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| 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 Answers Chapter 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 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 Index |
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