This video introduces a powerful technique to solve Partial Differential Equations (PDEs) called Separation of Variables. I demonstrate this technique to solve Laplace's equation in two-dimensions for the steady state heat distribution on a rectangle. It can be used for a huge variety of other problems in physics and engineering.
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This video was produced at the University of Washington
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0:00 Overview and Problem Setup: Laplace's Equation in 2D
5:12 Linear Superposition: Solving a Simpler Problem
8:38 Separation of Variables
15:39 Reducing the PDE to a system of ODEs
33:26 The Solution of the PDE
36:21 Recap/Summary of Separation of Variables
42:06 Last Boundary Condition & The Fourier Transform
