Objective(s):
To develop the mathematical background of student in vectors, tensors, matrices and some of their uses in the world of physics, to give basic understanding of group theory and complex variables used in physics.
Partial Differential Equations:
Introduction to important PDEs in Physics (wave equation, diffusion equation, Poisson’s equation, Schrodinger’s equation), general form of solution, general and particular solutions (first order, inhomogeneous, second order), characteristics and existence of solutions, uniqueness of solutions, separation of variables in Cartesian coordinates, superposition of separated solutions, separation of variables in curvilinear coordinates, integral transform methods, Green’s functions.
Complex Analysis:
Review (polar form of complex numbers and de Moivre’s theorem, complex logarithms and powers), functions of a complex variable, Cauchy-Riemann conditions, power series in a complex variable and analytic continuation with examples, multi-valued functions and branch cuts, singularities and zeroes of complex functions, complex integration, Cauchy’s theorem, Cauchy’s integral formula, Laurent series and residues, residue integration theorem, definite integrals using contour integration.