Mathematica Tutorial

What is Mathematica?

Mathematica is a product of Wolfram Research, Inc.

Mathematica is a software system and computer language for use in mathematical applications. The three classes of Mathematica computations are: numerical, symbolic, and graphical. Mathematica can

The Basics

Mathematica can run in either an ASCII terminal mode or as an X-window System client. To run Mathematica from an ASCII terminal, enter math. To run Mathematica as an X-window System client, enter mathematica.

Numerical Calculations

Arithmetic can be performed in Mathematica just as on a calculator. In this example, you would have typed 2 + 6 and then pressed [SHIFT-RETURN].

Variable Definition

In order to assign a specific value to a variable, simply tell Mathematica what you would like to name the variable and what value it should be assigned.

This action defines the variable x to have the value. 2. This value assignment is permanent until you remove it, or start a new Mathematica session.

Having assigned a value to x, you can now use x in further equations without having to ever type x's value.

For example:

Summations and Products

Mathematica will handle summations and products easily. The notation is intuitive. For a simple product, the notation would be Sum[f, {i, imin, imax}]. For example,

if we had this summation:

Two-Dimensional Plotting

Mathematica uses the Plot command to produce 2-D plots. You basically specify the equation to be plotted followed by a list that contains the variable and min and max values for a range. The statements usually look like this, Plot[f[x], {x, xmin, xmax}]. For example, here is a simple parabola:

Three-Dimensional Plotting

It is quite easy (and fun) to plot in three dimensions. The format is similar to above. One just uses the Plot3D command:

Animations

Mathematica can also produce animation of plots via a simple Do loop. This way you can see how a plot can vary over different conditions. Below is an animation of the Cosine function

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