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Équations aux dérivées partielles

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Mathematiques --- Equations differentielles ordinaires --- Equations aux derivees partielles --- Physique --- Fonctions d'une variable complexe --- Oeuvres reunies --- Optique --- Fonctions entieres --- Bureau, Florent --- Mathematiques --- Equations differentielles ordinaires --- Equations aux derivees partielles --- Physique --- Fonctions d'une variable complexe --- Oeuvres reunies --- Optique --- Optique geometrique --- Fonctions entieres

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Boundary value problems. --- Differential equations, Partial. --- Fourier series. --- Boundary value problems --- Differential equations, Partial --- Fourier series --- 517.95 --- 517.95 Partial differential equations --- Partial differential equations --- Fourier integrals --- Series, Fourier --- Series, Trigonometric --- Trigonometric series --- Calculus --- Fourier analysis --- Harmonic analysis --- Harmonic functions --- Boundary conditions (Differential equations) --- Differential equations --- Functions of complex variables --- Mathematical physics --- Initial value problems --- Équations aux dérivées partielles

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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).

Differential equations, Partial. --- Equations aux dérivées partielles --- 517.95 --- Partial differential equations --- Mathematics. --- Community ecology, Biotic. --- Partial differential equations. --- Physics. --- Partial Differential Equations. --- Mathematical Methods in Physics. --- Community & Population Ecology. --- 517.95 Partial differential equations --- Equations aux dérivées partielles --- Differential equations, Partial --- Biocenoses --- Biocoenoses --- Biogeoecology --- Biological communities --- Biomes --- Biotic community ecology --- Communities, Biotic --- Community ecology, Biotic --- Ecological communities --- Ecosystems --- Natural communities --- Ecology --- Population biology --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics