Abstract
The purpose of this project is to change the mode of instruction in
multivariable calculus, linear algebra, and differential equations. Currently,
these courses are taught using the traditional lecture format. Although
applications are often cited, students have very little hands-on experience
with real-world applications. By using only traditional pencil and paper
methods to solve equations, students experience minimal insight into the
graphical and qualitative nature of solutions. Changes in technology over
the past 10 years have opened new and exciting doors in the field of mathematics
education. New graphing technology allows huge amounts of information to
be assimilated in a matter of seconds by examining the graph of a solution.
The graphs of solutions provide compelling visual evidence of theoretical
deductions as well as an understanding of the qualitative properties of
solutions. The hardware and software utilized in this project support the
development and implementation of classroom demonstrations and interactive
lesson plans that encourage students to take a more active role in their
education. Laboratory activities make use of the Matlab software package.
Experiments using the Calculator Based Laboratory units from Texas Instruments
enable students to observe how physical systems are modeled by differential
equations. All developed materials are shared with colleagues as they develop
by posting them on the college's home page on the World Wide Web. This
project is significant because it can dramatically change the way college-level
mathematics courses are taught. The new curriculum can generate both enthusiasm
and a better understanding of these subjects, resulting in increased retention
and enrollment.
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