Chapter 25_ The Laplace Operator

This Chapter is a detour from the discussion of integer sequences.  Instead, it describes a solution to the problem of  the electrical potential in a membrane of mixed boundary conditions.  We derive the spectrum of the Laplace operator in an orthonormal basis using a decomposition of the 2 dimensional operator into a set of ordinary 1st order differential equations.

Laplace_1

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s