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Bibliographic Details

Title: Precalculus: Anticipating Calculus Using Mathematica Labs
Publisher: Cherkas Software Consultants, Inc.
Publication Date: 2002
Language: English
ISBN 10: 0971634718
ISBN 13: 9780971634718
Binding: Soft cover
Condition: Very Good

About this title

Synopsis

This laboratory manual/textbook complements the topics found in a traditional precalculus course to create a curriculum that is more effective at anticipating calculus. Used as the textbook for a laboratory course, it provides a convenient way to introduce relevant topics that are bypassed in traditional precalculus textbooks. It presumes access to the computer algebra system Mathematica�, presenting a nominal set of commands to introduce students to Mathematica�.

Mathematically-enhanced graphs are a hallmark of both calculus and precalculus textbooks, but this has not been the norm for either graphing calculators or computer algebra systems. The author has written the Graphing add-on package for Mathematica� that includes several commands to create mathematically-enhanced graphs for functions with singularities. The Graphing package is used with this textbook to help clarify for students the location and behavior of functions at points of singularity.

This text explores from a precalculus viewpoint the following topics that are traditionally reserved for treatment in calculus. Included are many examples that are impractical to treat using either paper and pencil methods alone or graphing calculators.

* Finding the turning points for polynomials of any degree
* Finding equations of tangent lines to polynomials
* Solving elementary optimization problems
* Distinguishing between plotting and graphing
* Exploring the polynomial asymptotic behavior of rational functions as |x|
* Finding the point of symmetry for any cubic

About the Author

Barry Cherkas is Professor of Mathematics and former Chair of Mathematical Sciences at Hunter College (City University of New York). He has done research into the teaching and learning of precalculus and written a number of papers on that subject while directing precalculus education at Hunter. Beginning in spring, 2000 he introduced a laboratory component to the traditional precalculus course at Hunter College where students learn to use Mathematica to solve both standard and selected nonstandard precalculus-level problems to prepare them better for calculus. The materials developed for that course, which evolved into this textbook, are part of an overall effort to improve precalculus education by enabling students to solve complex problems that have previously been considered inaccessible at the precalculus level.

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