Animating Calculus: Mathematica® Notebooks for the Laboratory (Texts and Studies in Religion; 68) - Softcover

Packel, Ed; Wagon, Stan

Softcover

ISBN 10: 0387947485 ISBN 13: 9780387947488

Publisher: Springer, 1996

Synopsis

Calculus and change. The two words go together. Calculus is about change, and approaches to teaching calculus are changing dramatically. Thus it is both timely and appropriate to apply techniques of animation to the varied and important graphical aspects of calculus. AB a computer algebra system, Mathematica is an excellent tool for numerical and symbolic computation. It also has the power to generate striking and colorful graphical images and to animate them dynamically. The combination of these capabilities makes Mathematica a natural resource for exploring the changing world of calculus and approaches to mastering it. In addition, Mathematica notebooks are easy to edit, allowing flexible input for commands to Mathematica and stylish text for explanation to the reader. Much has been written about the use and importance of technology in the teaching and learning of calculus. We will not repeat the arguments or feign objectivity. We are enthusiastic believers in the value of a significant laboratory experience as part oflearning calculus, and we think Mathematica notebooks are a most appropriate and exciting way to provide that experience. The notebooks that follow represent our choice of laboratory topics for a course in one-variable calculus. They offer a balance between what we think belongs in a first-year calculus course and what lends itself well to exploration in a Mathematica laboratory setting.

About this title

About the Author

Ed Packel is the Volwiler Professor of Mathematics and Computer Science at Lake Forest College, Lake Forest, Illinois.

From the Back Cover

Animating Calculus is designed to help you explore calculus and visualize concepts through the use of computation and animation. This collection of 22 labs, together with the computer algebra system Mathematica, can be used for self-study, demonstration, or as a laboratory supplement to an existing calculus sequence. Standard calculus topics as well as new and unusual extensions and applications are presented, including derivatives and rate of change, calculus and landing airplanes, population dynamics and iteration, the fundamental theorem, The Buffon needle problem, numerical and symbolic integration, rolling wheels (round and square), subtleties of the harmonic series, and more. Animating Calculus includes exercises and demonstrations that focus on important and fundamental ideas and applications rather than the everyday mechanics of a computer algebra system. Sophisticated animations are used to clarify geometric concepts in calculus. In addition, discussions of numerical and graphical pitfalls help the student to understand the importance of verifying results. Originally published by W. H. Freeman, this new TELOS edition of Animating Calculus includes the full set of labs for DOS/Windows as well as Macintosh platforms.

Edition details

• Publisher: Springer
• Publication date: 1996
• Language: English
• ISBN 10: 0387947485
• ISBN 13: 9780387947488
• Binding: Paperback
• Number of pages: 307