Notes on Cambridge Maths

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Laplace's equation


where .

Suppose is analytic. Then by Cauchy-Riemann Equations:

hence .

We want to solve the Laplace equation on with some boundary conditions on .

  • Find nice and conformal, with
  • Translate the boundary conditions on to
  • Then find a solution satisfying the boundary conditions and on .
  • Hence is a solution on .

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