Universities usually offer two courses on differential equations: one is just an introductory course (which requires basic knowledge of calculus), and another one presents further exposition of differential equations, including an introduction to partial differential equations. These courses form a main mathematical background for all students majoring in engineering, physics, geology, economics, biology, and other areas. In our days, information technologies play more and more significant role in modeling, therefore we observe a trend in an intensive use of available softwere packages. This tutorial is a part of introductory web sites that inform students, who are taking differential equations courses, with some applications of software packages that can be used. The tutorial accompanies the textbook Applied Differential Equations. The Primary Course by Vladimir Dobrushkin, CRC Press, 2015; http://www.crcpress.com/product/isbn/9781439851043
Therefore, the goal of this document is not to explain the material in the text; rather, it is to give you the tools to solve problems and to present the capabilities of available software packages as they are needed by someone studying the text. There are usually several different commands (or sets of commands) that will accomplish the same task. As a result, this tutorial will sometimes introduce several different ways to do the same thing. It is always good to be aware of these alternate pathways, but you are welcome to pick whatever notation you like the best. This tutorial can be used to introduce students who are taking the first course in differential equations (at Brown University, it is APMA 0330, Methods of Applied Mathematics - I) to a symbolic mathematical computation program MuPAD that is part of Matlab based on Maple. MuPAD is a great computer algebra system to use, especially if you are in applied areas where it is necessary to solve differential equations. MuPAD provides friendly tools to solve and plot solutions to differential equations. This computer algebra system has tremendous plotting capabilities.
This tutorial contains many MuPAD scripts. You, as the user, are free to use all codes for your needs, and have the right to distribute this tutorial and refer to this tutorial as long as this tutorial is accredited appropriately. Any comments and/or contributions for this tutorial are welcome; you can send your remarks to <Vladimir_Dobrushkin@brown.edu>