This is a collection of over three dozen animations of standard calculus and differential equations topics that are enhanced by visualization; the main sections include limits, derivatives, Riemann sums, multivariable Calculus, numerical methods and Statistics. All files are uncompressed avi files; for most animations, MathCAD code is available.
To enable students to gain a visual as well as conceptual understanding of selected mathematical concepts
Target Student Population:
Students in freshman and sophomore calculus and differential equations classes.
Prerequisite Knowledge or Skills:
Pre-calculus. Additional calculus for the advanced animations; elementary statistics for the Statistics animations.
Type of Material:
Classroom demo and introduction of concepts
Video player such as Quicktime or RealPlayer
Evaluation and Observation
This collection of animations includes a number of common math topics that benefit from visualization. A picture is worth 1000 words is quite apropos for this site. Animations on limits, derivatives and Riemann sums are valuable for beginning Calculus students; the multivariable animations are excellent for advanced Calculus students.
Potential Effectiveness as a Teaching Tool
As indicated by the author in his introduction, these animations provide a most effective means by which to introduce and illustrate dynamic mathematical concepts. The animation topics are well-chosen and cover a variety of subjects.
The animations, while able to stand alone, are best used with instructor preview and oversight. Students who were unfamiliar with the concepts involved would most likely have difficulty in understanding the import of the animations.
Ease of Use for Both Students and Faculty
The animations run smoothly in RealPlayer and Windows Media Player. The ability to stop the movie and play again is helpful for examining specific values of the variables involved.
The author warns that some of the .avi files are quite large (over 5MB) and that it is best to first download a file and then view it since plug-ins slow down the process and sometimes also display the animation at the wrong size, which leads to de-rezzing or illegible text. However, this reviewer experienced no difficulty when running the applets directly from the host server. A high-speed Internet connection would be helpful for the larger files.