What physics do I need to know to follow this book?

Looks like not much. The book is about using Python to implement numerical methods, mainly about teaching the Python part, and that's all explained. You might be missing motivation if you don't know any physics, but even so, basic mechanics using differential equations seems to be enough to give context, at least for the earlier parts

> Exercises by chapter

Click on a chapter to download:

Chapter 2: Python programming for physicists

Chapter 3: Graphics and visualization

Chapter 4: Accuracy and speed

Chapter 5: Integrals and derivatives

Chapter 6: Solution of linear and nonlinear equations

Chapter 7: Fourier transforms

Chapter 8: Ordinary differential equations

Chapter 9: Partial differential equations

Chapter 10: Random processes and Monte Carlo methods

Chapter 11: Data science

Just to give a bit of flavor, I was a math + physics major in the 80s. The physics curriculum had some oddly named courses such as "theoretical physics" that were not really physics courses but were meant to give you the math and computational background needed for the more advanced courses or for graduate work. The math was stuff that wasn't covered extensively enough in the math major courses, such as vector calculus.

Weber's Electrodynamics.

Only after working through Rudin’s Analysis first.