Laplace's Equation on a Rectangle - Partial Differential Equation | Lecture 9

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Equilibrium temperature distributions in higher spatial dimensions come from solving a PDE called Laplace's equation. Laplace's equation is difficult to solve in general and its solutions form the basis for harmonic theory. In this lecture we solve Laplace's equation on a rectangle, showing how we can decompose the solution using the principle of superposition and solve each component using separation of variables.

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  1. Jason Bramburger
  2. partial
  3. differential equation
  4. derivative
  5. pde
  6. Laplace
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Can we say that as we can solve eigenvalue problem (Lu=lambda×u) in continuous domain when with homogeneous boundary condition, for this reason you take d²(phi)/dy² + lambda×phi = 0 and solve this as at y=0&H, value of phi is zero...?

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