ABSTRACT
Physicists often encounter differential equations that cannot be solved analytically, even in terms of special functions. Of course, there are many algorithms that might be used for numerical solutions of differential equations. Numerical solution is possible for the same classes of problems for which physicists have discussed analytic solutions, namely ordinary and partial differential equations and systems of equations. This chapter discusses the syntax in Mathematica and then moves on to a few examples, followed by exercises. Physicists already have the machinery for solutions, numerically or otherwise, for solving partial differential equations. Many of physicists will recognize where they are going with this, namely forming Fourier series or Fourier transforms. Perhaps the best way to get across quantitative information is using a contour plot. There are a few other three-dimensional plotting commands, and plenty of options for all of them, so physicists are invited to explore these by following up with the documentation.
