ODE TO APPLIED PHYSICS: THE INTELLECTUAL PATHWAY OF DIFFERENTIAL EQUATIONS IN MATHEMATICS AND PHYSICS COURSES: EXISTING CURRICULUM AND EFFECTIVE INSTRUCTIONAL STRATEGIES
Author: Brandon Clark
Major: Mathematics & Physics
Graduation Year: 2017
Thesis Advisor: John Thompson
Description of Publication: The purpose of this thesis is to develop a relationship between mathematics and physics through differential equations. Beginning with first-order ordinary differential equations, I develop a pathway describing how knowledge of differential equations expands through mathematics and physics disciplines. To accomplish this I interviewed mathematics and physics faculty, inquiring about their utilization of differential equations in their courses or research. Following the interviews I build upon my current knowledge of differential equations in order to reach the varying upper-division differential equation concepts taught in higher-level mathematics and physics courses (e.g., partial differential equations, Bessel equation, Laplace transforms) as gathered from interview responses. The idea is to present a connectedness between the simplest form of the differential equation to the more compli- cated material in order to further understanding in both mathematics and physics. The main goal is to ensure that physics students aren’t afraid of the mathematics, and that mathe- matics students aren’t without purpose when solving a differential equation. Findings from research in undergraduate mathematics education and physics education research show that students in physics and mathematics courses struggle with differential equation topics and their applications. I present a virtual map of the various concepts in differential equations. The purpose of this map is to provide a connectedness between complex forms of differ- ential equations to simpler ones in order to improve student understanding and elevate an instructor’s ability to incorporate learning of differential equations in the classroom.
Location of Publication:
URL to Thesis: https://digitalcommons.library.umaine.edu/honors/450