3090 - Methods in theoretical physics (Fall 2015)
This class will be a smorgasbord of different mathematical tools and concepts that are essential for the study of advanced topics in physics.
Course description in pdf.
Syllabus: Topics to be covered include vector spaces and eigenvalue problems; complex variables and complex analysis; Fourier series and Fourier transforms; Laplace transforms; and Green's functions.
Course text: Mathematics for Physicists by Susan Lea. I strongly recommend buying this excellent text. We will be following it fairly closely.
Grading and tests: There will be weekly homework assignments, two midterm tests, and a final exam. Your final grade will be based as follows: your homework grade counts 30%, each midterm counts 20%, and your final exam counts 30%.
Homework problems are the most essential part of this class. Assignments will be due on Fridays either in class or turned into my office (or under my door) before 4pm. No extensions will be given unless there is an emergency or other extreme circumstance. Late homework will be penalized 10% per day late (or fraction thereof).
Expectations: I expect that all homework you turn in will be entirely your own work. You may discuss homework problems with your peers, but you must write your own solutions independently.
Homework assignments (due Fridays):
problem set #1 - due Sept 18.
problem set #2 - due Sept 25.
problem set #3 - due Oct 9.
problem set #4 - due Oct 16.
problem set #5 - due Oct 23.
problem set #6 - due Monday, Nov 2.
problem set #7 - due Nov 20.
problem set #8 - due Monday Nov 30.
problem set #9 - due Monday Dec 7.
Midterms: The first midterm is on Monday, Oct 5th in class.
Practice problems.
The second midterm is on Friday, Nov 6th in class. The topic is complex analysis.
Practice problems.
Final: Sunday, December 13th, 2-5pm, TEL 0007.
Office hours: Wednesdays 4-5pm or by appointment. My office is Petrie room 217.
Lecture time/date/location: Stong College Room 222 (note: room change), MWF, 9:30am.
Course notes:
Week 1 - Vector spaces, rotations, exponentiation of matrices.
Week 2 - Eigenvalue problems, coupled harmonic oscillators.
Week 3 - Introduction to complex numbers and functions.
Week 4 - Derivatives and integrals of complex functions.
Week 5 - Singularities and complex integrals.
Week 6 - Applications of residue theorem.
Week 7 - Fourier series.
Week 8 - Laplace transform and Green's functions.
Week 9 - Fourier transform.
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