1. komponenta

Lecture type	Total
Lectures	45
Exercises	60

* Load is given in academic hour (1 academic hour = 45 minutes)

COURSE AIMS AND OBJECTIVES: To familiarize students with the basics of differential and integral calculus in R. Rigorous mathematical concepts are introduced.

COURSE DESCRIPTION AND SYLLABUS:
1. Derivative. Motivation (geometry, physics) and definition of derivative, connection between derivability and continuity, basic rules for differentiation, derivative of elementary functions. Rolle's and Lagrange's middle value theorem, monotony, local extremes. Derivatives of higher order, Taylor's middle value theorem, convex functions, inflection. Asymptotes, analysis of function flow and graph of function. Some applications. (5 weeks)
2. Integrals. Motivation (plane area, work done by a force) and definition of Riemann integral. Integrability, monotony and continuous functions. Primitive function, Newton - Leibniz formula. Substitution, partial integration, integration of rational functions. Improper integrals. (5 weeks)
3. Series. Definition, criteria of convergence. Power series, Taylor series. Uniform convergence, function series. (3 weeks)

Enrollment :
Passed : Mathematical analysis 1

Mandatory course - Mandatory studij - Mathematics