Equations in Mathematical Physics
Springer Basel (Verlag)
978-3-0348-9503-3 (ISBN)
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. Oscillationsof 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.
Erscheint lt. Verlag | 23.8.2014 |
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Übersetzer | A. Iacob |
Zusatzinfo | VIII, 207 p. 1 illus. |
Verlagsort | Basel |
Sprache | englisch |
Maße | 155 x 235 mm |
Gewicht | 339 g |
Themenwelt | Naturwissenschaften ► Physik / Astronomie ► Allgemeines / Lexika |
Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik | |
Schlagworte | Boundary value problem • Cauchy problem • differential equation • electromagnetic wave • eliptic • Fourier integral • Helmholtz equation • hyperbolic • Integral • Mathematical Physics • ordinary differential equation • parabolic • partial differential equation • Partial differential equations • Poisson equation • Solution |
ISBN-10 | 3-0348-9503-8 / 3034895038 |
ISBN-13 | 978-3-0348-9503-3 / 9783034895033 |
Zustand | Neuware |
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