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Preface
This Study Guide is an enhancement of, not a replacement for, a standard calculus text. It amplifies what a calculus book can capture on a print page, and shows how Maple can be used to enrich the calculus learning experience. Each of its sections summarizes the essential information a user would need to recall while exploring examples that unfold the details of the calculus of a single variable. And this Guide contains more than 460 fully workedout examples illustrating calculus, Maple, and a pedagogy that emphasizes conceptual mastery before the acquisition of manipulative skills.
The paradigm is the Maple document, with live 2D math, a syntaxfree approach, and illustrations of all the tools built into Maple for making the calculus interactive and alive. Live 2D math means mathematical notation that looks just like the notation in a standard textbook, but which is "live" in the sense that it computes what it stands for. Math notation is entered via palette templates, which when filled in, become "executable" and compute that which the notation represents. So, an integral sign will execute the implied integration, the notation $g\prime \left(a\right)$ will return the derivative of $g\left(x\right)$ evaluated at $x\=a$, the sigma notation for a sum will actually compute the sum, etc.
Although Maple is a commandbased language, it's Document mode, used in this Guide, is an overlay that hides the syntax, and replaces it with syntaxfree tools such as palettes, Tutors, Assistants, Task Templates, and a Context Panel that implements mathematical operations with a click of a mouse button. The user of this Guide thereby learns the Maple resources in the context of specific examples, and is not burdened with the need to master syntax in order to implement mathematical constructs.
Examples generally have a "mathematical solution" and a "Maple solution," the first being a solution that reads like it would in a printed textbook; the second, a solution implemented in Maple. 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 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 "syntaxfree" as it could possibly be, and the main tool for this is the Context Panel. A rightclick (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.
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 "easeofuse" and "syntaxfree" 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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