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 |

SUMMARY

This primer on elementary partial differential equations presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs. What makes this book unique is that it is a brief treatment, yet it covers all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. Mathematical ideas are motivated from physical problems, and the exposition is presented in a concise style accessible to science and engineering students; emphasis is on motivation, concepts, methods, and interpretation, rather than formal theory. This second edition contains new and additional exercises, and it includes a new chapter on the applications of PDEs to biology: age structured models, pattern formation; epidemic wave fronts, and advection-diffusion processes. The student who reads through this book and solves many of the exercises will have a sound knowledge base for upper division mathematics, science, and engineering courses where detailed models and applications are introduced. J. David Logan is Professor of Mathematics at University of Nebraska, Lincoln. He is also the author of numerous books, including Transport Modeling in Hydrogeochemical Systems (Springer 2001)

CONTENT

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 Laplaceโ{128}{153}s 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 Duhamelโ{128}{153}s 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 Laplaceโ{128}{153}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* -- 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

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