Office: Chapman 301C Phone: 474-7693 eMail: ffelb@uaf.edu Office Hours online at www.dms.uaf.edu/~bueler/OffHrs.htm |
Class
Time: TTh 11:30-1:00 Classroom: NSCI 203. Credits: 3.0 Course Web Site: www.dms.uaf.edu/~bueler/Math611F05.htm (includes a detailed, tentative daily schedule) |

**Description:** Mathematical
methods for graduate-level physics. In particular, in 611 we will
study Fourier and Laplace transform methods, ODE boundary value
problems, Green's function methods, eigenfunction expansions, Hermitian
operators, Sturm-Liouville problems, certain special functions
including spherical harmonics, classical partial differential equation
methods, and some complex analysis. We will, of necessity, also
intermingle some review of standard undergraduate mathematical topics
in this course.

In MATH/PHYS 612 we will study conformal mapping, asymptotic
methods, vector and tensor fields and
their coordinate transformations, problems in the calculus of
variations, and some group theory.

The course does not teach physics except tangentially. Many
"mathematical physics" courses nationwide are narrowly focussed on the
mathematical needs of quantum mechanics and particle physics, but the
typical UAF student's needs are broader (and, in parts,
shallower). Because many UAF graduate students in math and
physics will work with systems of nonlinear PDEs, or other
complicated nonlinear models, in their research, and the instructor
will keep this in mind by emphasizing general strategies and
mathematical possibilities.

**Course Format:** The majority of
class time will consist of my lecture, in which I will encourage as
many on-the-topic questions as possible. The weekly homework
assignments should inspire questions as well. I hope that
students will 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 422 Introduction to Complex
Analysis or permission of instructor. (In particular, because of the prerequisite
of MATH 422, one must also have MATH 302 Differential
Equations. Linear
algebra (MATH 314), multivariable calculus (MATH 202 and MATH 421) ,
and an introduction to partial differential equations (MATH 421) are
all recommended.)

**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 textbook has 28 chapters. In 611 my goal is to
cover chapters 12 through the beginning of chapter 20.

The first 11 chapters are assumed. That is, the first 11
chapters serve this course as a review of prerequisite material and as
a set of common material all students should be able to use easily.

In 612 I plan to cover the remainder of chapter 20 and hen chapters
21, 22, 24 and some of 25. I will also add some supplementary
material. Chapters 26, 27, 28 (probability, statistics, and
numerical methods) are very useful but are too far afield for this
course.

I will discuss in class certain other textbooks and reference works,
including online references,
which I find useful.

- Midterm: Tuesday, Nov. 1 (in class)
- Final: 10:15 a.m.-12:15 p.m., Saturday, Dec. 17 (in regular classroom)

**Policies and makeup exams:** The
department
has specific 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.