Analytical Methods of Physics (Phys 301)

The final exam is scheduled on Thursday Dec. 11, from 7:30 am – 10:15 am, Art and Design Building 2026. It covers all topics since the midterm exam, e.g. Chapter 12 and 13. The format will be similar to the midterm exam.

Formula sheets: books or notes are not allowed in the final exam, but you can bring a self-prepared, letter-sized formula sheet (you may use both sides of the paper).

TIME AND LOCATION

9:00 am – 10:15 am, Tuesday and Thursday
Aug 25, 2014 – Dec 17, 2014
Art and Design Building 2026

INSTRUCTOR OFFICE HOURS

Erhai Zhao
Email: ezhao2[at]gmu[dot]edu (email communication is preferred)
Office: Planetary Hall, Room 207
Office HOURS: Tuesday and Thursday 2pm–3pm

COURSE WEBPAGE
Announcements, homework assignments etc. will be posted on the course webpage http://ezhao.spacs.gmu.edu/phys-301/

All e-mail communication from the instructor concerning this course will be sent to registered GMU accounts only. We will not use Blackboard for this course.

TEXTBOOK

Mathematical Methods in the Physical Sciences, Mary L. Boas

This is a clear, pedagogical book. It is also a good reference for you to use later on. The lectures can only cover parts of the book, and will not follow exactly the order of the chapters.

PREREQUISITE
You should know multiple variable calculus, linear algebra, vector analysis (e.g. Laplace operator in curvilinear coordinate systems), and elementary differential equations (Math 214 or equivalent). These topics are reviewed in Boas Chapter 3, 4, 5, 6, 8 and will not be repeated in the lectures. Due to time constraint, we will not cover Chapter 9, 10, 14, and 15.

TOPICS

This course provides training in mathematical concepts and techniques needed in upper level undergraduate (and graduate) courses in Physics. It will cover a broad range of topics (Boas Chapter 1-2, 7, 11-14), including

  • Infinite series. Power series of functions.
  • Harmonic oscillations, complex series and complex functions.
  • Fourier series, Fourier transformations, functional space and orthogonal basis, Dirac’s delta function.
  • Special functions defined by integrals or recursion relation, Gamma, Beta, and Erf. Asymptotic series of functions.
  • Series solutions to ordinary differential equations: Legendre polynomials, Bessel functions. Method of Frobenius. Sturm–Liouville problem, eigenfunction expansion.
  • Solving partial differential equations by separation of variables: Laplace equation, wave equation, diffusion and Schrodinger equation.
  • Poisson’s equation. Introduction to Green functions and integral equations (time permitting).

RESOURCES
1. NIST Digital Library of Mathematical Functions. This authoritative reference is the modern update of the classic “Abramowitz and Stegun”.

2. Wolfram Demonstrations Project. Mathematica makes it easy to explore Bessel functions, Lengendre polynomials etc.

3. Feynman Lecture on Harmonics.

HOMEWORK 

It is very important to solve homework problems independently. Otherwise you will get very little out of this course. Discussions with peers are encouraged. Simply copying someone else’s solution or the solution manual is not acceptable and will be considered an Honor Code violation (The GMU Honor Code: http://www.gmu.edu/catalog/9798/honorcod.html#code). Submitted homework must clearly show crucial steps taken. It is your responsibility to make your approach transparent. All writing must be legible.

Homework should be submitted before the start of the class on the due date. Late homework will not be accepted.

GRADES

Homework 50%,  Mid-Term Exam 25%,  Final Exam 25%

If you are a student with a disability and you need academic accommodation, please contact the Office of Disability Resources at 703.993.2474. All academic accommodations must be arranged through that office.