Experiments In Mathematics Using Maple

Christopher T.J. Dodson

• 08 november 1995
• 9783540592846

Samenvatting:

We believe that to understand and be comfortable with mathematical con­ cepts and methods, it is necessary to do mathematics and, traditionally, doing meant with a pencil and paper.

This book is designed for use in school computer labs or with home computers, running the computer algebra system Maple, or its student version. It supports the interactive Maple worksheets that we have developed and which are available free of charge from various sites. For example consult the anonymous ftp site (/pub/ednet/maths/maple), or the University of Toronto Instructional and Research Computing World Wide Web home page (hhtp://), over the Internet. The topics proceed through the full mathematics syllabus for the two senior years, from basic algebra, functions and sequences, to calculus and its additional explanatory text, answers to exercises, cross-referencing, bibliography and index.

We believe that to understand and be comfortable with mathematical con­ cepts and methods, it is necessary to do mathematics and, traditionally, doing meant with a pencil and paper. Now, a modest home computer can provide a platform for a computer algebra package like Maple, which can perform all of the operations encountered in secondary school mathematics and beyond, and pro­ vide graphical representations of functions, including animations. The capability of rendering accurate graphics for mathematical functions greatly enhances the learning experience, and helps intuition work in new situations, before beginning to do the algebra and calculus needed to solve a problem. For example, if you can see that a function has a clear minimum from its graph, then you are more likely to be able to identify its location precisely by analysis. This book is designed to support the interactive Maple worksheets that we have developed for the two senior secondary school years and made available via the Internet at the anonymous ftp site ftp. ut irc. utoronto . ca (/pub/ednet/maths/maple). This takes you from basic algebra, functions and sequences, to calculus and its applications. Thus, the book is a hardcopy version of the worksheets, with additional explanatory text, cross-referencing, appen­ dices containing worked solutions to all exercises, and indexing.