Math 234 - Methods for Initial and Boundary-Value Problems

The principal objective of Math 234 is to solve boundary value problems
involving partial differential equations.  A good background in calculus and
differential equations is essential. The heat, wave, and potential equations
are developed separately by deriving the mathematical model from physical
intuition.  The solution method of separation of variables receives the most
attention because it is widely used in applications and because it provides a
uniform method for solving the most important types of partial differential
equations.  Other techniques developed include D'Alembert's solution of the
wave equation, series solutions, numerical methods, and Laplace transforms.

Boundary value problems in partial differential equations arise in the
context of classical mechanics in higher dimensions, quantum mechanics, the
physics of elasticity, and fluid mechanics. Understanding a complex natural
process comes from combining or building on simpler and more basic models.  A
thorough knowledge of physical models, the differential equations that
describe them, and the solutions to these equations, is the first step toward
describing the complicated behavior of the real world.