01:750:464/16:750:511: Mathematical Physics

Instructor: Prof. Andrew Mastbaum
mastbaum@physics.rutgers.edu
Office: W320 Physics & Astronomy Building

Course Overview

This course is intended to provide a survey of mathematical tools for the practice of physics. We will aim to cover the essentials of topics such as group theory, complex analysis, and integral transforms, as well as topics in differential equations and statistical methods of practical importance. Throughout, we will emphasize computer-based methods to develop a working knowledge of useful tools for research.

Grading

Course grades will be based on homework problem sets, two exams, an independent study project, and participation.

Problem sets will be assigned every 1–2 weeks. Working together in groups is encouraged, but each student should hand in their own assignment.
A midterm exam will cover the first half of the course, and a final exam will be comprehensive but focus on the latter half.
Through an independent study project, students will learn about a topic related to the course and teach it to the class.
Participation means engagement with course content, including via class meetings and Canvas discussions.

Textbook

The primary, required textbook is:

Arfken, Weber, & Harris, Mathematical Methods for Physicists, Academic Press, 7th Edition (ISBN 9780123846549)

An electronic version of the textbook is available from the Rutgers University library: https://bit.ly/35Neg93. Additional chapters are available digitally here: https://booksite.elsevier.com/9780123846549/.

The following may also be useful for supplementary material, and are recommended but not required:

Brown & Churchill, Complex Variables and Applications, McGraw-Hill
Vaughn, Introduction to Mathematical Physics, Wiley
Cowan, Statistical Data Analysis, Oxford

Schedule

Week	Topic	Chapter(s)	Description
1–2	Preliminaries	1–2	Series, complex variables, matrices, computing tools
2–4	Intro to Group Theory	17	Representations, discrete groups, Lie groups
5–8	Complex Analysis	11	Complex functions, integrals, series, calculus of residues
9	Exam 1
9–12	Integral Transforms	20	Fourier transforms, Laplace transforms, convolutions
12–13	Nonlinear Methods	33	Nonlinear functions, differential equations, phase plane analysis
13	Independent Projects
14–15	Statistical Methods	23	Probability, statistical tests, parameter estimation, machine learning
	Final Exam