Mathematical Methods in Physics
Instructor: Sriram Ganeshan, Marshak 313
Class hours: Tue-Thu 4:00 to 5:40 Office hours: Thursday 2-4 pm.
Text: Mathematical Methods for Physicists: A Comprehensive Guide
By George Brown Arfken, Hans-Jurgen Weber, Frank E. Harris
Prerequisites: Mathematics 39100-39200 and Physics 20700-20800. The core
topics are covered with an eye on mathematics used in quantum physics but
most topics have general usage.
The following topics will be covered: Linear vector spaces, Ordinary differential
equations, eigenvalue problems, partial differential equations and its application
to heat flow problems, special functions, complex variable theory, Probability
and statistics (if time permits.). Attempt will be made to solve some problems
using numerical algorithms. The sequence of topic covered is roughly based on:
1. Complex variable theory: Analyticity, Cauchy-Reimann equations,
Cauchy Integral theorem, Contour integrals, Taylor and Laurent series, Analytical
Continuation, Conformal mapping and more..
2. Linear Vector Spaces, Matrices and Determinants, Eigenvalues and
Eigenvectors, Singular Value Decomposition etc..
3. Ordinary differential equations: First Order, Second Order, Frobenius
method, series solution, Eigen value problems, Special functions etc…
Grades in the course will be based on
weekly problems sets - 1/3 of grade
two in-class exams - 1/3 of grade
final exam - 1/3 of grade