### Author Topic: Question while calculating the solution to Laplace using separation of vars  (Read 361 times)

#### Zhonghan CHEN

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• Karma: 0 ##### Question while calculating the solution to Laplace using separation of vars
« 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
« Last Edit: March 19, 2023, 01:01:34 AM by Zhonghan CHEN »

#### Victor Ivrii ##### Re: Question while calculating the solution to Laplace using separation of vars
« Reply #1 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