# Preface

This tutorial was made solely for the purpose of education and it was designed for students taking Applied Math 0330. It is primarily for students who have very little experience or have never used *Mathematica* and programming before and would like to learn more of the basics for this computer algebra system.
As a friendly reminder, don't forget to clear variables in use and/or the kernel. The *Mathematica* commands in this tutorial are all written in **bold black font**,
while *Mathematica* output is in normal font.

Finally, you can copy and paste all commands into your *Mathematica* notebook, change the parameters, and run them because the tutorial is under the terms of the GNU General Public License
(GPL). You, as the user, are free to use the scripts for your needs to learn the *Mathematica* program, and have
the right to distribute this tutorial and refer to this tutorial as long as
this tutorial is accredited appropriately. The tutorial accompanies the
textbook *Applied Differential Equations.
The Primary Course* by Vladimir Dobrushkin, CRC Press, 2015; http://www.crcpress.com/product/isbn/9781439851043

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## Glossary

# Getting Started

As mentioned above, *Mathematica* has many capabilities, such as the
fact that one can write programs made up of *Mathematica* commands.
The simplest way to use *Mathematica*, though, is as an interactive
computing environment (essentially, a very fancy graphing calculator).
You enter a command and the
*Mathematica* kernel (the part of the software that actually
does the computation) executes it and returns the result. Here is an
example

The input cell (labeled by In[1]:=) contains the expression 2+3, which
*Mathematica* evaluates, returning the result (5) in
the output cell (indicated by Out[1]=). I only type "2+3";
*Mathematica* automatically supplied the label "In[1]:=". *Mathematica* has a very useful shortcut for reusing the existing expressions.

- % the last result generated
- %% the next-to-last result generated
- %n the result on output line
**Out[n]**

Looking to the far right of this document, you will see the brackets that indicate the grouping of the material into the cells. (You will not see the brackets when the notebook is printed.) Moreover, the cells are nested. For example, the input and output cells are grouped together in an input/output cell, which is grouped together will the text cells and more input/output cells into this section of the document. Several sections are grouped together into this introductory chapter. Finally, all of the chapters are grouped in a single cell, the notebook.

Semicolons in *Mathematica* are used after an expression to suppress an output.

By default, when you type something in a *Mathematica* notebook, it is regarded as input.
First of all, *Mathematica* can do arithmetic with integers and rational numbers exactly, regardless of the
number of digits involved:

*Mathematica*automatically put in the times symbol (*) between two numbers separated by space. So two inputs as

In[2]:= 2*3

*Mathematica*knows the standard elementary functions, such as the trigonometric functions, logarithms and exponentials, the square root function, and so forth. It also knows the common mathematical constant π (=3.141926...), which can be entered either as

**Pi**or, as

**\[Pi]**. The easiest way to insert a Greek letter is to do it via the special characters palette. To find this palette, navigate to the

*Mathematica*toolbar and find Palettes. Under Palettes, select Special Characters. The special characters assistant will then pop-up aside your notebook file. If you don’t see it immediately, it is likely hiding behind one your many windows you have up. Now all you need to do is select a Greek letter from the special characters bar and it will appear in your notebook file where your cursor is blinking. It is important to note that you should not use pi as a variable because it is a protected symbol by

*Mathematica*and will always be equal to \( \pi \approx 3.1415926 \ldots . \) For those who do not wish to use the toolbar, you can also type Greek letters right into your notebook file through three methods, all of which can be seen in the table, accessible from Wolfram web site.

Some famous constants are built-in *Mathematica*. We list some of them.

`SetPrecision`

:

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Return to the Part 1 (Plotting)

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