Partial Differential Equations: An Accessible Route Through Theory and Applications 1470418819, 978-1-4704-1881-6

This text on partial differential equations is intended for readers who want to understand the theoretical underpinnings

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Partial Differential Equations: An Accessible Route Through Theory and Applications 1470418819, 978-1-4704-1881-6

Table of contents :
Content: IntroductionWhere do PDE come fromFirst order scalar semilinear equationsFirst order scalar quasilinear equationsDistributions and weak derivativesSecond order constant coefficient PDE: Types and d'Alembert's solution of the wave equationProperties of solutions of second order PDE: Propagation, energy estimates and the maximum principleThe Fourier transform: Basic properties, the inversion formula and the heat equationThe Fourier transform: Tempered distributions, the wave equation and Laplace's equationPDE and boundariesDuhamel's principleSeparation of variablesInner product spaces, symmetric operators, orthogonalityConvergence of the Fourier series and the Poisson formula on disksBessel functionsThe method of stationary phaseSolvability via dualityVariational problemsBibliographyIndex

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