Equations in Mathematical Physics: A practical course - Hardcover

Pikulin, V.P.; Pohozaev, Stanislav I.

9783764365011: Equations in Mathematical Physics: A practical course

Hardcover

ISBN 10: 3764365013 ISBN 13: 9783764365011

Verlag: Birkh�user, 2001

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1. Elliptic problems.- 1.1 The Dirichlet problem for the Laplace equation in an annulus.- 1.2 Examples of Dirichlet problems in an annulus.- 1.3 The interior and exterior Dirichlet problems.- 1.4 The Poisson integral for the disc. Complex form. Solution of the Dirichlet problem when the boundary condition is a rational function R(sin ?, cos ?).- 1.5 The interior and exterior Dirichlet 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 Helmholtz equations.- 1.11 Boundary value problem for the Helmoltz equation in a cylinder.- 1.12 Boundary value problems for the Helmoltz equation in a disc.- 1.13 Boundary value problems for the Helmoltz equation in a ball.- 1.14 Guided electromagnetic waves.- 1.15 The method of conformal 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 Answers.- 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 met hod.- 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 membrane.- 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 Answers.- Chaper 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 Answers.- References.

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Rese�a del editor

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.

Rese�a del editor

Mathematical modeling and numerical simulation in fluid mechanics are topics of great importance both in theory and technical applications. The present book attempts to describe the current status in various areas of research. The 10 chapters, mostly survey articles, are written by internationally renowned specialists and offer a range of approaches to and views of the essential questions and problems. In particular, the theories of incompressible and compressible Navier-Stokes equations are considered, as well as stability theory and numerical methods in fluid mechanics. Although the book is primarily written for researchers in the field, it will also serve as a valuable source of information to graduate students.

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