Syllabus
* Series
(a) Convergence, divergence, necessary condition of convergence, harmonic series.
(b) Criteria of convergence.
(c) Riemann theorem.
(d) Cauchy product, Mertens theorem.
(e) Complex series.
* Integral.
(a) Basic properties of antiderivatives, substitution theorem, Darboux property of derivative, integration by parts.
(b) Integration of rational functions.
(c) Riemann integral.
(d) Newton integral.
(e) Convergence of Newton integral.
(f) Applications of integral.
* Ordinary differential equations
(a) Differential equations with separated variables.
(b) Linear differential equations of the first order.
(c) Lineární differential equations of n-th order with constant coefficients.
(d) Systems of differential equations: Peano theorem, Picard theorem.
(e) Systems of linear differential equations.
Annotation
The second part of a four-semester course in mathematical analysis for bachelor's programs General Mathematics and Information Security.