Equations in Mathematical Physics : A Practical Course

A Practical Course

By: A. Iacob (Translator), V.P. Pikulin, Stanislav I. Pohozaev

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Hardcover | 1 August 2001

At a Glance

Hardcover
220 Pages

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23.5 x 17.15 x 1.91

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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.

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Non-Fiction Science Physics Mathematical Physics Mathematics Calculus & Mathematical Analysis Differential Calculus & Equations Education

Preface
Introduction	p. 1
Elliptic problems	p. 7
The Dirichlet problem for the Laplace equation in an annulus	p. 7
Examples of Dirichlet problems in an annulus	p. 10
The interior and exterior Dirichlet problems	p. 11
The Poisson integral for the disc. Complex form. Solution of the Dirichlet problem when the boundary condition is a rational function R(sin[actual symbol not reproducible], cos[actual symbol not reproducible])	p. 14
The interior and exterior Dirichlet problems	p. 18
Boundary value problems for the Poisson equation in a disc and in an annulus	p. 20
Boundary value problems for the Laplace and Poisson equations in a rectangle	p. 19
Boundary value problems for the Laplace and Poisson equations in a bounded cylinder	p. 27
Boundary value problems for the Laplace and Poisson equations in a ball	p. 33
Boundary value problems for the Helmoltz equations	p. 43
Boundary value problems for the Helmoltz equation in a cylinder	p. 44
Boundary value problems for the Helmoltz equation in a disc	p. 46
Boundary value problems for the Helmoltz equation in a ball	p. 49
Guided electromagnetic waves	p. 54
The method of conformal mappings (for the solution of boundary value problems in the plane)	p. 55
The Green function method	p. 60
Other methods	p. 68
Problems for independent study	p. 73
Hyperbolic problems	p. 81
The travelling-wave method	p. 81
The method of selection of particular solutions	p. 93
The Fourier integral transform method	p. 96
The Laplace integral transform method	p. 111
The Hankel integral transform method	p. 115
The method of standing waves: Oscillations of a bounded string	p. 121
Some examples of mixed problems for the equation of oscillations of a string	p. 124
The Fourier method. Oscillations of a rectangular membrane	p. 130
The Fourier method. Oscillations of a circular membrane	p. 136
The Fourier method. Oscillations of a beam	p. 141
The perturbation method	p. 145
Problems for independent study	p. 149
Parabolic problems	p. 161
The Fourier integral transform method	p. 161
The Lapalce integral transform method	p. 170
The Fourier method (method of separation of variables)	p. 174
A modification of the method of separation of variables for solving the Cauchy problem	p. 190
Problems for independent study	p. 197
References	p. 205
Index	p. 207
Table of Contents provided by Blackwell. All Rights Reserved.

Equations in Mathematical Physics : A Practical Course

A Practical Course

At a Glance

Hardcover

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How to return your order

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