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Applied Partial Differential Equations
This text presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs. Emphasis is placed on motivation, concepts, methods, and interpretation, rather than on formal theory. The concise treatment of the subject is maintained in this thi...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cham :
Springer International Publishing : Imprint: Springer,
2015.
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| Edición: | 3rd ed. 2015. |
| Colección: | Undergraduate Texts in Mathematics,
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| Temas: | |
| Acceso en línea: | Texto Completo |
Tabla de Contenidos:
- Preface to the Third Edition
- To the Students
- 1: The Physical Origins of Partial Differential Equations
- 1.1 PDE Models
- 1.2 Conservation Laws
- 1.3 Diffusion
- 1.4 Diffusion and Randomness
- 1.5 Vibrations and Acoustics
- 1.6 Quantum Mechanics*
- 1.7 Heat Conduction in Higher Dimensions
- 1.8 Laplace's Equation
- 1.9 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 Well-Posed Problems
- 2.4 Semi-Infinite Domains
- 2.5 Sources and Duhamel's Principle
- 2.6 Laplace Transforms
- 2.7 Fourier Transforms
- 3. Orthogonal Expansions
- 3.1 The Fourier Method
- 3.2 Orthogonal Expansions
- 3.3 Classical Fourier Series.-4. Partial Differential Equations on Bounded Domains
- 4.1 Overview of Separation of Variables
- 4.2 Sturm-Liouville Problems - 4.3 Generalization and Singular Problems
- 4.4 Laplace's Equation
- 4.5 Cooling of a Sphere
- 4.6 Diffusion inb a Disk
- 4.7 Sources on Bounded Domains
- 4.8 Poisson's Equation*.-5. Applications in the Life Sciences.-5.1 Age-Structured Models
- 5.2 Traveling Waves Fronts
- 5.3 Equilibria and Stability
- References
- Appendix A. Ordinary Differential Equations
- Index. .