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Physical Sciences and Mathematics Commons™
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Full-Text Articles in Physical Sciences and Mathematics
Carrying Biomath Education In A Leaky Bucket, James A. Powell, Brynja R. Kohler, James W. Haefner, Janice Bodily
Carrying Biomath Education In A Leaky Bucket, James A. Powell, Brynja R. Kohler, James W. Haefner, Janice Bodily
Mathematics and Statistics Faculty Publications
In this paper, we describe a project-based mathematical lab implemented in our Applied Mathematics in Biology course. The Leaky Bucket Lab allows students to parameterize and test Torricelli’s law and develop and compare their own alternative models to describe the dynamics of water draining from perforated containers. In the context of this lab students build facility in a variety of applied biomathematical tools and gain confidence in applying these tools in data-driven environments. We survey analytic approaches developed by students to illustrate the creativity this encourages as well as prepare other instructors to scaffold the student learning experience. Pedagogical results …
New Symbolic Tools For Differential Geometry, Gravitation, And Field Theory, Ian M. Anderson, Charles G. Torre
New Symbolic Tools For Differential Geometry, Gravitation, And Field Theory, Ian M. Anderson, Charles G. Torre
Mathematics and Statistics Faculty Publications
DifferentialGeometry is a Maple software package which symbolically performs fundamental operations of calculus on manifolds, differential geometry, tensor calculus, spinor calculus, Lie algebras, Lie groups, transformation groups, jet spaces, and the variational calculus. These capabilities, combined with dramatic recent improvements in symbolic approaches to solving algebraic and differential equations, have allowed for development of powerful new tools for solving research problems in gravitation and field theory. The purpose of this paper is to describe some of these new tools and present some advanced applications involving: Killing vector fields and isometry groups, Killing tensors, algebraic classification of solutions of the Einstein …