TOPICS:
Review of linear analysis, Calculus on normed spaces, Theory of monotone operators and fixed Point theorems, Solvability analysis of ordinary differential and integral equations; Mathematical theory of finite dimensional controls-controllability, observability and optimal control of linear & nonlinear systems; Elements of Sobolev spaces, Approximation theorems, Imbedding and compactness theorems; Linear eigenvalue problem-Krein-Rutman type problem, Mountain pass theorem with applications to nonlinear partial differential equations.