Instructional Materials
Here are some materials I've developed to fill gaps or address deficiencies in standard texts. Please email me if you end up using them in a course (or if you find a mistake). I will add more as I make them.- Taylor series -- three kinds. These notes explain why you shouldn't expect Taylor series to converge.
- Lagrangian mechanics, derived. A video that derives Lagrangian mechanics from Newton's laws.
Videos
For the transition to online learning in Spring 2020, I made a series of videos for undergraduate math methods. The complete playlist may be accessed here.- Fourier Series (blackboard style)
- Partial Differential Equations (blackboard style)
- Vector Calculus (with fancy graphics!)
Courses I teach
Here are the courses I have taught, along with some thoughts. I am always looking for more ideas (and happy to share my own), so feel free to email me to start a conversation.- Graduate classical mechanics (Fall 2016, 2019, 2020). This course is tricky, as I don't think any of the standard books (Landau, Goldstein, Arnold) is really suitable on its own. I use my own notes that draw from all three and also include other topics that I consider especially interesting or important. Non-holonomic constraints are a really fun example: Did you know that parallel parking is computing a commutator to show that the car is non-holonomic? (These notes are not quite ready to be posted publicly, but I am happy to send them to you if you email me.)
- Graduate general relativity (Spring 2016, 2017, 2019, 2021). I closely follow Carroll's book. This is a rare text that can please students and experts alike. I think he did a great job of being pedagogical without sacrificing clarity or sophistication.
- Undergraduate electromagnetism I (Spring 2018, Spring 2022). I like Griffith's book and follow it closely. But I do disagree somewhat with the attitude: Griffiths regards point particles as the fundamental building block of the classical theory, with occasional footnotes that this doesn't really make sense because of self-energy and self-force effects. I would prefer a treatment more in the spirit of modern effective field theory, where you emphasize that different physical models are useful at different scales, with divergences a natural consequence. I give this viewpoint in lecture, but it would be nice to find a book with this attitude. (If you know of one, please let me know.) However, Griffiths has an amazing gift for exposition, and he keeps the students engaged.
- Undergraduate Math Methods (Fall 2018, Spring 2020). At Arizona we teach linear algebra as part of a math methods course. I have mixed feelings about this, but it does give us a chance to skip over some boring detail and get to the stuff that is interesting for physics (read: eigenvalues). I divvy up the course as follows: infinite series (2 weeks), complex numbers (1 week), linear algebra (5 weeks), Fourier Series and PDEs (2 weeks), vector analysis (2 weeks), probability (2 weeks). I used the book by Boas because of good amazon reviews from students, and because I disliked it less than I disliked other books like Riley and Hobson. I think many of the students are just going from the lecture, however.
Past Students
Arun Ravinshankar (Ph.D., Arizona, 2021). Currently a data scientist at Rover.Theo Drivas (B.S., Chicago, 2011). Currently a professor of mathematics at Stony Brook.
Daniel Brennan (B.S., Maryland, 2014). Currently a postdoc at the University of Chicago