Physics 475: Introduction to Mathematical Physics
Spring 2009
Lectures: Tuesday and Thursday, 12:301:50 p.m. in Small 238
Instructor: Irina Novikova
Office: Small 332 
Email: ixnovi[at]wm.edu 
Office hours: by appointment 
Telephone: (757) 2213693 
Website: http://www.physics.wm.edu/~inovikova/phys475.html 

Grader: Zhifeng Shi 

Office: Small 243 
Email: zshi@wm.edu 
Office hours (grading questions only): by appointment 
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.
Homework: 10 problems + 1 extra credit problem per week due each Friday at 5 p.m.
Course schedule and Homework Assignments
Grading:
Homework 
25% 
Two midterm tests 
25% each 
Final exam 
25% 
Tentative course content
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.
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
Infinite Series, Power Series (Boas, Chapter 1)
Convergence of Infinite Series; Interval of Convergence for Power Series; Expanding Functions in Power Series
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; Timedependent differential equations