This manual is a Calculus supplement which examines the basic topics and techniques of
Calculus through the computer algebra system Mathematica®.
Its purpose is not to teach Mathematica®, but to teach how to use it as a tool to learn
and visualize the most important ideas in Calculus. Therefore the information on
Mathematica® is concise and directed toward helping students understand and solve
problems. The Mathematica commands are introduced without distracting the attention form
the mathematical concepts.
The topics are presented following the sequence of any standard course in Calculus. It
provides many examples to enhance the students' understanding and geometric perception of
the topics. It also includes a section on Linear Algebra. Each section contains a set of
problems to stimulate discovery and to encourage students to experiment on their own.
Bending the Tangent Line into the Taylor Polynomial
This paper is an introduction to the Taylor polynomial from a very geometric and
intuitive point of view. The Taylor polynomial appears as the formalization of the process
of "manually" bending the tangent line into the shape of the curve. We
incorporate the use of Mathematica® to help us visualize the procedure and predict the
successive steps.
These notes are designed for high school teachers who are interested in expanding the
meaning of geometry to learn some of the main ideas in Differential Geometry. Using
Mathematica®, the concepts are introduced in a geometric and intuitive way avoiding the
usual mathematical background needed to study these topics.
