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):
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
Solutions
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
Solutions
Sept. 7Uniqueness of Fourier Series 
Sept. 12Conditions for Uniform Convergence 
Sept. 14Convolutions 
Sept. 19Good Kernels 
Sept. 21Abel Summability 
Sept. 26Class RescheduledHomework 3: Exercise 2.19, 2.20
Solutions
Sept. 28Vector Spaces, Hilbert Spaces 
Oct. 3Mean-Square Convergence of Fourier SeriesHomework 4: Exercise 3.5, 3.10; Problem 3.2
Due Thursday, Oct. 12
Oct. 5Mean-Square Convergence of Fourier Series Pt. 2 
Oct. 10Fall Break (Optional Review Session at 3pm) 
Oct. 12Midterm 
Oct. 17Heat Equation on the Ring and the Heat Kernel 
Oct. 19Midterm Review and Discussion 
Oct. 24The Fourier Transform Pt. 1Homework 5: Exercise 5.1, 5.2
Due Tuesday, Oct. 31
Oct. 26Examples, The Schroedinger Equation 
Oct. 31Schwarz Space 
Nov. 2Gaussians and Fourier Inversion