Applied Mathematical Modules for Use in a Linear Algebra Service Course

摘要

The purpose of this study was to develop several applications which could be usedto supplement an undergraduate course in linear algebra for non-mathematics majors. These applications were drawn from the fields of biology, graph theory, and physics. The biology application examined how a system of linear equations could be used to determine the concentration of substances dissolved in a colored liquid. In the graph theory application, linear algebra was applied to analyze properties of spanning trees and to illustrate how they would be employed to solve transportation problems. The third application showed how linear algebra is used to solve systems of second order linear differential equations, which could be used to model small vibrations in molecules. Each application was designed so that and instructor of linear algebra could use it either as and independent study project or as an integrated part of the course. These three applications are arranged by degree of difficulty and sequenced as they would be introduced in a linear algebra course. On the whole, the students participating in the testing of these applications felt that exposure to examples such as these during their Mathematics 175 course would have increased their understanding and enjoyment of linear algebra. This finding supports the overall goal of this study. (kr)