Interdisciplinary courses like PHYS481/MATH481 “Mathematics for Scientists and Engineers” play an important role in undergraduate curriculum: physics students get exposure to advanced mathematical ideas that they might otherwise miss in their undergraduate studies, and both mathematics and physics students get experience directly applying mathematical ideas and techniques to real-world problems. Several in-state and peer institutions offer an additional course in mathematical physics. Although the advantages of a second course are plentiful, Morehead State University currently does not. In this talk we report on the progress of creating the cross-listed course “Advanced Mathematics for Physics” and mathematical techniques currently missing from coursework that would be most beneficial to graduating physics majors. As an example, we focus specifically on Schwarz-Christoffel (SC) transformations from complex analysis. SC transformations are functions that map points in the extended upper half of the complex plane to the vertices of a polygonal region. These mappings are quite useful in the realm of physics; in a general sense these mappings can be useful in contexts such as electric fields, magnetic fields, and fluid dynamics. For this project, it is specifically helpful when working in the context of electric field distributions and electric potentials within that electric field distribution. We conclude by discussing our computational project that introduces students to these SC transformations and helps them apply SC transformations in an appropriate physics context. This computational project introduces the SC transformation and implements these transformations in both Python and Mathematica.
Knupp, Richard and Qualls, Joshua, "Schwarz Christoffel Mappings In Undergraduate Mathematical Physics" (2021). 2021 Celebration of Student Scholarship - Oral Presentations. 4.