Preface

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No doubt, the differential equations topic has become the most successful mathematical tool in modeling of real world phenomenon. Therefore, the corresponding course has been included in the curriculum of universities around the world for more that two hundred years, typically, as a two-semester course.

This tutorial, accompanied by the textbook Applied Differential Equations. The Primary Course by Vladimir Dobrushkin, CRC Press, 2022; https://www.routledge.com/Applied-Differential-Equations-The-Primary-Course/Dobrushkin/p/book/9781138606586, corresponds to the Applied Math courses, which at Brown are APMA 0330, 0340 0350, or 0360. The objective of the tutorial is three fold:

• To acquire the reader with the partial differential equations topic. Since the focus is made on various applications, the tutorial does not usually contain detailed proofs and instead refers the user to other sources.
• The tutorial could be used as a reference to the differential equations and their applications. Therefore, it contains more information about partial differential equations than any published textbook.
• The tutorial is accompanied by different software packages that are proven to be robust and useful in applications. Therefore the user can learn a particular software along with studying the course in differential equations.

This tutorial contains software programs that are free: you can redistribute codes and/or modify scripts under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This tutorial is distributed in the hope that its material and codes will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. For full version of GNU General Public License, see https://www.gnu.org/licenses/gpl-3.0.en.html.

This tutorial 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 while using Mathematica.

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. Any comments and/or contributions for this tutorial are welcome; you can send your remarks to <Vladimir_Dobrushkin@brown.edu>