Introduction

These worksheets are a tool to help you learn and discover how to use Maple. Each worksheet contains explanations of Maple commands, examples of the use of the commands, and exercises that you are asked to do right in the worksheet. The best way to use these worksheets is to download one of them to your computer, use Maple to open the worksheet, and then "work your way through the worksheet". By this I mean, read the explanations, execute the Maple commands, look carefully at the output of each command and give that output some thought, do the exercises that are in the worksheets, and finally, and most importantly, play around with the content of the worksheet, modify some of the commands and re-execute them, use the help system to look up more information about the commands, enter your own commands into the worksheet, etc. In short, use all the interactive features of the Maple interface to explore Maple. This ability to play around with the content of each worksheet is what makes Maple, and other computer programs like it, a new way to learn mathematics. Maple worksheets are a kind of interactive textbook, something that we will all be seeing much more of in the near future.

Besides helping you to learn how to use Maple, these worksheets have three other goals. The first is to get you to think hard about some common mathematical concepts that you may not understand as well as you think you do. A few examples are the concepts of variables, equations, functions, and the meaning of an equal sign (=). As we will see, each of these ideas is more subtle than you might think, and Maple has to treat each of them very carefully. As you learn how Maple handles each of these basic ideas, hopefully you will also gain a firmer grasp of how these ideas are used in mathematics.

Another goal of these worksheets is to introduce you to some basic ideas from the subjects of computer programming and computer science. Maple is a programming language; to really use Maple to solve sophisticated math problems you will probably need to do some programming in Maple. Also, mathematics and computer science are surprisingly close subjects, and learning some basic concepts from computer science should once again reinforce in your mind some of the basic, though subtle, ideas of mathematics. And finally, in the real world these days, all math is done with computers, mostly by programming them. So as math majors you need to know something about computer programming.

The last goal of these worksheets is to give you a very rough idea of how Maple works internally. How does Maple do all of these algebraic tricks that it is capable of? How does Maple know what the derivative of a function is? Learning a bit about the answers to these questions is both interesting and a nice way to make use of many of the ideas that we will go over in these worksheets.

Finally, don't be afraid to begin using Maple right away in any of your other math or science courses. After you do the first worksheet or two from this course, which shouldn't take more than a week, you will know enough about Maple to be able to use it to help you do calculations in many other courses. Maple also works well for producing lab reports in science courses since Maple can do calculations, plot data, graph functions, and typeset equations, all of which are useful for preparing lab reports (and many other kinds of homework assignments). If you want to use Maple for another course and you feel that you need some extra help or advice on using it, don't hesitate to ask me.