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Partial differential equations : an introduction with Mathematica and MAPLE

Author: Ioannis P Stavroulakis; Stepan A Tersian
Publisher: River Edge, N.J. : World Scientific, ©1999.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:

A self-contained introduction to partial differential equations. It covers the basic equations of mathematical physics and the properties of their solutions, based on classical calculus and ordinary  Read more...

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Document Type: Book
All Authors / Contributors: Ioannis P Stavroulakis; Stepan A Tersian
ISBN: 9810238916 9789810238919
OCLC Number: 42290191
Description: x, 297 pages : illustrations ; 23 cm
Contents: 1. First-order Partial Differential Equations --
1. Introduction --
2. Linear First-order Equations --
3. The Cauchy Problem for First-order Quasi-linear Equations --
4. General Solutions of Quasi-linear Equations --
5. Fully-nonlinear First-order Equations --
2. Second-order Partial Differential Equations --
6. Linear equations --
7. Classification and Canonical Forms of Equations in Two Independent Variables --
8. Classification of Almost-linear Equations in R[superscript n] --
3. One-Dimensional Wave Equation --
9. The Wave Equation on the Whole Line. D'Alembert Formula --
10. The Wave Equation on the Half-line. Reflection Method --
11. Mixed Problem for the Wave Equation --
12. Inhomogeneous Wave Equation --
13. Conservation of the Energy --
14. Weak Derivatives and Weak Solutions --
4. One-Dimensional Diffusion Equation --
15. Maximum-minimum Principle for the Diffusion Equation --
16. The Diffusion Equation on the Whole Line --
17. Diffusion on the Half-line --
18. Inhomogeneous Diffusion Equation on the Whole Line --
5. Shock Waves and Conservation Laws --
19. Conservation laws --
20. Burgers' Equation --
21. Weak Solutions. Riemann Problem --
22. Discontinuous Solutions of Conservation Laws. Rankine-Hugoniot Condition --
6. The Laplace Equation --
23. Harmonic functions. Maximum-minimum Principle --
24. Green's Identities --
25. Green's Functions --
26. Green's Functions for a Half-space and Sphere --
27. Harnack's Inequalities and Theorems --
7. Fourier Series and Fourier Method for PDEs --
28. Fourier Series --
29. Orthonormal Systems. General Fourier series --
30. Fourier Method for the Diffusion Equation --
31. Fourier Method for the Wave Equation --
32. Fourier Method for the Laplace Equation --
8. Diffusion and Wave Equations in Higher Dimensions --
33. Diffusion Equation in Three Dimensional Space --
34. Fourier Method for the Diffusion Equation in Higher Dimensions --
35. Kirchoff's Formula for the Wave Equation. Huygens' Principle.
Responsibility: Ioannis P. Stavroulakis, Stepan A. Tersian.

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