There are four major areas in the study of ordinary differential equations that are of interest in pure and applied science. Of these four areas, the study of exact solutions ...

A partial differential equation (PDE) is a relationship between an unknown function u(x_1,x_2,…,x_n) and its derivatives with respect to the variables x_1,x_2,…,x_n. Here is ...

If the Mathematica client cannot get a license from MathLM, you are given the option of entering a single-machine password. When using a single-machine password, Mathematica ...

A standard electronic calculator does all your calculations to a particular accuracy, say ten decimal digits. With Mathematica, however, you can often get exact results. ...

Picking out elements of lists. We will use this list for the examples. Here is the last element of t.

Here is the integral ∫x^n dx in Mathematica. Here is a slightly more complicated example. Mathematica knows how to do almost any integral that can be done in terms of ...

There are a number of functions built into Mathematica which, like Plot, have various options you can set. Mathematica provides some general mechanisms for handling such ...

Mathieu and related functions. The Mathieu functions MathieuC[a,q,z] and MathieuS[a,q,z] are solutions to the equation y^′′+[a-2qcos(2z)]y0. This equation appears in many ...

When installing MathLM and Mathematica on a Linux system, you may need to mount the CD or DVD. Mathematica is available for Linux on DVD. MathLM is available for Linux ...

Particularly when you use transformation rules, you often need to name pieces of patterns. An object like x_ stands for any expression, but gives the expression the name x. ...