Mathematica Help

Mathematics is a participatory "sport" not a spectator "sport." The only way to learn mathematics and to learn how to use mathematics is by doing and using mathematics. These modules are interactive. You are expected to be an active participant not a passive reader. Often your participation will involve working with one of the computer algebra systems -- Maple, Mathematics, MathCad, or the TI-92. You will frequently see the following "buttons" in a navigation frame at the top of your browser window.

Clicking on one of the icons will load one of the the following CAS programs.

Mathematica
Maple
MathCad
TI-92

Clicking on one of the question marks will take you to a file like this one with help for the corresponding CAS.

This help files provides help for the following topics.

CONTENTS

General help -- setting up your screen
Defining sequences
ListPlot -- plotting a list or sequence
Table -- defining a list or table
TableForm -- printing a list or table

General help -- setting up your screen

As you work you will want to switch back-and-forth between your CAS system and your other work. We recommend that the first time you use your CAS that you set up your screen with two windows slightly offset as shown in the picture below. Then you can switch back-and-forth between the two by clicking on the window you want to use.

Mathematica is very fussy about upper and lower case and about syntax and punctuation. You need to be very careful typing exactly the right form. For example, to use the function Log you must type -- upper case "L"; lower case "o"; and lower case "g" and to compute Log[12.34] you must use square brackets exactly as shown not the parentheses that you might expect. In addition, you must be very careful about commas, and semicolons and you must use = and == and := exactly as shown.

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Defining sequences

The following examples illustrate two ways in which a sequence can be defined in Mathematica

By an algebraic expression
```
Clear[Pop]
Pop[n_] := n^2
```

By an initial condition and a change equation


Clear[Pop]
Pop[1] := 100 
Fcn[p_] := 2.8 (1 - .001 p) p 
Pop[n_] := Fcn[Pop[n - 1]

Notice that it is good practice to Clear an item like Pop before defining it. Mathematica remembers everything that you do in a given session and it may use old knowledge at inappropriate times. Notice also that the two lines


Fcn[p_] := 2.8 (1 - .001 p) p
Pop[n_] := Fcn[Pop[n - 1]

are better than the single line


Pop[n_] := 2.8 (1 - .001 Pop[n - 1]) Pop[n - 1]

Either way will work correctly but the first way is much faster.

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Table -- defining a list or table

This procedure generates a table or a list. The example below generates a table with 10 entries. The i-th entry is 2^i.


Table[2^i, {i, 1, 10}]

The example below generates a table with 20 entries given by

pop[1], pop[2], ... pop[20] where the sequence pop was defined earlier.


Table[2^i, {i, 1, 10}]

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ListPlot -- plotting a list or table

This procedure plots the entries in a table or list. It is frequently used together with Table to plot a sequence as shown below


ListPlot[Table[{i, money[i]}, {i, 1, 20}],
         PlotJoined -> True,
         PlotRange -> {0, 2000}]

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TableForm -- printing a list or table

This procedure prints the entries in a table or list. It is frequently used together with Table to print a sequence as shown below


TableForm[Table[{i, money[i]}, {i, 1, 20}]]

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