Fall 2024 PY501 - Mathematical Physics

PY501 reviews mathematical methods used in physics. The focus is on methods frequently encountered in all areas of physics. The main topics we will discuss are: the calculus of variations; vectors, tensors and calculus on manifolds; Fourier analysis; complex analysis, and statistics.

Lectures: Mondays and Wednesdays 10:10 am – 11:55 am, SCI B58

Faculty Instructor: Hongwan Liu (hongwan@bu.edu)

Hongwan’s Office Hours: Fridays 4 pm, PRB 573

Graduate Teaching Fellow: Eashwar Sivarajan (eashwar@bu.edu)

Eashwar’s Office Hours: Thursdays 3 pm, PRB 553

Syllabus: Available here, and will be updated throughout the course.

Lecture Notes: Continually updated as one single document, available here.

Homework: Problem sets are posted on GradeScope, and solutions should be submitted there as well. Solutions will be posted here. You can check the due dates on either GradeScope or on the solutions page. Late homework will be penalized at 20% of the total points per day, and will not be accepted more than two days late.

Exams: There will be two in-class midterms and a final. The tentative exam schedule is as follows:

• Midterm 1: Wednesday, October 2
• Midterm 2: Wednesday, October 30
• Final: Monday, December 16, 9 am – 11 am

Grading: Problem Sets 35%, Midterm 1 20%, Midterm 2 20%, Final 20%, Class Participation 5%. Grades will be curved.

Online Discussion: All announcements, questions and discussions (about both logistics and physics) should be posted on the Piazza page for this course.

Students’ Responsibility: Students should know and understand the provisions of the CAS Academic Conduct Code and the BU Code of Student Responsibilities.

Materials: There are many good reference textbooks, many of which are available to you both electronically and in hardcopy through the BU library system. Other good reference materials are easily available on the internet. The lectures will be drawn from various sources, but you may find the following books and notes helpful (links are to online copies where available):

• General References
  • Mathematical Methods for Physicists: A Comprehensive Guide by Arfken, Weber and Harris
  • Mathematics for Physics: A Guided Tour for Graduate Students by Stone and Goldbart (link is to Stone’s online version of the textbook, which may have typos!)
  • Mathematics for Physicists: Introductory Concepts and Methods by Altland and von Delft
  • Mathematics of Classical and Quantum Physics by Byron and Fuller
  • Basic Training in Mathematics: A Fitness Program for Science Students by Shankar
• Calculus on Manifolds
  • Spacetime and Geometry: An Introduction to General Relativity by Carroll, based on his Lecture Notes on General Relativity
• Complex Analysis
  • Complex Variables and Applications by Brown and Churchill
  • Introductory Complex Analysis by Silverman
  • An Introduction to Fourier Analysis and Generalized Functions by Lighthill
• Statistics
  • Statistical Data Analysis by Cowan (see also his statistics course website)
  • Statistics IB notes by Weber

Miscellaneous

1. Abiding by the BU Academic Conduct Code is expected.

2. The use of Mathematica is encouraged, but keep in mind that you are expected to be familiar enough with the mechanics of performing calculations to do so during the in-class midterms and exams.

3. Working in groups on problem sets is also highly encouraged, but please indicate at the top of your solutions who you worked with, and always write up the solution yourself. If you would like to work with someone but are having trouble finding people to work with, let me know.

4. You should feel comfortable asking me for reasonable and stochastically occurring accommodations. Please plan ahead and ask for them early. Students who require accommodations throughout the course should approach BU Disability & Access Services.

5. Every effort should be made to maintain an open and respectful environment in class, where everyone feels comfortable expressing their opinions and asking questions.