PH 201	Mathematical Physics	3-1-0-8
Syllabus: Complex Analysis: Functions, Derivatives, Cauchy-Riemann conditions, Analytic and harmonic functions, Contour integrals, Cauchy-Goursat Theorem, Cauchy integral formula, Taylor series, Laurent series, Singularities, Residue theorem and applications, conformal mapping and application. Partial Differential Equations: Method of separation of variables, Laplace equation, Heat Equation, Wave equations in Cartesian and curvilinear coordinates, Green's function and its applications Integral transformations: Laplace transformations and applications to differential equations, Fourier series, Fourier integrals; Fourier transforms, sine and cosine transforms; solution of PDE by Fourier transform. Group Theory: Groups, subgroups, conjugacy classes, cosets, invariant subgroups, factor groups, kernels, continuous groups, Lie groups, generators, SO(2) and SO(3),SU(2), crystallographic point groups. Texts: 1. J Brown and R V Churchill, Complex Variables and Applications, McGraw-Hill, 8th Edition (2008) 2. G B Arfken, H J Weber and F.E. Harris, Mathematical Methods for Physicists, Seventh Edition, Academic Press (2012) 3. A W Joshi, Elements of Group Theory, New Age International Publishers; Fifth edition (2018) References: 1. M L Boas, Mathematical Methods in Physical Sciences, John Wiley & Sons (2005) 2. P Dennery and A Krzywicki, Mathematics for Physicists, Dover Publications (1996) 3. Sneddon, Elements of Partial Differential Equations, McGraw Hill 5. T. Lawson, Linear Algebra, John Wiley & Sons (1996)