy problem
190(7)
Problems for independent study
197(5)
Answers
202(3)
References 205(2)
Index 207

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