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Calculus Explorations using Mathematica

Allen Hibbard
Organization: Central College
Department: Mathematics and Computer Science
Education level


The full complement of laboratory notebooks are available to any institution adopting the Calculus Explorations using Mathematica text. To obtain information on how to acquire these files, please contact the author at hibbarda@central.edu

Calculus Explorations Using Mathematica is a Mathematica-based laboratory supplement for any calculus course. In addition to the printed version, the complete collection of labs and appendices are available in the form of Mathematica notebooks. These contain the Mathematica code which provides the functionality for many of the labs.

  • The focus of the labs is learning Calculus. Mathematica is used as the tool to accomplish that end.
  • No prior knowledge of Mathematica is assumed. Commands are slowly introduced with many examples. Summaries are provided for each lab, as well as a cumulative summary.
  • Graphical or visual images (and animations) are used to illustrate mathematical concepts whenever helpful.
  • The labs follow the spirit and order of presentation in Calculus from Graphical, Numerical, and Symbolic Points of View by Arnold Ostebee and Paul Zorn, but the labs are independent of this text. There are no concepts or exercises that depend on this text. The collection of labs should be suitable for the first two semesters of any calculus course with most texts.
  • The exercises in the labs occur in the stream of exploring the calculus concepts. The questions are designed to be thought provoking and not simply fill-in-the-template type.
  • The labs are ready for version 2.2, 3.0, or higher, under Macintosh, Windows, and other platforms that support the notebook concept.
  • An Instructor's Guide is available that contains notes and suggestions for each lab, as well key questions to assign. A Solutions notebook is also available.
  • Sample lab notebooks can be obtained by contacting from the web page below.

  • Preface
  • An Introduction to Mathematica
  • Basic Tools for our ToolBox
  • The Old Transformed into New: Transforming Functions
  • Machine Graphics and Families of Functions
  • The Derivative: A First Look
  • The Derivative: A Second Look
  • The Limit: The Key to Calculus
  • The Derivative: A Third Look
  • The Value of a Mean Theorem
  • In the Best Possible Worlds: Optimization
  • Polynomials Tailored for a Curve
  • Newton's Method: Getting to the root of a function
  • Parametric Equations
  • An Introduction to Area
  • Approximations to Area
  • Numerical Integration
  • Putting the Integral to Work
  • Next in the Sequence of Labs
  • One more in a Series
  • The Power of Series
  • Differential Equations
  • Going in Circles: Polar plotting
  • Appendix A. Tips and Suggestions for working with Mathematica
  • Appendix B. ToolBox Summary

*Mathematics > Calculus and Analysis > Calculus
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*Calculus Explorations using Mathematica   [in Books]