Textbook: Mathematical Methods for Physicists, Arfken, 6th edition, Elsevier Academic Press.
References:
Advanced Engineering Mathematics for Kreyszig is a good reference for reviewing the basic concepts.
Mathematical Methods for Physicists: A concise introduction, Tali Chow.
Course Content:
6.1‐6.8 Functions of a Complex Variable I Analytic Properties, Mapping
7.1‐7.3 Functions of a Complex Variable II
9.1‐9.8 Differential Equations
10.1‐10.5 Sturm‐Liouville Theory‐ Orthogonal Functions
11.1, 11.2, 11.5 Bessel Functions
14.1‐14.7 Fourier Series
15.1‐15.12 Integral Transforms