howdy howdy
Here I share my notes from my Mathematical Methods of Physics course by Professor Mark Oreglia. This class had a prerequisite of either Honors Calculus 3, Honors Physics E&M, or Intro to Math Methods of Physics. I completed the last one (with the absolute GOAT David Reid) which was basically calculus applied to E&M.
This class was really the first hard math/physics class I took. Most people took the Honors route to the course, so they were much more familiar with math topics like differential equations and some linear algebra. This was probably the class I felt the most unprepared for as well as Mechanics, which I took concurrently to this class. While learning these complicated math topics, we were also expected to apply them to physics Mechanics problems which made it a bit easier to physically understand what’s going on, but was very time consuming. I don’t think the curriculum was well thought out for students without Honors experience, but it has changed. I had to spend a lot of time outside of the class to simply catch up and get used to understanding what these math topics were, and then applying them was even harder. This class was a struggle, but worth it to learn about the math needed for upper level physics. Also, this class was taught completely virtually.
The textbook for this class was the godly Riley Hobson Bence: Math Methods for Physics and Engineering 3rd Edition (RHB). I literally had to start with the basic calculus to work up to the rest of the class’s speed. A weird thing he did in the class was not grade the psets
This class covered the following topics (that kind of overlap):
Looking back, I have no idea how I survived this class (probably by sacrificing my Mechanics grade to better understand this). Finishing the course, I didn’t feel completely comfortable with all of the topics, but I got good surface level exposure so that when I encountered a problem where I needed one of these tools, it was quick and familiar to review.
Here are my Lecture notes:
While reading over the relevant chapters of RHB, I found myself taking notes straight from the textbook to reinforce the concepts in my head. Here are the notes over those chapters
Chapter 5: Partial Differentiation
Chapter 8: Matrices and Vector Spaces
Chapter 12: Series Solutions of Differential Equations
Chapter 13: Integral Transforms
Chapter 14: First Order Ordinary Differential Equations
Chapter 15: Higher Order Ordinary Differential Equations
Chapter 16: Series Solutions of Ordinary Differential Equations
Chapter 17: Eigenfunction Methods for Differential Equations
Chapter 20: Partial Differential Equations General and Particular Solutions
Chapter 21: Partial Differential Seperation of Variables and Other Methods