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Introduction to Linear Algebra with *Mathematica*

## Glossary

# Preface

This tutorial was 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. 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.

# Airy Functions

The following equation

*Mathematica*: AiryAi[x] and AiryBi[x].

N[%]

0.00197238 x^6 - 0.000513531 x^7 + 0.0000273941 x^9 - 5.7059 x 10^^{-6} + )(x)^10

A Sturm-Liouville equation is a second-order linear differential equation of the form

*x = a, b*are finite, then some boundary conditions are imposed at these points so that the differential operator

*L*becomes self-adjoint.

Airy functions are solutions to the Airy differential equation

y''[x] - x y[x] == 0

There are two linearly independent solutions, called by *Mathematica* as

AiryAi[x] and AiryBi[x].

N[%]

0.00197238 x^6 - 0.000513531 x^7 + 0.0000273941 x^9 - 5.7059 x

10^^{-6} + )(x)^10

**Example:**

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