Mathematics Analysis

Code	Completion	Credits	Range
B6B01MAA	Z,ZK	5	2P+2S+2D

The course cannot be taken simultaneously with:

Mathematical Analysis 1 (B0B01MA1)
Mathematical Analysis 1 (B0B01MA1A)

Garant předmětu:

Natalie Žukovec

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:

https://moodle.fel.cvut.cz/courses/B6B01MAA

Time-table for winter semester 2022/2023:

	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
Wed
Thu	roomT2:C3-51 Žukovec N. 09:15–10:45 (lecture parallel1 parallel nr.101) Dejvice T2:C3-51roomT2:C3-51 Žukovec N. 11:00–12:30 (lecture parallel1 parallel nr.102) Dejvice T2:C3-51roomT2:C3-340 Žukovec N. 14:30–16:00 (lecture parallel1) Dejvice T2:C3-340
Fri	roomT2:C4-78 Žukovec N. 09:15–10:45 (lecture parallel1 parallel nr.103) Dejvice T2:C4-78roomT2:C4-78 11:00–12:30 (lecture parallel1 parallel nr.104) Dejvice T2:C4-78

Time-table for summer semester 2022/2023:

Time-table is not available yet

The course is a part of the following study plans:

Software Engineering and Technology (compulsory course in the program)
Software Engineering and Technology (compulsory course in the program)
Software Engineering and Technology (compulsory course in the program)
Software Engineering and Technology (compulsory course in the program)
Software Engineering and Technology (compulsory course in the program)
Software Engineering and Technology (compulsory course in the program)