| Preface to the Second Edition To the Student Chapter 1：The physical origins of partial differential 1.1 Mathematical models 1.2 Conservation laws 1.3 Diffusion 1.4 PDEs in biology 1.5 Vibrations and acoustics 1.6 Quantum mechanics 1.7 Heat flow in three dimensions 1.8 Laplace’s equation 1.9 Classification of PDEs Chapter 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 Systems Chapter 3： Orthogonal Expansions 3.1 The Fourier Method 3.2 Orthogonal Expansions 3.3 Classical Fourier Series 3.4 Sturm-Liouville Problems Chapter 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 Chapter 5： Partial Differential Equations in the Life Sciences 5.1 Age-Structured Models 5.2 Traveling Wave Fronts 5.3 Equilibria and Stability Appendix： Ordinary Differential Equations Table of Laplace Transforms References Index |
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