Chapter 1 - A Primer of Mathematica

Abstract

Commands in Mathematica are given in natural language form such as “Solve” or “Simplify.” The format of a command is the word starting with a capital letter and enclosing the argument in square brackets. The calculator level of Mathematica comes in the form of Palettes, which are very handy tools. Palettes are found under the File menu and there are several of them. If one wants to use a trigonometric function, for example, one can either type in its name or go to the Basic Calculations menu and then to the Trigonometric and Exponential Functions. Mathematica has a huge number of built-in functions from the mundane to the exotic, but one can work with them more or less in the same way. Table, plot, map, and plot 3D are the four most useful commands because they do so much with so little. In contrast to a procedural language, in which one would have to write a looping structure to evaluate a function at several different values or for a range of values, Table hides all this from the user and provides just the vector of output values. Plot does the same thing, except that one sees the graph of the function's values rather than the values themselves. The output of a function is a List, that is, a vector. One can combine a set of values, such as the set of dependent values, with a set of independent variable values into a matrix.