A Taylor Series Expansion Tutorial for Upper-division Physics Contexts

Undergraduate physics students are often taught mathematical methods across multiple courses, but may still not be prepared to transfer those methods to physics contexts. Here, we sought to develop a tutorial for students to learn how physicists approach the strategy of “Taylor Series Expansions” to effectively model complicated physics situationss. After piloting our materials in one-on-one student interview settings and getting feedback from Physics and Math experts, we recorded small groups of students working on the tutorial during a standard period of their E&M class and Junior Mechanics class. We provided examples of a potential graph, classical pendulum, and charged disk with a gradual reduction of scaffolding between sections. We intend that this tutorial can be used in a Math Methods course, or an upper-division E&M or Quantum Mechanics course. We aim to include a focused amount of physics content without requiring extensive background knowledge, in contrast to some existing tutorial/explanation sections of textbooks. We hope that this tutorial and research will help us better support students who will use Taylor Series Expansions in physics courses, as we continue to find sources of student confusion to revise our tutorial and the respective instructor guide with this feedback.

Material based on work supported by NSF PHY 1912152 and 2336911. Any opinions, findings, conclusions, or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of NSF.