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 regular fonts.
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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Introduction to Linear Algebra
Glossary
Finite Difference Methods
In this section, we extend Euler methods to systems of differential equations. It is a custom to denote by t the independent variable that we associate with time. Then denoting the derivatives by dots, we illustrate the concepts by considering the iniiytal value problem
A numerical solution to the given system over the interval \( a \le t \le b \) is found by considering the differentials
Example: Consider the initial ■
- Christiansen G., American Journal of Physics, 1978, Vol. 46, pp. 748
- Cromer A., Stable solutions using the Euler approximation, American Journal of Physics, 1981, Vol. 49, pp. 455 https://doi.org/10.1119/1.12478
- Stanley, R.W., Numerical methods in mechanics, American Journal of Physics, 1984, Vol. 52, pp. 499--507.
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