PHYS GU4019: Mathematical Methods of Physics

Instructor: Sebastian Mizera

Term: Fall 2025

Lectures: Tuesdays and Thursdays, 2.40pm - 3.55pm, room TBD

Office hours: Wednesdays, 2.40pm - 3.55pm, Pupin 905

Teaching assistant: TBD

Assignments: Bi-weekly problem sets

This is a website for the Columbia University course “Mathematical Methods of Physics” offered in the Fall 2025-2026 term.

Prerequisites: Mechanics (PHYS 3003UN); Electricity-Magnetism (PHYS 3007UN); proficiency in differential and integral calculus as well as linear algebra. This course will present a wide variety of mathematical ideas and techniques used in the study of physical systems. Topics will include: matrices and determinants; vector spaces; Hilbert spaces and operators; eigenvalue problems; generalized functions; ordinary and partial differential equations; Sturm-Liouville theory; perturbation theory; Green’s functions; complex analysis; holomorphic functions; residues and discontinuities; special functions; group theory and representations; Fourier analysis; integral transforms; integral equations; calculus of variations; probability and statistics.

Textbook: “Mathematical Methods for Physicists: A Comprehensive Guide” by George B. Arfken, Hans J. Weber, Frank E. Harris; Academic Press (2012), 7th edition