ME565 Lecture 10: Analytic Solution to Laplace's Equation in 2D (on rectangle)

ME565 Lecture 10
Engineering Mathematics at the University of Washington
Analytic Solution to Laplace's Equation in 2D (on rectangle)
Notes: faculty.washington.edu/sbrunto...
Course Website: faculty.washington.edu/sbrunto...
faculty.washington.edu/sbrunton/

[@shahryarhabibi7187]

Thanks a lot, Prof.

[@sevenindigo5945]

at 41:30, why the 2 is missing from An??

[@cediemacalisang7713]

Would it still be valid if I assume u(x,y,z) = F(x)G(y)H(z)? How do we deal with this such that they will relate to lambda?

[@wowowowdog]

This might not answer your question but I would say in general the separation between two sets of variables, such as time and space, is sufficient for most physical problem, even the space is in 3D. So u(t,x)=F(t)G(x) where x could be vector of space variables.

[@svelob1944]

@@wowowowdog yeah but you would still end up with a PDE in x,y and z for the spacial function, how would you solve that?

[@michaellewis7861]

How does the boundary condition on F(x) (being f(y) implying that there exists x s.t. F(x)=f(y)) make sense if you have already assumed that it has no y as an argument.

[@nesslange1833]

I guess they fulfil Dirichlet conditions, claiming that if the boundary of a (differentiated) function domain is fully described then a (unique) solution can be found. Since the square surrounds the domain of that function the solution is determined by that infinit sum with one boundary having constant value *f(y)*

[@kylejohnson8447]

Because it is equaling some constant. The only way for a function of 2 separate variables to be equal is if they are equaling some constant

[@cips35]

Im going to deal with this 💀💀💀💀