Flow in a Rectangular Channel | Fourier Series & Laplace's Equation

Chapters:
00:00 Introduction
00:45 2D Problem
05:40 3D Problem
08:00 Solving Laplace's Equation
13:10 Calculating Fourier Series
17:00 Surprising Infinite Sums

[@arneaj4540]

Lovely video, I wish I could do science communication that well myself

[@ammonium3757]

Excellent video!
I've been trying to follow along and derive the equations, one thing that I'm not sure off is at ~8:40, where you write the boundary conditions after seperating the variables.
Why is it f(-/+w) = -g(y) and not 0

[@exploringmaths9336]

Ah, good question. If you look at 7:55, the values of the particular solution on the boundaries (left hand side) aren't all 0. So we need the general solution (right hand side) to balance those out, so that it works when we add the 2 solutions together

[@ammonium3757]

@@exploringmaths9336 Yes, thank you that makes a lot of sens! And thank you again for this great video