This is a basic introduction to Mathematica. Since Mathematica is a very powerful programStarting Mathematica

with many features only a small fraction of its capabilities will be discussed here. See

http://bartok.ucsc.edu/peter/115/math_intro/node1.html

or go to Mathematica\help. Unlike conventional computer languages Mathematica can do

symbolic manipulation, has a huge number of built-in numerical functions, can do

numerical calculations to arbitrary precision, and has powerful plotting routines which

interface directly with the results of calculations. Mathematica can also be used for

programming in styles which are quite different from those of C and fortran, but we will

not discuss programming in Mathematica here.

There are two interfaces to Mathematica: (i) a command line interface, and (ii) the

notebook interface. The same commands are given in both, but the notebook interface has

some additional features.

If one starts Mathematica in Windows by clicking on an icon one goes straight into the

notebook interface in which a separate window appears into which Mathematica commands are

` typed. To execute a command in Windows, you need to hold down the Shift key as well as`

pressing Enter (just pressing Enter allows you to continue entering your command on the

next line but does not execute it).

Mathematica understands the usual operators + - * / and for exponentiation. It alsoA Simple Mathematica Session

`understands basic constants pi and E. It also knows about a large number of mathematical `

functions such as Exp[x], Sin[x], Cos[x], ArcSin[x], Log[x]

The following session illustrates some of these features:

x = 7

y = 19

x y

(x + 3) y

2^x

Exp[ Pi]

The basic plotting command is Plot[f, {x, xmin, xmax}]Two-Dimensional Plots

which plots the function f(x) from xmin to xmax

For example,

The command Show can also be used to combine plots. Suppose we create plots of
two functions using two separate

calls to Plot, e.g.

Integration

Defining Functions

There are many functions in Mathematica but it is often very useful to be able to define

functions oneself. This is illustrated by the following example, which defines the

function . f(x) = x + x^2

Note two things about the first line:. First of all the underscore after the x, which is

called a ``blank'', stands for ``any expression'', so when the function is called, the

argument can be named anything, not necessarily x. Secondly, the use of :=, rather than =,

which means that the assignment is delayed until the function is called. In the present

example it wouldn't have made any difference if we had used =, the normal assignment

` operator, but it would if the function depended on a parameter. `

Mathematica can work out series of complicated functions to very high order. The commandSeries Expansions.

is Series[f, {x, x0, n}] which expands f in powers of up to n-th order, e.g. to get the

first 20 terms in the expansion of about x=0:

Three-Dimensional Plots