Focus on Calculus
A Newsletter for the Calculus Consortium Based at Harvard University
Winter 1998, Issue No. 14

IN THIS ISSUE
Mathematics in Engineering: Notes from a Foreign Correspondent
Brad Osgood

AP Calculus Success
Christine S. Lucas

International Conference on the Teaching of Mathematics
ODE Architect: Building Order Out of Chaos
Robert L. Borrelli and Courtney S. Coleman

On-Line Gateway Exams in Calculus
John Lindsay Orr and William J. Lewis

From the Publisher
About this Newsletter

Calculus Comes Alive... Electronically

Paul R. Wellin, Wolfram Research, Inc.


Computers and mathematical software have been an important tool for educators who are transforming the way undergraduate mathematics is taught and learned. Graphing calculators and technical computing software such as Mathematica have given students and teachers the tools to go beyond pencil and paper methods to address real-world problems and to explore mathematics numerically and graphically as well as algebraically. This spring, the marriage of technology and textbooks in the calculus classroom will take another leap forward as the calculus textbook itself becomes an electronic tool.

Through a collaboration with Wolfram Research, Inc. (makers of Mathematica), John Wiley & Sons will publish CD-ROM versions—known as Calculus Live—of both CCH calculus texts: Calculus, by Hughes-Hallett, Gleason, et al., and Multivariable Calculus, by McCallum, Hughes-Hallett, Gleason, et al.

Each CD-ROM presents the entire paper textbook in electronic form for students to use in any way that suits their needs. Students can browse through sections of the textbook or search for topics using a sophisticated on-line interface called the Help Browser.

But there is more. Because the electronic textbook uses the powerful Mathematica computational engine, the book can "come alive" by allowing students to modify tables and graphics in the book. Simply by clicking a button, students can change a function or its range of values and recompute and display its graph in place of the textbook graph. Tables of computed values of functions can be modified by either changing the function itself or the range of values at which it is computed. This powerful feature lets students more fully explore the examples and tables in the text without a great deal of effort.

In addition to making the text come alive, the Mathematica engine also provides a set of computational tools that allow students to make their own plots, compute integrals, solve systems of equations, and set up various problems as given in the textbook. These tools provide a "lab" that students can use to set up a wide variety of problems and let the computer do some of the dirty work. Of course, they will still have to set things up properly and interpret the results as they would with any mathematical software.

Navigation
Like the paper textbook, the electronic version has a table of contents and an index to quickly locate topics being studied. Unlike the paper text, however, the CD-ROM brings these features to life through the Help Browser interface. If you've used Mathematica's on-line Help and documentation, you are familiar with the way the Help Browser can be used to search for and link to topics automatically.

The table of contents, for example, lists chapters, sections, and subsections exactly as they appear in the table of contents of the printed book. Each topic heading is a link, however, that takes you directly to that section or subsection of the book.

The index operates similarly, but allows you to search for a particular topic. From the Master Index, for example, a student could type in "optimization" to see a listing of topics about optimization. Clicking any of the topics in the list takes the student to that place in the textbook. Like most Web browsers, the Help Browser also has a "Back" button that will take you back to the previously displayed text.

From the Help Browser, students can also work with the tables and graphs in the book, change the magnification of the text display, and print information displayed there. A ruler and separate toolbar for the computational tools can be turned on and off as needed.

Start-Up Requirements
The Help Browser interface is designed to be easy to use and familiar to students who use Web browsers or other software with on-line help. Because Calculus Live uses Mathematica as the "engine" doing the work behind the scenes, students do not need to learn to use Mathematica itself. The built-in computational tools present students with a series of dialog boxes that guide their input and eliminate the need for up-front training with the tools.

Of course, the best way to learn about this innovative blend of text and software is to see it for yourself. You will need a computer (a Macintosh running System 7.1 or higher, PowerMacintosh running System 7.1.2 or higher, or Windows-compatible 486DX/66 or greater) with a 2x CD-ROM drive, a color monitor (SVGA, 256 colors), and 16 MB of RAM. To request a pre-publication version or demo, contact your local Wiley representative.

Full versions of both texts will be available in May for fall adoption.



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