In this video, I introduce the concept of separation of variables and use it to solve an initial-boundary value problem consisting of the 1-D heat equation and a couple of homogenous Dirichlet boundary conditions.

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Prereqs:…

An introduction to partial differential equations.

PDE playlist: http://www.youtube.com/view_play_list?p=F6061160B55B0203

Topics:
-- idea of separation of variables
-- separation of variables for the wave equation (3:58)
-- summary (16:46)

How to solve Laplace's PDE via the method of separation of variables. An example is discussed and solved.

The electronic Schrödinger equation can only be solved analytically for the hydrogen atom, and the numerically exact full configuration-interaction method is exponentially expensive in the number of electrons. Quantum Monte Carlo methods are a possible way…