**Course Program**

In common with the course "Analysis for Biology":

Logic, sets, relations and functions, cartesian product of sets

Natural numbers and the induction principle, integers, rationals and basic operations, decimal expression, real numbers, complex numbers.

Sequences and series, convergence criteria

In common with the course "Complementary Topics of Mathematics" for students in Mathematics and Physics:

Topology of Rn.

Metric spaces, completeness and the contraction theorem.

Sequences and series of functions, pointwise and uniform convergence.

Power series. Limits of derivatives and integrals.

Functions of several real variables. Partial and directional derivatives. Differential. Total

differential theorem. Hessian matrix.

A few hints on functions from Rn to Rm, Jacobian matrix, differentiation of composite functions.

Implicit functions. Regular curves. Conservative vector fields and potentials.

Differential equations and Cauchy problems. Local existence and uniqueness theorem. Linear differential equations and systems.

**Exam**Written and oral exam

**Prerequisites**

First year students in Chemistry