TOPICS:
Multi-variable Calculus(Implicit and Inverse function theorems, Gauss-Greens theorems), Analysis (Ascoli-Arzela theorem, elements of measure theory, L^2 space); Ordinary Differential Equations (existence theory & stability results); Partial Differential Equations (First order linear & nonlinear hyperbolic PDEs, Second order linear elliptic & parabolic PDEs (Green's function with properties, maximum principle etc.), wave equation (d'Alembert formula, reflection principle etc.)); Mathematical Modeling (basics of modeling with examples from industrial problems); Finite Difference Methods for PDEs with hands on computing (stability, consistency and convergence of numerical schemes for PDEs; iterative methods like Jacobi, Gauss-Seidel and SOR).