This course builds on the first semester course PHY 305 and introduces mathematical techniques which are crucial to the formulation and solution of fundamental theories in Physics. It is biased towards the application of Mathematics in solving problems rather than the development of rigorous Mathematics. It is aimed at enabling students to solve Physics problems through complex analysis and extend the definition of special functions to the complex plane. Key topics treated include functions of complex variables, Bessel, Gamma, Beta and Error functions, Integral transforms, and Legendre Polynomials.