250027 VO Analysis 2 (2024S)

The course is a continuation of Analysis 1. A rough plan for the course is as follows:

- Normed vector spaces and their topology, especially in the finite-dimensional case (all norms are equivalent). Continuity, completeness, Banach fixed point theorem.
- Sequences and series of functions (pointwise and uniform convergence), completeness of the topology of uniform convergence. Differentiation of a limit of functions.
- Power series, Weierstrass' M-test.
- Differentiability of functions of several variables (partial derivatives and differentiability, Taylor's theorem in several variables), local extrema with and without constraints, implicit functions theorem, inverse functions theorem,
- Ordinary differential equations (initial value problems, Picard-Lindelöf theorem, Picard iteration).