Mathematica How-Tos

By W. Garrett Mitchener

Here are some useful how-tos for Mathematica. Each is available in PDF, notebook, and web-page formats. The help links in the web-page versions are broken, apparently due to a bug in Mathematica's save-as-html command. (*sigh*) The notebook files can be opened in Mathematica and have functioning help links.

Plotting How-To: Plotting and graphics.

Curve Fitting How-To: Curve fitting, including linear regression, non-linear least squares, and maximum likelihood. Also demonstrates numerical and symbolic maximization and minimization, and some simple use of random numbers.

Cusp Catastrophe How-To: Illustrates how to reproduce the cusp figure associated with a cusp catastrophe (the unfolding of a pitchfork bifurcation). Shows manipulation of polynomials, how to extract their coefficients, and computing discriminants. Also demonstrates parametric plotting and the Thread function.

Plotting and Dynamical Systems How-To: Plotting vector fields and solution curves for dynamical systems.

Learning to Program: Notes and exercises that should give you a good introduction to very basic functional programming, structure manipulation, iteration, random numbers, linear algebra, and discrete simulations.