Graphical and Qualitative Investigations In Multivariable Calculus, Linear Algebra, and Differential Equations

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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.