Phys 500A - Mathematical Methods in Physics


Term: Fall 2017

Time/Location: T/R 9:35-10:50 AM, Neckers 410

Instructor: Dr. Eric Chitambar, (Office: Neckers 480, Email: echitamb@siu.edu)

Office Hours: Tues. 4:00 PM - 5:30PM; Thurs. 8:05 AM - 9:35 AM; Fri. 1:00PM - 4:00PM

Course Website: http://www.physics.siu.edu/~echitamb/Teaching/Phys500A/Phys500A_Fall_2017.html

Primary Text: Fourier Analysis - An Introduction by Elias Stein and Rami Shakarchi

Objectives: This course will cover the mathematial theory of Fourier Analysis with an emphasis on applications in physics. Topics covered include solutions to the wave and heat equations, convergence of functions, Fourier series, Fourier transform, Legendre polynomials, Bessel functions

Homework and Grading Policy: To master the subject material, all exercises and problems at the end of the chapter should be attempted. This is a realistic and managable goal. Every week, four specific exercise/problems will be assigned. Of those, two will be graded.
Homework - 50%
Midterm - 25%
Final - 25%
Syllabus (This will evolve throughout the semester): (Due Thursday, Sep. 14)
DateTopicsSupplemental Notes, Homeworks, Solutions
Aug. 22Introduction, Simple Harmonic Motion, Derivation of The Wave EquationHomework 1: Exercises 1.1, 1.3, 1.10; Problem 1.1
(Due Tuesday, Sep. 5)
Aug. 24d'Alembert's Formula, Separation of Variables 
Aug. 29Plucked String Example, Derivation of the Heat Equation 
Aug. 31Dirichlet problem on 2-D disc, Cauchy sequences 
Sept. 5Fourier Series definitions, Convergences of SequencesHomework 2: Exercise 2.6, 2.7, 2.8
Sept. 7Uniqueness of Fourier Series 
Sept. 12Conditions for Uniform Convergence