Course: PHYS 510 Graduate Mathematical Physics

INSTRUCTOR: Dr. Heidi Fearn

TEXT:

Notes will be handed out in class. I am recommending the standard graduate text by George B. Arfken Mathematical Methods for Physicists. You may also find some Schaum books useful for vector analysis and complex variable. The book by Mary Boas is also good. You will also be making use of Tables of integrals, mathematical handbooks.

EXAMS/PROBLEMS:

There will be one midterm and a final exam, the midterm is worth 45% and the final worth 55%. Problems will be assigned on a regular basis and will be taken from the book and hand out problems. Each assignment will be given to you in xerox form. I will NOT grade these problems and I DO NOT expect them to be handed in. Instead I will put aside a lecture every 2 weeks to go over problems in class. I will pick on students at random to present their calculations on the board in front of the class, so I recommend you try the problems in advance!!

COURSE CONTENT:

Chap 1. Review vectors, tensors notation

Chap 2. Review curvi--cords

Chap 5. Taylors theorm

Chap 3. Determinants and matrices

Chap 8. PDE's with boundary conditions and initial conditions

Chap 9. Sturm-Liouville theory and orthofonal poly's

Chap 10--13 Special functions including, gamma, beta, bessel, Hermite, Laguerre, Legendre, Mathew etc

Chap 14,15 Fourier and Laplace transforms

Complex variable, residue theory

Time permitting, a brief look at the calculus of variations