Transcription of The mathematics of PDEs and the wave equation
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The mathematics of PDEs and the wave equation
The mathematics of PDEs and the wave equationMichael P. Lamoureux University of CalgarySeismic Imaging Summer SchoolAugust 7 11, 2006, CalgaryAbstractAbstract: We look at the mathematical theory of partial differential equations asapplied to the wave equation . In particular, we examine questions about existence anduniqueness of solutions, and various solution techniques. Supported by NSERC, MITACS and the POTSI and CREWES 2006. All rights Lecture One: Introduction to PDEs equations from physics Deriving the 1D wave equation One way wave equations Solution via characteristic curves Solution via separation of variables Helmholtz equation Classification of second order, linear PDEs Hyperbolic equations and the wave equation2. Lecture Two: Solutions to PDEs with boundary conditions and initial conditions Boundary and initial conditions Cauchy, Dirichlet, and Neumann conditions Well-posed problems Existence and uniqueness theorems D Alembert s solution to the 1D wave equation Solution to the n-dimensional wave equation Huygens principle Energy and uniqueness of solutions3.
The mathematics of PDEs and the wave equation Michael P. Lamoureux ∗ University of Calgary Seismic Imaging Summer School August 7–11, 2006, Calgary
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