Courses

Topological vector spaces, Banach spaces, nonlinear analysis. We start with the introduction of the topological vector spaces and prove their basic properties. We introduce the normed spaces, we define the metric produced via norm and give the definition of the Banach spaces. Then we discuss the theory of the bounded linear operators. We present the basic theorems of functional analysis such as the Banach-Steinhaus, open mapping and closed graph theorems. We make the introduction to the theory of Lebesgue integral and the theory of Sobolev spaces. We define the norm, strong and weak convergence of the sequence of opera- tors in normed spaces. Finally we give the introduction to nonlinear analysis.