| Description: This course will introduce students to partial differential equations. Partial differential equations are fundamental for modeling objects from physics to biology and economics. For example the the wave equation and the heat equation in physics; reaction diffusion equations in biology; and the Black-Scholes equation in mathematical finance. Solving partial differential equations is much more complicated than solving ordinary differential equations. Indeed there are even linear partial differential equations which are locally unsolvable. We will begin by examining some of the fundamental partial differential equations, such as the wave equation, and looking for different schemes to solve them. One method, separation of variables, allows us to reduce the problem of solving the partial differential equation to a family of connected ordinary differential equations. This context motivates the study of Fourier series, which we will spend some time studying. |
