Physics 475: Introduction to Mathematical Physics

Spring 2007

Lectures:  Tuesday and Thursday, 12:30-1:50 p.m. in Small 102

Instructor: Irina Novikova

Office: Small 332	E-mail: ixnovi[at]wm.edu
Office hours: Thursdays, 2-4 p.m., or by appointment	Telephone: (757) 221-3693
Web-site: http://www.physics.wm.edu/~inovikova/phys475.html

Required text: Mary Boas: Mathematical Methods in the Physical Sciences, 3rd Ed., Wiley.

Supplementary text: Mathematical Methods for Physicists, by George B. Arfken and Hans J. Weber, 4^th Ed., Academic Press.

(Both textbooks are on reserve in Swem library)

Homework:   10 problems + 1 extra credit problem per week due each Friday at 5 p.m.

Grading:

Homework	25%
Two midterm tests	25% each
Final exam	25%

Tentative course schedule

This course is intended to provide basic mathematical concepts needed in junior/senior/graduate courses in Physics. It will cover a broad range on topics, including infinite series, complex numbers and functions, Fourier analysis, special functions, etc.

Infinite Series, Power Series (Boas, Chapter 1)

Convergence of Infinite Series; Interval of Convergence for Power Series; Expanding Functions in Power Series

Complex Numbers, Functions of a Complex Variable (Boas, Chapters 2, 14)

Real and Imaginary Parts of a Complex Number; Complex Conjugate; Analytic Functions; Contour Integrals; The Residue Theorem

Fourier Series and Transforms (Boas, Chapter 7)

Fourier Series (Regular and Complex Forms); Fourier Transforms

Special Functions (Boas, Chapter 11)

Gamma and Beta Functions; The Error Function; Stirling's Formular;

Series Solutions of Differential Equations (Boas, Chapter 12)

Legendre and Bessel Polynomials and Functions; Hermite and Lagguerre Polynomilas

Partial Differential Equations (Boas, Chapter 13)

Laplace's Equation in Different Coordinate Systems; Time-dependent differential equations