PHYS 231

Methods of Theoretical Physics

Prof. Flip Tanedo (PHYS 3053, flip.tanedo@ucr.edu)

Syllabus and course materials are on GitHub.

This is a crash course on the mathematical methods necessary to succeed in the first year graduate curriculum. Our primary focus will be to be able to solve partial differential equations using Green's functions. This will pull in techniques from linear algebra and complex analysis. If time permits, we may explore other topics toward the end of the course such as statistical methods for physics and astronomy.

Meeting Times

10:00 - 10:50am on Monday, Wednesday, and Friday

Winston Chung Hall 139

Course Materials

Typed up course notes (typed up as the course progresses)

There is no required textbook for the course, though I particularly like Mathematics for Physics & Physicists by Appel (ISBN: 9780691131023).

I strongly recommended that you have access to at least one general "math methods for physicists" reference. If you have a favorite one from undergrad, you may use that (e.g. Arfken & Weber or Boas). The book by Byron and Fuller is a solid choice and is inexpensive as a Dover edition. You can also find many free digital references through the UCR library.

Mathematics of Classical and Quantum Physics, Byron and Fuller
Mathematical Methods in the Physical Sciences, Mary Boas
Mathematical Physics: a Modern Introduction to its Foundations, Sadri Hassani; digital version free from UCR Library.
Mathematics of Classical and Quantum Physics, Byron and Fuller
Mathematical Methods of Physics, Mathews and Walker

If you find references that you really like, please feel free to e-mail me to share them.

Prior versions of this course

Each year this course is slightly different based on the feedback of the previous years' students and the discretion of the instructor. The number of blatant errors should be decreasing (mostly monotonically) with time. The number of subtle errors is also decreasing adiabatically.

Fall 2018
Fall 2017 (Our complex analysis notes are from 2017)
Fall 2016

XKCD 2207

Homework

Each assignment is split between a short homework (due by the next lecture) and a long homework (due in two weeks). This is sometimes called rapid-response teaching; it helps keep both the instructor and the students aware of individual progress.

Dimensional analysis and linear algebra
- Short (due Friday 10/4): dimensional analysis refresher
  - Problem 1: presented by Zach M., 10/4
- Long (due Monday 10/14): differential operators and linear algebra
  - Problem 2: presented by Yash A., 10/8
  - Problem 3: presented by Bayu M., 10/10
Playing with Green's Functions
- Short (due Wednesday 10/16):
  - Problem 1: the i in the momentum operator (Chris) 10/16
- Long (due Monday 10/28): solving for Green's functions
  - Problem 1: 10/23: Wei-Cheng L.
  - Problem 2: 10/25: Garrett L.
  - Problem 3: 10/28: Fasi M.
  - Pizza Problem: 11/1: Kayla R.
  - Extra Credit 1: 10/28: Charilou L.
Complex Analysis Basics
- Short (Due Wed 10/30): Closed contour integrals of analytic functions.
  - Problem 2 & 3: Niusha A.
- Long (Due Mon 11/11): Residues and Fourier
  - Problem 1: 11/06 MacKenzie V.
  - Problem 2: 11/08 Drew W.
  - Problem 3: 11/13 (Wed) Ario M.
Green's Functions of Harmonic Oscillators
- Short (Due Friday 11/15): Simple Harmonic Oscillator
  - Problem 1: 11/15 (Fri) Kening Z.
- Long: (Due Monday 12/2): Damped Harmonic Oscillator and Extra Dimensions
  - Problem 1.1 11/18 (Mon): Ryan A.
  - Problem 1.2 11/20 (Wed): Zhiyuan S.
  - Problem 1.4 11/22 (Fri): Qiran W.
  - Problem 2.1 11/25 (Mon): Tianyi O.
  - Problem 2.2 11/25 (Mon): Yirui G.
  - Problem 2.3 11/27 (Wed): Renyu W.
  - Problem 2.4 12/2 (Mon): Haoyu L.
  - Problem 4.1 12/4 (Wed): Xingrui L.

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