Equations of the Mathematical Physics

Argumento de Equations of the Mathematical Physics

Chapter II. Generalized Functions
5. Test and Generalized Functions
6. Differentiation of Generalized Functions
7. The Direct Product and Convolution of Generalized Functions
8. Generalized Functions of Slow Growth
9. The Fourier Transform of Generalized Functions of Slow Growth
10. The Laplace Transform of Generalized Functions (Operational Calculus)

Chapter III. Fundamental Solutions and the Cauchy Problem
11. Fundamental Solutions of Linear Differential Operators
12. The Wave Potential
13. The Cauchy Problem for the Wave Equation
14. Wave Propagation
15. Riemann´s Method
16. The Cauchy Problem for the Heat Conduction Equation

Chapter IV. Integral Equations
17. Introduction
18. The Method of Successive Approximations
19. Fredhol`s Theorems
20. Integral Equations with a Hermitian Kernel
21. The Hilbert-Schmidt Theorem and its Corollaries

Chapter V. Boundary Value Problems for Equations of Elliptic Type
22. The Eigenvalue Problem
23. The Sturm-Liouville Problem
24. The Bessel Functions
25. Harmonic Functions
26. Spherical Functions
27. Foruer`s Method for Eigenvalue Problems
28. The Newtonian Potential
29. Boundary Value Problems for Laplace`s and Poisson`s Equations in Space
30. Green`s Function of the Dirichlet Problem
31. Helmholtz´s Equation
32. Boundary Value Problems for Laplace`s Equation in a Plane

Chapter VI. Mixed Problems
33. Fourier`s Method
34. A Mixed Problem for an Equation of Hyperbolic Type
35. A Mixed Problem for an Equation of Parabolic Type

References
Name index
Subject index