Syllabus Fall 2019 Physics 36100

Physics 361 Mathematical Methods in Physics Fall 2019 Instructor:      Sriram Ganeshan, Marshak 313 x6085, sganeshan@ccny.cuny.edu Class hours:     Tue-Thu 4:00 to 5:40 Office hours:  Tuesday 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, Green’s 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