Instructor: Prof. Andrew Mastbaum
mastbaum@physics.rutgers.edu
Office: W320 Physics & Astronomy Building
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.
Course grades will be based on homework problem sets, two exams, an independent study project, and participation.
The primary, required textbook is:
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:
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 |