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Physical Sciences and Mathematics Commons™
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Full-Text Articles in Physical Sciences and Mathematics
Leading Students To Investigate Diffusion As A Model Of Brine Shrimp Movement, Brynja R. Kohler, Rebecca J. Swank, James W. Haefner, James A. Powell
Leading Students To Investigate Diffusion As A Model Of Brine Shrimp Movement, Brynja R. Kohler, Rebecca J. Swank, James W. Haefner, James A. Powell
Mathematics and Statistics Faculty Publications
Integrating experimental biology laboratory exercises with mathematical modeling can be an effective tool to enhance mathematical relevance for biologists and to emphasize biological realism for mathematicians. This paper describes a lab project de-signed for and tested in an undergraduate biomathematics course. In the lab, students follow and track the paths of individual brine shrimp confined in shallow salt water in a Petri dish. Students investigate the question, “Is the movement well characterized as a 2-dimensional random walk?” Through open, but directed discussions, students derive the corresponding partial differential equation, gain an understanding of the solution behavior, and model brine shrimp …
Superposition Formulas For Darboux Integrable Exterior Differential Sys-Tems, Ian M. Anderson, Mark E. Fels, Peter J. Vassiliou
Superposition Formulas For Darboux Integrable Exterior Differential Sys-Tems, Ian M. Anderson, Mark E. Fels, Peter J. Vassiliou
Mathematics and Statistics Faculty Publications
In this article we solve an inverse problem in the theory of quotients for differential equations. We characterize a family of exterior differential systems that can be written as a quotient of a direct sum of two associated systems that are constructed from the original. The fact that a system can be written as a quotient can be used to find the general solution to these equations. Some examples are given to demonstrate the theory.