Preface

This Study Guide for multivariate calculus extends to multivariate calculus, the paradigm first articulated in the Calculus Study Guide. That paradigm, based on the Maple document, with live 2-D math, a syntax-free approach, and illustrations of all the tools built into Maple for making the calculus interactive and alive, again infuses this new work. That Maple can implement the calculations and manipulations pertinent to a study of multivariate calculus is taken for granted. What is much more important is the way Maple is used to enlighten and enhance the material.

Again in this ebook, the principle of "resequencing concepts and skills" is apparent. Maple has all the tools it takes to "get an answer." But here, it is used to present and emphasize conceptual development, and to illustrate the steps that go into building the relevant concepts. This shift in focus makes the Study Guide valuable both as a pedagogic tool and as a roadmap to Maple's tools for the arena of multivariate calculus.

As with the Calculus Study Guide, this new ebook is focused on being a "study guide," so it does not attempt to re-present all the material that the student will find in a typical calculus text. Access to such a text is assumed, so each section summarizes the essential information the user would need to recall while exploring the examples. The unfolding of the details of the calculus is left primarily to the examples.

Examples generally have a "mathematical solution" and two "Maple solutions," the first being a solution that reads like it would in a printed textbook. The Maple solutions are (1), interactive and (2), coded. By separating the mathematical details from their implementation in Maple, a greater clarity is achieved. Trying to mix Maple calculations with mathematical exposition has proven to be less than ideal. Instead, the conceptual content of an example can be articulated in a mathematical framework, leaving the Maple implementation free of extraneous details that might otherwise be a distraction.

Thus, the interactive Maple solutions are free to make use of all the various devices available in Maple for illuminating and simplifying computation. There are embedded animations, links to interactive tutors and task templates, ample use of palettes and the Context Panel system. Indeed, the goal has been to make the use of Maple as nearly "syntax-free" as it could possibly be, and the main tool for this is the Context Panel. A right-click (or its equivalent) with a mouse brings up a menu with options tailored to the item upon which it was launched. Selecting options from this menu results in the relevant calculation, free of the underlying syntax of the command(s) that support the action.

The coded Maple solutions illustrate the syntax for the relevant commands. Solutions crafted this way often seem "shorter" because commands can be wrapped around each other, thereby compressing multiple operations into one step. The price one pays for this apparent brevity is the need for a good memory for the syntactical details of the commands.

For the most part, the examples in each section are listed sequentially in one place, so the reader can scan the list and determine which are the most relevant for any particular purpose. A hyperlink then leads to a separate document in which the example is fully implemented. Access to each chapter, and the sections in each chapter, is via the hyperlinked Table of Contents. Key concepts referenced in the sections or the examples are connected to their sources by hyperlinks, so it is not necessary to thumb through an index to find where a particular idea was introduced.

It is hoped that the Appendix proves useful for the new user of Maple. It contains discussions and examples of how to get Maple to do the things the reader most likely wants Maple to do. While recent Maple development has served the paradigm of "ease-of-use" and "syntax-free" computing, there is an accumulation of wisdom in working with a software tool that marks the experienced user from the novice. This Appendix was added so that the transition from novice to expert could be made as rapidly as possible.

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