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Partial differential equations : theory and technique /
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York :
Academic Press,
1976.
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Partial Differential Equations: Theory and Technique; Copyright Page; Table of Contents; PREFACE; INTRODUCTION; I.1 DEFINITIONS AND EXAMPLES; CHAPTER 1. THE DIFFUSION EQUATION; 1.1 DERIVATION; 1.2 PROBLEMS; 1.3 SIMPLE SOLUTIONS; 1.4 PROBLEMS; 1.5 SERIES SOLUTIONS; 1.6 PROBLEMS; 1.7 NONHOMOGENEOUS END CONDITIONS; 1.8 PROBLEMS; 1.9 THE MAXIMUM PRINCIPLE; 1.10 PROBLEMS; CHAPTER 2. LAPLACE TRANSFORM METHODS; 2.1 INTRODUCTORY EXAMPLE; 2.2 PROBLEMS; 2.3 A FINITE INTERVAL PROBLEM; 2.4 PROBLEMS; 2.5 DELTA FUNCTION; 2.6 PROBLEMS; 2.7 SUPPLEMENTARY PROBLEMS; CHAPTER 3. THE WAVE EQUATION
- 3.1 DERIVATION3.2 PROBLEMS; 3.3 AN INFINITE-INTERVAL PROBLEM; 3.4 PROBLEMS; 3.5 SERIES SOLUTIONS; 3.6 PROBLEMS; 3.7 A PROBLEM WITH RADIAL SYMMETRY; 3.8 PROBLEMS; 3.9 TRANSFORMS; 3.10 PROBLEMS; 3.11 UNIQUENESS; 3.12 SUPPLEMENTARY PROBLEMS; CHAPTER 4. THE POTENTIAL EQUATION; 4.1 LAPLACE'S AND POISSON 'S EQUATIONS; 4.2 PROBLEMS; 4.3 SIMPLE PROPERTIES OF HARMONIC FUNCTIONS; 4.4 SOME SPECIAL SOLUTIONS-SERIES; 4.5 PROBLEMS; 4.6 DISCONTINUOUS BOUNDARY DATA; 4.7 COMPLEX VARIABLES AND CON FORMAL MAPPING; 4.8 PROBLEMS; CHAPTER 5. CLASSIFICATION OF SECOND-ORDER EQUATIONS; 5.1 CAUCHY DATA ON y-AXIS
- 5.2 CAUCHY DATA ON ARBITRARY CURVE5.3 PROBLEMS; 5.4 CASE I: B2
- AC> 0; 5.5 CASE II: B2
- AC = 0; 5.6 CASE III: B2
- AC <0; 5.7 PROBLEMS; 5.8 DISCONTINUITIES; SIGNAL PROPAGATION; 5.9 PROBLEMS; 5.10 SOME REMARKS; CHAPTER 6. FIRST-ORDER EQUATIONS; 6.1 LINEAR EQUATION EXAMPLES; 6.2 PROBLEMS; 6.3 QUASI-LINEAR CASE; 6.4 PROBLEMS; 6.5 FURTHER PROPERTIES OF CHARACTERISTICS; 6.6 PROBLEMS; 6.7 MORE VARIABLES; CHAPTER 7. EXTENSIONS; 7.1 MORE VARIABLES; 7.2 PROBLEMS; 7.3 SERIES AND TRANSFORMS; 7.4 PROBLEMS; 7.5 LEGENDRE FUNCTIONS; 7.6 PROBLEMS; 7.7 SPHERICAL HARMONICS; 7.8 PROBLEMS
- CHAPTER 8. PERTURBATIONS8.1 A NONLINEAR PROBLEM; 8.2 PROBLEMS; 8.3 TWO EXAMPLES FROM FLUID MECHANICS; 8.4 BOUNDARY PERTURBATIONS; 8.5 PROBLEMS; CHAPTER 9. GREEN'S FUNCTIONS; 9.1 SOME CONSEQUENCES OF THE DIVERGENCE THEOREM; 9.2 THE LAPLACIAN OPERATOR; 9.3 PROBLEMS; 9.4 POTENTIALS OF VOLUME AND SURFACE DISTRIBUTIONS; 9.5 PROBLEMS; 9.6 MODIFIED LAPLACIAN; 9.7 PROBLEMS; 9.8 WAVE EQUATION; 9.9 PROBLEMS; CHAPTER 10. VARIATIONAL METHODS; 10.1 A MINIMIZATION PROBLEM; 10.2 PROBLEMS; 10.3 NATURAL BOUNDARY CONDITIONS; 10.4 SUBSIDIARY CONDITIONS; 10.5 PROBLEMS; 10.6 APPROXIMATE METHODS; 10.7 PROBLEMS
- 10.8 FINITE-ELEMENT METHOD10.9 SUPPLEMENTARY PROBLEMS; CHAPTER 11. EIGENVALUE PROBLEMS; 11.1 A PROTOTYPE PROBLEM; 11.2 SOME EIGENVALUE PROPERTIES; 11.3 PROBLEMS; 11.4 PERTURBATIONS; 11.5 APPROXIMATIONS; 11.6 PROBLEMS; CHAPTER 12. MORE ON FIRST-ORDER EQUATIONS; 12.1 ENVELOPES; 12.2 CHARACTERISTIC STRIPS; 12.3 COMPLETE INTEGRAL; 12.4 PROBLEMS; 12.5 LEGENDRE TRANSFORMATION; 12.6 PROBLEMS; 12.7 PROPAGATION OF A DISTURBANCE; 12.8 COMPLETE INTEGRAL AND EIKONAL FUNCTION; 12.9 HAMILTON-JACOBI EQUATION; 12.10 PROBLEMS; CHAPTER 13. MORE ON CHARACTERISTICS; 13.1 DISCONTINUITIES-A PRELIMINARY EXAMPLE