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APM346-2023S => APM346--Lectures & Home Assignments => Chapter 6 => Topic started by: Zhonghan CHEN on March 19, 2023, 12:46:09 AM

Title: Question while calculating the solution to Laplace using separation of vars
Post by: Zhonghan CHEN on March 19, 2023, 12:46:09 AM

Hi Prof:

I have a question for solving the Laplacian operation using the separation of variables.
Slide: Week 9 Lecture 1 Page 4.

The queston happens in solving ${\theta}'' + \lambda \theta = 0$.

Q: I do not understand how do you derive the $\lambda_{n} = n^2$.

Also, I do not understand why we can get a expression for $\lambda$ ? To my understading, $\lambda$ is just a constant in the ODE.

Thanks

Title: Re: Question while calculating the solution to Laplace using separation of vars
Post by: Victor Ivrii on March 24, 2023, 08:28:50 PM

Section 4.1ODE is not enough. You need to take into account also boundary conditions. See Section 4.1