Time and place: Tuesday and Thursday, 11:00 -- 12:15, Room 218 Physics
Bldg.
Instructor: H.J. Weber,
Room 106C
Physics Bldg, Tel. 924-6810, hjw@theory.phys.virginia.edu
My office hours in fall: Tuesday & Thursday 9 to 10 am, or any other time you
find me in my office.
Grader: David Djajaputra,
Room 157 Physics Building, New North Wing, Tel. 924-7958,
dd4b@virginia.edu
Text: Mathematical Methods for Physicists (4th ed., 1995)
by G.B. Arfken and H.J. Weber.
PHYS 725 is the only mathematics (core) course for
graduate students in Physics and related fields.
PHYS 725 is recommended for PHYS 751, 752 Quantum Mech.,
PHYS 521 Class. Mech. and PHYS 742, 743 Electricity and Magnetism I, II.
.
PHYS 725 is offered in the fall. It starts with a review of linear
algebra, vector analysis and tensors,
continues with symmetries and group
theory,
infinite and asymptotic series, complex functions in one variable,
partial and ordinary differential equations with applications to special
functions.
EXAMS: Midterm on Thursday, Oct.10 at 11 am in Rm 218 Physics Bldg.
Final on Thursday, Dec.12 from 9 am to noon in Rm 218 Physics
Bldg.
There are biweekly problem sets counting ~30% towards the grade,
midterm ~30% and final ~40%.
Syllabus 1996:
1. Introduction, outline, notations and historical remarks
2. Linear algebra
Brief review of vectors and vector calculus
Linear equations
Matrices (orthogonal, unitary, symmetric, Hermitian and determinants)
Eigenvalues and eigenvectors
3. Symmetries and group theory
4. Tensors
5. Infinite series and products
Convergence tests
Taylor series
Bernoulli numbers
Asymptotic series
6. Functions of a complex variable
Cauchy integrals
Analytic continuation
Singularities
Taylor and Laurent series
Multivalent functions
Calculus of residues
7. Ordinary differential equations (first and second order)
Singularities
Taylor expansion
Independent second solution
Sturm-Liouville theory
8. Partial differential equations
Characteristics, boundary conditions, types, etc.
Separation of variables
Green's functions for inhomogeneous equations
9. Gamma (and beta) functions
10.Bessel (Hankel and spherical Bessel) functions
11.Legendre polynomials (and spherical harmonics)
12.Hermite and Laguerre polynomials
13.Fourier series and integrals.
Your comments, questions, suggestions, and inquiries about this course are welcome.