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:

  1. determining a Fourier series representation of a function, and
  2. 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.