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Limits of infinite sequences. Infinite series - definition and convergence criteria.
Applications of differential calculus of functions of one variable. L'Hospital's Rule, Taylor's formula.
Integral - methods of integration. Riemann integral, improper integrals.
Relations, equivalence relations, mappings.
Metric spaces.
Limits and continuity of mappings. The properties of continuous mappings.
The convergence and the limit of sequences of mapping.
Power series, Taylor series.
Multi variable functions: the domain, level curves, continuity, differentiablity.
Applications of the derivative of multi variable function, gradient. The second derivative and its applications: the local extrema, the constrained local extrema, the global extrema.
Applications of derivatives: invertible mapping, implicit mapping.
Elements of measure theory: algebra and sigma-algebra, premeasure and measure, Lebesgue measure.
Measurable functions, Lebesgue integral of measurable functions.
Lebesgue integral and its properties.
Multiple integrals, change of variables theorem.
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