### 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