**PHYS 6520/4520 (same as Math 6265/4265)**
** MATHEMATICS OF PHYSICS
II**
**SUMMER SEMESTER 2001**

**Tuesday, Thursday 4:45 pm - 7:30
pm --- 527 General Classroom Building**

__Instructor__: Mark Stockman
__Office__: 455 Science Annex

Phone: (404)651-2779

E-mail: mstockman@gsu.edu

Internet: http://www.phy-astr.gsu.edu/stockman/

Grading: Homework 40%, midterm exam 20%, final exam 40%.

Final Exam: Friday, August 2 from 5 to 7 pm in
the regular classroom (527 G)

__Text__: Erwin Kreysig,* Advanced Engineering Mathematics *(Eighth
Edition)*,* J. Wiley, New York, 1999

Prerequisite: Math 3260

- Power series solutions
- Legendre equation and polynomials
- Frobenius method
- Bessel equation and functions
- Sturm-Liouville problem and orthogonal functions
- Solutions by orthogonal eigenfunction expansions

- Periodic functions
- Fourier series
- Even functions and Cosine series; Odd functions and Sine series
- Complex Fourier Series
- Fast Fourier transform (FFT)
- Example: Solving periodic and aperiodic mechanical problems using FFT

- Introduction. Equations of mathematical physics: Hyperbolic (wave equation), parabolic (diffusion or heat equation and Schroedinger equation), and elliptic (Laplace equation and Poisson equation)
- Solving one-dimensional wave equation (vibrating spring): Separation of variables and Fourier expansion
- General solutions of differential equations: D'Alembert solution of the wave equation
- Diffusion equation: Solution by Fourier series and integrals.
- Two dimensional wave equation: Vibrating rectangular membrane
- Laplacian in polar coordinates. Use of Fourier-Bessel series. Vibrating circular membrane
- Laplace equation in three dimensions. Spherical Bessel functions, Legendre polynomials and functions, and spherical harmonics. Potential problems
- Green's functions

- Complex numbers, complex plane, modulus and argument
- Derivative, analytic functions
- Cauchy-Riemann and Laplace equations
- Conformal mapping
- Analytic properties of elementary functions: square root, exponential function, trigonometric and hyperbolic functions, and logarithm
- Branch cuts and Riemann surfaces

- Laurent series
- Poles and residues
- Residue integration method
- Evaluation of real integrals