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: vectors, tensors and linear algebra; the calculus of variations; complex analysis; Fourier 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: Mondays, 4:30 pm, PRB 573

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 your solutions should be submitted there as well. All grades will also be posted there. Solutions will be posted here. You can check the due dates on either GradeScope or on the solutions page. Problem sets are generally released on Wednesdays, and are due the end of the following Wednesday. Late homework without reason 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. These exams will be closed-book, but a formula sheet will be provided. You are free to ask for things to be put on the formula sheet on Piazza in the week before the exam, I’ll usually be okay with it. The tentative exam schedule is as follows:

  • Midterm 1: Monday, October 6
  • Midterm 2: Monday, November 3
  • Final: Monday, December 8

Grading: Problem Sets 20%, Midterm 1 25%, Midterm 2 25%, Final 25%, 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):

Use of AI: AI is now a fact of life. You are free to use AI to help you along in this course, but please use it critically, and do not accept anything it tells you on face value. This is a graduate course, and I trust that learning this material is important to you. Please make sure you use it wisely to support your learning. You will need to learn the material well enough for the exams!

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.