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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

Mathematics Analyze

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Code Completion Credits Range
BD6B01MAA Z,ZK 5 14KP+6KC
Lecturer:
Natalie Žukovec
Tutor:
Natalie Žukovec
Supervisor:
Department of Mathematics
Synopsis:

This course is an introduction to differential and integral calculus. It covers basic properties of functions, limits of functions, derivative and its applications (graphing, Taylor polynomial) and definite/indefinite integral with its applications, sequences and series.

Requirements:

High-school mathematics.

Syllabus of lectures:

1. Introduction to calculus.

2. Real numbers, basic mathematical terminology.

3. Functions, elementary functions.

4. Limit of a function, continuity.

5. Derivative, properties and interpretations.

6. L'Hospital's rule, the Taylor polynomial.

7. Extrema of functions. Graph sketching.

8. Indefinite integral (antiderivative), basic methods.

9. Integrating rational functions using partial fractions.

10. Definite integral, properties and evaluation.

11. Improper integral, applications of integral.

12. Sequences.

13. Series.

Syllabus of tutorials:

Practical classes follow lectures thematically. While on lectures, the focus is on understanding of notions and on justifications of validity of claims, in exercises students learn to solve routine problems.

1. Introduction to calculus.

2. Real numbers, basic mathematical terminology.

3. Functions, elementary functions.

4. Limit of a function, continuity.

5. Derivative, properties and interpretations.

6. L'Hospital's rule, the Taylor polynomial.

7. Extrema of functions. Graph sketching.

8. Indefinite integral (antiderivative), basic methods.

9. Integrating rational functions using partial fractions.

10. Definite integral, properties and evaluation.

11. Improper integral, applications of integral.

12. Sequences.

13. Series.

Study Objective:
Study materials:

1. M. Demlová, J. Hamhalter: Calculus I. ČVUT Praha, 1994

2. P. Pták: Calculus II. ČVUT Praha, 1997.

3. Math Tutor http://math.feld.cvut.cz/mt

Note:
Further information:
http://math.feld.cvut.cz/0educ/pozad/bd6b01maa.htm
Time-table for winter semester 2019/2020:
06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
Tue
Fri
Thu
Fri
roomKN:E-127
Žukovec N.
12:45–14:15
EVEN WEEK

(lecture parallel1)
Karlovo nám.
Kotkova cvičebna K4
Time-table for summer semester 2019/2020:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2020-06-03
For updated information see http://bilakniha.cvut.cz/en/predmet4471406.html