The objective of this course is to provide the main concepts and fundamental methods of Functional Analysis to enable a student to treat various concrete problems arising in applied mathematics and engineering like PDEs, integral equations, best approximation problems, control theory, calculus of variations, numerical analysis.
Metric & Normed spaces. Uniform convergence and spaces of continuous functions. Compactness in infinite dimension. Lebesgue integral, Lp-spaces. Linear Operators, cornerstone theorems of FA. Dual Spaces, weak convergence. Hilbert Spaces, Fourier series. Adjoint operators. Compact operators. Introduction to spectral theory. Introduction to operator semigroups. Applications to PDE, integral equations, calculus of variations, and numerical analysis.
Linear Algebra. Complex numbers. Differential and integral calculus of functions of real variables.