Spring 2019 Syllabus Physics 36100

Physics 361

Mathematical Methods in Physics

Fall 2018

Instructor: Sriram Ganeshan, Marshak 313

x6085, sganeshan@ccny.cuny.edu

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:

0. Preliminaries

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