Web Sites for Teaching Undergraduate Calculus and Pre-calculus

Calculus with Analytic Geometry, by Richard H. Crowell and William E. Slesnick, presented by Peter Doyle at Dartmouth University.

This is a 1963 book of 11 chapters, put into pdf format for web access. It starts with ``Functions, Limits, and Derivatives'' and ends with ``Differential Equations.'' An Appendix gives answers to problems.

College Algebra Modules, from California State University at San Bernardino.

This has 10 modules, ranging from The Coordinate Plane to Sequences. There is a separate menu for all exercises and demonstrations, which contain Java Applets.

DAU Math Refresher, by George Mason University Faculty for the Defense Acquisition University.

This has a convenient navigator into Algebra and Elementary Calculus, neatly mapped for both a big picture and details. Each module begins with learning objectives, which usually includes a key definition (e.g., function) with related concepts (e.g., linearity) and methodology (e.g., basic operations, like sum and product).

Flash Card Slide Show, by Roxanne M. Byrne at CU-Denver.

This shows flashcards (about 20 per set) on basic derivatives, derivative rules and infinite series. It is particularly useful for students to use to study at their own pace.

Graphics for the calculus classroom, by Douglas N. Arnold at Penn State.

This has a collection of graphics with associated calculus concepts. Each graphic has an associated animation, which is viewed by clicking on the graphic. The default animations are gifs from Mathematica, but there are also Java versions, which are better to view but slower to load. For example, one graphic is entitled "How the ball bounces," which is accompanied by the animation of a bouncing ball and an explanation of the underlying calculus. There is also a "student worksheet" (in postscript) about the functionals.

Limits and Tangent planes, by E. Klotz and E. Magness at Swarthmore University.

These give visualization of functions of two variables. The Limits page explains why some have a limit and some do not. If you have QuickTime movie player, you can see some animation. The Tangent Planes page uses QuickTime movie to show how the surface flattens when zooming closer.

Mathematics Animated, by Lou Talman at Metropolitan State College of Denver.

This is a collection of Quicktime movies that animates such things as the tracing of the sine curve from a point moving around a circle. Similar principles are used to show how the secant line converges to the tangent line of a function.

On-Line Finite Mathematics and Applied Calculus Resource, by Stefan Waner and Steven R. Costenoble at Hofstra University.

This has tutorials, quizzes and more. Its default pages use frames and java, but alternatives are provided, so any browser can access the materials.

Problem Sets for Honors Multivariate Calculus, by Stephen B. Maurer at Swarthmore College.

These are in dvi and pdf files for viewing and printing.

Math Problems, by Mike Shack.

There are more than 120 problems, which are rated as "Moderate, Difficult, Strenuous, and Very Hard!" A difficult problem generally requires some calculus, and very hard might require some ODEs. One distinguishing feature is that he provides both an answer and a solution, showing the difference.

The University of Minnesota Calculus Initiative, within The Geometry Center.

This contains a series of modules, with emphasis on applications.

Virtual Classroom - Calculus, by S.C. Li at Yew Chung International School.

This is a collection of java applets, showing limits, derivatives, and integrals.

Visual Calculus, by Larry Husch at University of Tennessee.

This includes pre-calculus views, such as conic sections. The "visualization" is not always a graph; it could be just a table of values, depending upon the particular exercise. It would be a useful supplement for students to see.

Visual Dictionary of Special Plane Curves, by Xah Lee at Network General Corp.

This catalogs curves, giving a bit of history and description for each one. Some appear in QuickTime movies, some in Sketchpad and some in Cabri. In most cases the Mathematica source file can be downloaded. In "Classification of Curves" the author talks first about algebraic vs. non-algebraic curves, then about "How Curves are Named" and more. This could be motivational for pre-calculus.

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