Advanced Engineering Math
Math 4582
Introduction
Math 4582 focuses primarily on the use of Fourier series in solving
boundary value problems in partial differential equations. A boundary
value problem is a differential equation, accompanied with a
specification of the values of the solution along the boundary over
which the solution is defined.
Two recurring themes in the course are:
- determining a Fourier series representation of a function, and
- using separation of variables to find the solution to a partial
differential equation by reducing it to an ordinary differential
equation.
These methods, combined with an occasional change of variables, will
help in solving boundary value problems arising from the heat equation,
the wave equation, and the potential equation (also known as Laplace's
equation).
One of the frequent interests in this course arises from the application
of Fourier series in signal processing.