The course studies fundamental concepts of analysis and the calculus of functions of several variables.
Some basic concepts of linear functional analysis: bounded operators, compact operators, spectral theory for symmetric and compact operators, Hahn-Banach theorem, the open mapping and closed graph theorems.
Fundamental techniques and theories for partial differential equations of evolution. Application to basic examples: first-order equations, wave equation, heat equation. The Cauchy-Kowalevsky theorem, abstract problems of evolution.