This project incorporates PowerMac computers as instruments of active teaching and learning into Calculus I, II, and III; Multivariable Calculus; and Numerical Analysis I and II, using the software Mathematica. These courses take advantage of the graphics and programming capabilities of Mathematica, allowing students to gain insight into the core of the subject matter. Mathematica supports the development of "notebooks;" a writer can present paragraphs of text, embedded equations, tables, and graphs. The student can read the text, manipulate the equations, generate new graphs, and experiment with parameter values. Students can use the material in more active and creative ways. In Calculus courses, fundamental concepts, such as function and limit, continuity and differentiability, and instantaneous rates of change, are greatly illuminated by graphical and numerical treatments. When Mathematica is used as a tool, students of Multivariable Calculus can easily visualize three-dimensional problems using 3D plot and rotation. In the Numerical Analysis course, it is now possible to take on more relevant problems that otherwise would not be covered because of their extreme complexity. Mathematica can easily deal with complex, repetitive computations that are inherent to the course, allowing students to concentrate on more difficult concepts; thus, students, engineers, and mathematicians are better equipped for research.
