Textbooks
- Mathematical Methods for Physicists, by Arfken, Weber, and Harris, 7th ed., 2013. A useful resource for your physics bookshelf. [online from CU domains]
- Mathematical Methods for Physics and Engineering, by Riley, Hobson, and Bence, 3rd ed., 2006. The traditional textbook for many past iterations of this course. [on reserve at Gemmill Library]
- Mathematical Methods of Physics, by Mathews and Walker, 2nd ed., 1970. Old, but classic source of next-level analytic tricks.
- Mathematical Physics: A Modern Introduction to its Foundations, by Hassani, 2nd ed., 2013. Another good source; heavier on proofs and pure-math abstractions. [online from CU domains]
- Numerical Recipes: The Art of Scientific Computing, by Press, Teukolsky, Vetterling, and Flannery, 3rd ed., 2007. It's where I learned numerical methods, and I refer back to it often. [lots of material online]
- Numerical Methods that (Usually) Work, by Acton, 2nd ed., 1990. Also old, but full of insight and irreverent entertainment. Like some professors I know?
- A First Course in Numerical Methods, by Ascher and Greif, 2011. Good coverage of many of the numerical topics that we'll discuss. [online]
- Fundamental Numerical Methods and Data Analysis, by George Collins, 1990, 2003. Solid, if sometimes crusty advice from my first research advisor. [online]
- Computational Fluid Dynamics: An Open Source Approach, by Vermeire, Pereira, and Karbasian, 2020. If you're intending to dive into the application of this course's techniques to computational models of fluid flow, this is a good place to start. [online book] and [github site]
Other Online Lecture Notes
- Doron Zeilberger ("Dr. Z") is the unique math professor who taught me Calculus I and II in 1985, and I was gratified to learn that he's still teaching, and hosting insightful lecture notes on his website on linear algebra and ODEs and integral transforms.
- I think that Mathematical Physics: A Guided Tour for Graduate Students (by Stone and Goldbart) is now a published book, but the original 919-page lecture-notes document is still right there on Goldbart's web page.
- There's a fantastic, 428-page set of lecture notes online by Prof. Brad Osgood about Fourier series & Fourier transforms, but note that it uses the electrical engineering notation conventions.