Introduction
These Maple worksheets are intended to help students as they study the examples in the current Math 308 textbook ``Fundamentals of Differential Equations and Boundary Value Problems'', 4th Edition, by Nagle, Saff, and Snider, Pearson/Addison/Wesley Publ. 2004. The worksheets were prepared using the version Maple 9.5, and saved as .mw files (i.e., in "Maple Worksheet" format). No previous knowledge of Maple is assumed; however, new users may benefit from browsing through the New User's Tour, available by clicking the Help tab in a Maple window.
It is not the primary purpose of these worksheets to teach students Maple and how it can be used in solving differential equations. Math 308 has a computer lab component for this purpose. Rather, they are intended to provide a different viewpoint, but generally only a little different, from the explanations and solution methods covered in the textbook, with the aim of making the book examples easier to understand. Moreover, the worksheet format makes it easy for students to explore the effects of changes to the examples. And although teaching Maple is not the main purpose of the worksheets, it is likely some such learning will inevitably occur; this could be quite beneficial to Math 308 students who may be seeing Maple for the first time.
Since the primary objective of the worksheets is to help illucidate the book examples, rather than to show how to obtain problem solutions in the most expeditious manner, the full power of Maple to solve differential equations is not taken advantage of. For example, Maple has a powerful command, dsolve, for solving differential equations, but since its use sheds little light on what the examples are attempting to illustrate, dsolve is infrequently used in these worksheets. On the other hand, when the book skips a step in a solution, stating that the step may be performed by a method explained previously, we may use Maple to show a different solution for that step, if it is felt advantageous to do so.
Some students may not see much value in the approach taken here, that of showing slightly different solutions to examples that have already been worked out in the text. They may think they would be better off spending their time learning the full power of Maple applied to differential equations. Indeed, some students won't have any difficulty reading the book and understanding the examples. For such students, these worksheets may be superfluous. However, all students should be aware that a thorough understanding of the textbook examples is an extremely important part of the course. Using Maple to facilitate such understanding seems an appropriate and efficient way to use the computer technology which is already a part of the course. Moreover, while technology, including calculators and software such as Maple and matlab, is constantly improving, it is essential that students learn certain fundamental ideas about differential equations, distinct from what software to use and which keys to press. These Maple worksheets were written with this focus in mind.
David L. Barrow, August, 2006