Lecturer(s)


Burkotová Jana, Mgr. Ph.D.

Fürst Tomáš, RNDr. Ph.D.

Tomeček Jan, doc. RNDr. Ph.D.

Fišer Jiří, RNDr. Ph.D.

Ligurský Tomáš, RNDr. Ph.D.

Kouřilová Pavla, Mgr. Ph.D.

Course content

1. Introduction: On the structure of mathematics, sets, basic logic. 2. Sequences: The notion of limits, theorems on limits, boundedness and convergence. 3. Functions: The notion of functions, continuity, properties of continuous functions, limits, limits of composite functions, elementary functions. 4. Differentiation: Relation to limits and continuity, the differential of a function, mean value theorems, Taylor's polynomials, L'Hospital's rule. 5. Integration: Motivation, Newton's formula and the relation to differentiation, primitive functions, integration by parts, integration by substitution, integration of rational functions, more on integration techniques, the Riemann integral and the proof of Newton's formula. 6. Applications: Length, surface, volume, center of gravity, moment of inertia, numerical methods.

Learning activities and teaching methods

Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming)
 Attendace
 78 hours per semester
 Preparation for the Course Credit
 40 hours per semester
 Preparation for the Exam
 60 hours per semester
 Homework for Teaching
 30 hours per semester

Learning outcomes

Understand differential calculus of functions of a single real variable
Comprehension Understand the mathematical tools of differential and integral calculus of functions of a single variable.

Prerequisites

Grammar school mathematics

Assessment methods and criteria

Oral exam, Written exam
Credit: the student has to pass two written tests (i.e. to obtain at least half of the possible points in each test).

Recommended literature


J. Kopáček. (2005). Matematická analáza pro fyziky I. Matfyzpress, Praha.

J. Veselý. (2001). Matematická analýza pro učitele I. Matfyzpress.
