Mathematical Methods of Physics I
Instructor
Roman Grigoriev
Office: Howey W304
Phone: (404) 385-1130
E-mail:
TA
Zachary Jackson
Office: Howey W503, hours: Thursday 12pm-1pm
E-mail: zjackson3@gatech.edu
Place and Times
Monday, Wednesday, and Friday, 11:15am-12:05pm
Howey N210
Course Description
This graduate-level course provides an overview of the essential mathematical methods illustrated by applications to problems from various branches of physics.
Textbook
The recommended, but not required, textbook that covers most of the topics that will be covered is Arfken, Weber, and Harris, Mathematical Methods for Physicists, Seventh Edition: A Comprehensive Guide (Academic Press, 2012). An earlier (5th or 6th) edition of the book will also work, if you already have one. We will rely on lecture notes for subjects that are not adequately covered in the textbook.
Objectives
The purpose of the course is to make sure that all first-year physics graduate students have a working knowledge of the most common mathematical tools they might need in the classroom and during their thesis work.
Grading
There will be no exams, your performance will be assessed based on the homeworks, so day-to-day participation is very important. There will be one homework assignment per week. Completed assignments will be due on Mondays in class. You can discuss problems
with each other, but the solutions have to be executed and submitted individually. All students are expected to comply with
the academic honor code.
Grading scale (for those taking the course pass/fail, a passing grade is C or better):
A = 80-100%,
B = 70-80%,
C = 60-70%,
D = 50-60%,
F = 0-50%
Course Outline
- Functions of complex variables
- Complex variables
- Calculus of residues
- Conformal maps and their appications
- Integral and discrete transforms
- Fourier series and Fourier transform
- Laplace transform
- Hilbert transform
- Linear operators and matrices
- Vectors and matrices
- Eigenvalue problem
- Properties of eigenvectors and eigenvalues
- Normal modes
- Tensors
- Differential equations
- Separation of variables in PDEs
- Boundary value problem
- Sturm-Liouville problem
- Green's function for ODEs
- Green's function for PDEs
- Ill-posed boundary value problems
- Variational calculus
- Euler equation
- Constrained minimization
- Rayleigh-Ritz method
Homework Problems