This document is a guide that can be used by undergraduate physics students alongside Richard J. Jacob and Professor Emeritus’s Tutorials in the Mathematical Methods of Physics to aid in their understanding of the key mathematical concepts from PHY201 and PHY302. This guide can stand on its own and be used in other upper division physics courses as a handbook for common special functions. Additionally, we have created several Mathematica notebooks that showcase and visualize some of the topics discussed (available from the GitHub link in the introduction of the guide).

Introductory physics is one of the most difficult course sequences one can take as an undergraduate, due in no small part to the prerequisite knowledge of mathematics. Over the past six years, David Meltzer and his research group have developed a diagnostic meant to test students’ abilities in core mathematical concepts believed to be crucial foundations for learning physics. Concepts tested include the ability to solve systems of equations, work with trigonometric functions, manipulate fractions, and interpret information from graphs among others. With over 7000 students having taken the diagnostic, some patterns have begun to emerge, confirming work from other studies that suggest there is in fact a link between prerequisite math knowledge and success in an introductory physics course. However, most students take the diagnostic either in a classroom setting or online, so student responses are largely limited to being categorized as simply correct or incorrect. Even when students’ work is present it is impossible to assess their mindset when working through a problem without making inferences and logical leaps. In an attempt to better understand the nature of students’ misconceptions in mathematics I have conducted seven semi-formal interviews with introductory physics students just after they have completed the diagnostic where they walked me through their solutions and thought processes.