Physics 5013
Mathematical Methods of Physics
Fall 2016
Instructor. K. A. Milton
Class Meetings. M W: 3:00–4:15, NH 103
Office. NH 325, x36325
Office Hours. M W 2:00–3:00 pm, by appointment, or any other time you can catch me
in my office.
Prerequisites. Some familiarity with the following subjects will be assumed:
Complex numbers
Fourier series and transforms
Matrices and determinants
Eigenvalue problems
Differential equations
Differential operators in curvilinear coordinates
Textbook.
Frederick W. Byron, Jr., and Robert W. Fuller, Mathematics of Classical and Quantum Physics (Dover, 1992), ISBN: 0-486-67164-X
References on reserve in the physics library.
G. Arfken and H.-J. Weber, Mathematical Methods for Physicists, 6th edition.
C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and
Engineers (Springer, 1999)
R. V. Churchill, J. W. Brown, and R. F. Verhey, Complex Variables and Applications
R. Courant and D. Hilbert, Methods of Mathematical Physics
L. M. Jones, An Introduction to Mathematical Methods of Physics
J. Mathews and R. L. Walker, Mathematical Methods of Physics
P. M. Morse and H. Feshbach, Methods of Theoretical Physics
E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, 4th edition
Handbooks. Two standard references that every physicist should possess are:
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, U. S. Government Printing Office, 1964 (available as a Dover paperback). This is now available on
the web as an interactive resource: http://dlmf.nist.gov/ as the NIST Digital Library
of Mathematical Functions.
I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, Academic
Press, 1965. A more complete, but less readable, Russian integral table is A. P.
Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series, 3 volumes,
Gordon and Breach, 1986 and 1990.
Lecture notes. Will be available on the web, at
http://www.nhn.ou.edu/%7Emilton/p5013-16.html
and on D2L.
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Grading.
Homework
Hour Exams (2 × 20%)
Final Exam
30%
40%
30%
Homework. Will be assigned roughly weekly. Solving the problems will be the most
significant learning aspect of the course, and is essential for success in the examinations.
Late homework will not be accepted.
Exams. In-class examinations will all be of the closed-book variety—no crib sheets may
be used. Make-up examinations will not be given.
Exam schedule.
Exam I
Exam II
Final Exam
Wednesday October 12
Wednesday, November 16
Monday, December 12, 4:30pm–6:30pm
Assistance. May be had from instructor at any time.
Tentative Course Outline
Topic
Infinite Series
Continued Fractions
Functions of a Complex Variable I
Analytic Properties, Taylor and Laurent Expansions
Functions of a Complex Variable II
Calculus of Residues
Padé Approximants
Asymptotic Expansions
Linear Operators—Sturm–Liouville Theory—
Abstract vector spaces—Hilbert space
Orthogonal Functions
Partial Differential Equations—Separation of Variables
Bessel Functions
Legendre Functions
Green’s Functions for Partial Differential Equations
Policy on Religious Holidays
“It is the policy of the University to excuse absences of students that result from
religious observances and to provide without penalty for the rescheduling of examinations
and additional required classwork that may fall on religious holidays.”
Reasonable Accommodation Policy
“Any student in this course who has a disability that may prevent him or her from
fully demonstrating his or her abilities should contact me personally as soon as possible so
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we can discuss accommodations necessary to ensure full participation and facilitate your
educational opportunities.”
Academic Integrity
Although collaborative learning is encouraged, including working on problems together, it is expected that assignments turned in represent your own work. Cheating on
examinations will not be tolerated. The following is a link to OU’s integrity website:
http://integrity.ou.edu
Adjustments for Pregnancy/Childbirth Related Issues
“Should you need modifications or adjustments to your course requirements because
of documented pregnancy-related or childbirth-related issues, please contact me as soon
as possible to discuss. Generally, modifications will be made where medically necessary and similar in scope to accommodations based on temporary disability. Please
see http://www.ou.edu/content/eoo/faqs/pregnancy-faqs.html for commonly asked
questions.”
Title IX Resources
“For any concerns regarding gender-based discrimination, sexual harassment, sexual
misconduct, stalking, or intimate partner violence, the University offers a variety of resources, including advocates on-call 24.7, counseling services, mutual no contact orders,
scheduling adjustments and disciplinary sanctions against the perpetrator. Please contact
the Sexual Misconduct Office 405-325-2215 (8-5) or the Sexual Assault Response Team
405-615-0013 (24.7) to learn more or to report an incident.”
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