PHYS0720
Methods of Mathematical Physics [ Course Website ]
This course is designed for sophomores in physical sciences, especially those intending to take sophomore level or higher Physics courses. Basic elements of and practical examples in linear algebra (particularly as applied to quantum mechanics), the solution of ordinary and partial differential equations, Fourier analysis, complex analysis and application to contour integrals, all taught with the aim of preparing students for Physics 500 and all 1000-level Physics courses. Pre-requisites: PHYS 0600 or 0800, MATH 1800, 2000, or 3500, or consent of the instructor.
Instructor: R. Pelcovits, Robert_Pelcovits@brown.edu
Textbook:
Shankar, Basic Training in Mathematics
Arfken and Weber, Mathematical Methods for Physicists
Course Outline:
Linear algebra (coverage of this topic will depend on the background of the class)
Fourier Series and Fourier Transforms
Ordinary Differential Equations:
- Solutions in Closed Form
- Power Series Solutions
Ordinary Differential Equations:
- Solutions in Closed Form
- Power Series Solutions
Partial Differential Equations:
- Classification of PDE’s
- Separation of Variables
- Integral Transform Methods
Complex Analysis:
- Functions of a Complex Variable, Riemann Surfaces
- Analytic Functions, Cauchy’s Theorem, Series, Residues
- Contour Integration
