## MATH/PHYS 612: Mathematical Physics II

**Description:** Mathematical
methods for graduate-level physics. In MATH/PHYS 612 we will
study complex analysis (including conformal mapping), eigenfunction
expansions, Hermitian
operators, Sturm-Liouville problems, some group theory, vector and
tensor fields (if
possible), and the calculus of
variations (if possible).

The course does not teach physics except tangentially. Many
"mathematical physics" courses nationwide are narrowly focussed on the
mathematical needs of quantum mechanics, quantum field theory, and/or
general relativity. The
typical UAF student's needs are broader (and sometimes
shallower), frequently including geophysics. Many UAF graduate
students in math and
physics will work with systems of nonlinear PDEs or other nonlinear
models. Therefore this
course emphasizes general strategies and
mathematical possibilities.

**Course Format:** The majority of
class time will consist of my lecture. I will encourage as
many on-the-topic questions as possible. Weekly homework
assignments should inspire questions as well. Students should come to
my office, individually and in groups, to discuss
problems from the class. I also encourage students to talk to me
about mathematical issues which arise in the context of a
project/thesis/dissertation.

**Prerequisites: ** MATH/PHYS 611.

**Textbook: ** The required
text is

K. F. Riley, M. P. Hobson, and S. J.
Bence, Mathematical
Methods for Physics and Engineering,

2nd edition, Cambridge University
Press 2002.

This thick and imperfect textbook has 28 chapters, only a subset of
which are at the right level for 611-612. In 612 my goal is to
cover chapters 20, 17, 18, 19, and 24 (and possibly 21 and 22) in this
order.
Some supplementary material will be added from other sources.

**Grade = Exams + Homework :** F**ifty
percent** of the grade will be
based
on **weekly homework assignments**. An in-class midterm exam and a take-home final exam make up the other fifty
percent.

- Midterm: Thursday, March 9 (in class)
- Final: 5:00
pm Thursday, May 11 (take-home due at this time)

**Policies and makeup exams:** DMS
has reasonable policies on incompletes, late withdrawals, and early
final
examinations, etc; see http://www.dms.uaf.edu/dms/Policies.html
. You are covered by the UAF Honor Code. I will work with
the Office of Disabilities Services (203 WHIT, 474-7043) to provide
reasonable accommodation to student with disabilities.