This video shows how to solve Partial Differential Equations (PDEs) with Laplace Transforms. Specifically we solve the wave equation on a semi-infinite domain.
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This video was produced at the University of Washington
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0:00 Overview and Problem Setup (Initial Conditions and Boundary Conditions)
3:46 Laplace Transform in Time: PDE to ODE
8:20 Solving the ODE in Space
12:57 General Solution of the Wave Equation
15:38 The Heaviside Function
19:36 Illustration and Method of Characteristics