MATH/PHYS 611: Mathematical Physics I

Ed Bueler,       Fall 2005 UAF

Office: Chapman 301C
Phone: 474-7693
Office Hours online at
Class Time: TTh 11:30-1:00
Classroom:  NSCI 203.
Credits: 3.0
Course Web Site:
     (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.

Grade = Exams + Homework :  Fifty percent of the grade will be based on weekly homework assignments.  Two in-class exams will be given, a midterm exam and a final exam at the regularly scheduled time:

Policies and makeup exams:   The department has specific policies on incompletes, late withdrawals, and early final examinations, etc; see .  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.