PY 355 - Methods of Theoretical Physics - Spring 2026

Course Information

PY355 is a survey of mathematical and computational methods used in modern theoretical physics. Mathematical topics include differential and integral calculus; complex variables and analytic functions; vectors, fields, and vector calculus; linear algebra of matrices and function spaces; bras and kets; eigensystems; Fourier analysis; basics of ordinary and partial differential equations. Introduction to scientific programming in Python, computational visualization and numerical methods complementing each of the analytic topics.

Instructor: Prof. Martin Schmaltz (schmaltz@bu.edu)

Lectures: Tuesday/Thursday, 12:30-1:45, SCI 113
Sections: Monday, PRB 146, 3:35-4:25 (D1), 4:40-5:30 (D2), 2:30-3:20 (D3)

Office hours: Fridays, 1:45-3:30pm, PRB 561

TF: Eashwar Sivarajan (eashwar@bu.edu), Office hours: Fridays, 3:00pm-5:00pm, SCI 121
LA: Xiang Jin (xjin1@bu.edu), Office hours: Fridays, 8:45-10:45am, SCI 121
Grader: Eashwar Sivarajan (eashwar@bu.edu)

Online Discussion: The class has a Slack PY355 Q&A site for announcements and discussion. (Open in Slack App)

Materials: There are four recommended reference textbooks for the course -- we will not be following any one precisely.

• The most complete modern text is Mathematics for Physicists: Introductory Concepts and methods by A. Altland and J. von Delft (CUP).
• A complementary, somewhat more elementary, text is Basic Training in Mathematics: A Fitness Program for Science Students by R. Shankar (Springer).
• Mathematical Methods for Physicists: A Comprehensive Guide by Arfken, Weber and Harris (Elsevier) covers 3D vector calculus at the same level that we will cover it.
• Finally, Mathematical Methods in the Physical Sciences by Mary L. Boas (WILEY) is a classic that I like.

Scientific programming will be taught through a series of interactive Jupyter notebook assignments which will be made available through the JupyterHub.

Lecture notes and material on computational aspects of the course will be posted on the schedule page.

Homework: There will be weekly written and Jupyter homeworks due Mondays by electronic submission (by 11:59pm).

• Written homework should be submitted through GradeScope.
• Computational homework should be submitted using the submission tool in the JupyterHub.

Late homework will lose 20% per day and will not be accepted more than two days late.

Exams: There will be two midterms and a final. Exam schedule:

Midterm 1	Thursday, February 26
Midterm 2	Thursday, April 2
Final	Thursday, May 7, 12-1:30pm, SCI 113 (SCI B58, extra time room)

Grading: Homework 10%, Jupyter 10%, Midterm 1 25%, Midterm 2 25%, Final 30%

Grades will be curved.

Syllabus/Schedule

The plan is subject to change as the course develops. This is the rough plan of topics:

    [Week 1-2]     Single Variable Calculus; Intro to Python
    [Week 3]       Complex Variables and Functions
    [Week 4-7]     Vector Calculus
    [Week 8-11]    Vector Spaces, Matrices, Eigenproblems
    [Week 12-13]   Differential Equations

Students' responsibility

Students should know and understand the provisions of the CAS Academic Conduct Code and the BU Code of Student Responsibilities. Cases of suspected academic misconduct will be referred to the Dean's office.