Sinossi
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.
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