4. The Laplace equation

The weak maximum principle

A small correction: 18:25 The maximum of -u is of course minus the minimum of u, not just the minimum. But the conclusion in the video is correct: since -u attains its maximum on the boundary, u attains its minimum on the boundary.

Poisson's formula (for a disk)

Corrections to some silly (and rather obvious) slips of the tongue: 05:47 "if theta is zero" should be "if lambda is zero". 07:51 "where m is a positive integer" should be "where m is a nonnegative integer". 13:06 "linear ODE" should be "linear PDE". 16:14 "A₀ over zero" should be "A₀ over two". 21:17 "complex number times its conjugate" should be "complex number plus its conjugate". 22:17 "r² divided by r²" should be "r² divided by a²".

Sidansvarig: Hans Lundmark
Senast uppdaterad: 2021-03-25