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Applied partial differential equations /
This textbook is for the standard, one-semester, junior-senior course that often goes by the title "Elementary Partial Differential Equations" or "Boundary Value Problems". The audience consists of students in mathematics, engineering, and the physical sciences. The topics includ...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York :
Springer,
©1998.
|
| Colección: | Undergraduate texts in mathematics.
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 1: The Physical Origins of Partial Differential Equations
- 1.1 Mathematical Models
- 1.2 Conservation Laws
- 1.3 Diffusion
- 1.4 Contaminant Transport in Aquifers*
- 1.5 Vibrations of a String
- 1.6 Quantum Mechanics*
- 1.7 Heat Flow in Three Dimensions
- 1.8 Laplace's Equation
- 1.9 Acoustics*
- 1.10 Classification of PDEs
- 2: Partial Differential Equations on Unbounded Domains
- 2.1 Cauchy Problem for the Heat Equation
- 2.2 Cauchy Problem for the Wave Equation
- 2.3 Ill-Posed Problems
- 2.4 Semi-Infinite Domains
- 2.5 Sources and Duhamel's Principle
- 2.6 Laplace Transforms
- 2.7 Fourier Transforms
- 2.8 Solving PDEs Using Computer Algebra Packages
- 3: Orthogonal Expansions
- 3.1 The Fourier Method
- 3.2 Orthogonal Expansions
- 3.3 Classical Fourier Series
- 3.4 Sturm-Liouville Problems
- 4: Partial Differential Equations on Bounded Domains
- 4.1 Separation of Variables
- 4.2 Flux and Radiation Conditions
- 4.3 Laplace's Equation
- 4.4 Cooling of a Sphere
- 4.5 Diffusion in a Disk
- 4.6 Sources on Bounded Domains
- 4.7 Parameter Identification Problems*
- 4.8 Finite Difference Methods*
- Appendix: Ordinary Differential Equations
- Table of Laplace Transforms
- References.