# Preface

This is a
tutorial made solely for the purpose of education and it was designed
for students taking Applied Math 0340. It is primarily for students who
have some experience using *Mathematica*. If you have never used
*Mathematica* before and would like to learn more of the basics for this
computer algebra system, it is strongly recommended looking at the APMA
0330 tutorial. As a friendly reminder, don't forget to clear variables in use and/or the kernel.

Finally, the commands in this tutorial are all written in bold black font,
while *Mathematica* output is in regular fonts. This means that you can
copy and paste all commands into *Mathematica*, change the parameters and
run them. You, as the user, are free to use the scripts
to your needs for learning how to use 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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Introduction to Linear Algebra

## Glossary

# Method undetermined coefficients

Homogeneous differential equations of arbitrary order with constant coefficients can be solved in straightforward matter by converting them into system of first order ODEs.

Example. Consider ODE of order 3:

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