 CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2021/2022

# Mathematics Analysis

Code Completion Credits Range
B6B01MAA Z,ZK 5 2P+2S+2D
The course cannot be taken simultaneously with:
Mathematical Analysis 1 (B0B01MA1)
Lecturer:
Natalie Žukovec (guarantor)
Tutor:
Natalie Žukovec (guarantor)
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:
https://moodle.fel.cvut.cz/courses/B6B01MAA
Time-table for winter semester 2021/2022:
 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 roomT2:C3-51Žukovec N.09:15–10:45(lecture parallel1parallel nr.101)DejviceT2:C3-51roomT2:C3-51Žukovec N.11:00–12:30(lecture parallel1parallel nr.102)DejviceT2:C3-51roomT2:C3-337Žukovec N.14:30–16:00(lecture parallel1)DejviceT2:C3-337 roomT2:A4-204Žukovec N.09:15–10:45(lecture parallel1parallel nr.103)DejviceUčebnaroomT2:C4-78Žukovec N.11:00–12:30(lecture parallel1parallel nr.104)DejviceT2:C4-78 roomT2:C4-78Žukovec N.09:15–10:45(lecture parallel1parallel nr.103)DejviceT2:C4-78
Time-table for summer semester 2021/2022:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2022-08-15
For updated information see http://bilakniha.cvut.cz/en/predmet3130506.html