Real Analysis: Series and sequences, limits, continuity and derivatives of functions, closed and open sets, compactness, metric spaces, uniform convergence. Convex Analysis: Algebra of convex sets, convex functions and their properties. Linear Algebra: Algebraic structures, vector spaces, linear transformations, canonical forms, solution of linear systems of equations, techniques for Eigenvalue extraction, iterative solvers. Introduction to variational calculus: Weighted residual technique, numerical integration, integral transforms, solution of differential and partial differential equations using integral transforms. Introduction to Partial Differential Equations (PDE), linear convection (First order wave) equation, method of characteristics. Non-linear convection equation (Burgers equation): Discontinuous solutions and expansion waves, Riemann problem, Hyperbolic Systems of PDEs, Parabolic PDEs, Elliptic PDEs.
David Logan J., An Introduction to Nonlinear PDEs, 2nd edition, Wiley Interscience. Courant R.and Hilbert D., Methods of Mathematical Physics, Wiley-VCH. Gilbert Strang, Introduction to Applied Mathematics, Wellesley Cambridge Press.
S. V. Raghurama Rao, S. Gopalakrishnan and D. Ghose