Course objectives

Students will learn the notions and procedures used in the investigation of the behaviour of functions (local extremes, convex function and concave function and their geometrical interpretations). Furthermore, they will learn the meanings of the antiderivative, indefinite integral, method of integration by parts, method of integration by substitution, integration of rational functions, and Riemann’s definite integral and its application. Infinite number series, power series and the development of functions into series will also be presented to the students. The last topic are functions of several variables, particularly partial derivatives and finding extrema.

Learning outcomes

At the end of the course students will be able to: -find local extremes and intervals of monotony of a function -find points of inflection and intervals of convexity and concavity of a function -evaluate an indefinite integral (by parts, by substitution), definite integral and describe its applications -describe basic properties of infinite series and power series -find local extremes of a function of two variables

Teaching methods

PS: (full time students) 2 hours per week of lectures and 2 hours per week of seminars (2/2); KS: (part time students) 12 seminars (90 min each). Lectures for present studies will be split into theoretical as well as practical part. Theoretical parts will be always explained on practical examples. Even more interactive form of study is applied in KS (part time study). Students in full time study program should attend 75% of seminars as a minimum. Students in part time study program should attend 50% of seminars as a minimum.

Assessment methods

Compulsory seminar participation is 75% in full-time study. The subject is completed by credit test and written examination. Passing a written test (min. 60%) is required to award the credit. Prerequisite for taking the exam is the credit. Grading will be based on an individual written examination.