Syllabus
More details of integrals of functions of one variable: partial fractions decomposition, simple standard substitutions, fundamental theorem of calculus.
Integrals of functions of several variables: Riemann's integral on a box, Fubini's theorem, calculation by repeated integration.
Differential calculus of functions of several variables:
- Partial derivatives, differential, C^1 functions.
- Rules for calculation (chain rule).
- Use: extremes on an open set, saddle points classification, implicitly defined functions, constrained extremes (Lagrange multipliers).
- Informatively line integral.
- Extremes of continuous function on a compact set.
Metric spaces: a framework for the whole analysis, limits, continuity, informatively topology.
Annotation
The second part of the mathematical analysis course for students of computer science with the focus on the differential function of several variables.
Students will learn to use partial derivatives and differentials to analyze multivariate functions (extremes, approximations).
The knowledge of integrals obtained in Mathematical Analysis 1 will be deepened and extended.
A comprehensive framework for the whole study will be provided by a study of metric spaces.
It will be assumed that the students understand material covered by Mathematical Analysis 1.