Author | Logan, J. David. author |
---|---|
Title | Applied Partial Differential Equations [electronic resource] / by J. David Logan |
Imprint | New York, NY : Springer New York : Imprint: Springer, 2004 |
Edition | Second Edition |
Connect to | http://dx.doi.org/10.1007/978-1-4419-8879-9 |
Descript | XII, 212 p. online resource |
1: The Physical Origins of Partial Differential Equations -- 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 Laplaceโs Equation -- 1.9 Classification of PDEs -- 2: Partial Differential Equations on Unbounded Domains -- 2.2 Cauchy Problem for the Wave Equation -- 2.3 Ill-Posed Problems -- 2.4 Semi-Infinite Domains -- 2.5 Sources and Duhamelโs Principle -- 2.6 Laplace Transforms -- 2.7 Fourier Transforms -- 2.8 Solving PDEs Using Computer Algebra Systems* -- 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 Laplaceโs 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* -- 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