Mathematical Analysis 1

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Code	Completion	Credits (ECTS)	Range	Language
B0B01MA1	Z,ZK	7	4P+2S	Czech

Relations:

During a review of study plans, the course B6B01MAA can be substituted for the course B0B01MA1.

During a review of study plans, the course B0B01MA1A can be substituted for the course B0B01MA1.

It is not possible to register for the course B0B01MA1 if the student is concurrently registered for or has already completed the course B0B01MA1A (mutually exclusive courses).

It is not possible to register for the course B0B01MA1 if the student is concurrently registered for or has previously completed the course A8B01MC1 (mutually exclusive courses).

It is not possible to register for the course B0B01MA1 if the student is concurrently registered for or has previously completed the course B6B01MAA (mutually exclusive courses).

Course guarantor:

Jiří Velebil

Lecturer:

Jiří Velebil

Tutor:

Pavel Berkman, Josef Dvořák, Petr Habala, Jiří Velebil

Supervisor:

Department of Mathematics

Synopsis:

The aim of the course is to introduce students to basics of differential and integral calculus of functions of one variable.

Requirements:

See web page.

Syllabus of lectures:

1.Real numbers. Elementary functions.

2. Limit and continuity of functions.

3. Derivative of functions, its properties and applications.

4. Mean value theorem. L'Hospital's rule, Taylor polynomial.

5. Local and global extrema and graphing functions.

6. Indefinite integral, basic integration methods.

7. Integration of rational and other types of functions.

8. Definite integral (using sums). Newton-Leibniz formula.

9. Improper integral. Application of integrals.

10. Sequences and their limits.

11. Rows, criteria of convergence.

12. Introduction to differential equations.

13. Other topics of mathematical analysis.

Syllabus of tutorials:

1.Real numbers. Elementary functions.

2. Limit and continuity of functions.

3. Derivative of functions, its properties and applications.

4. Mean value theorem. L'Hospital's rule, Taylor polynomial.

5. Local and global extrema and graphing functions.

6. Indefinite integral, basic integration methods.

7. Integration of rational and other types of functions.

8. Definite integral (using sums). Newton-Leibniz formula.

9. Improper integral. Application of integrals.

10. Sequences and their limits.

11. Rows, criteria of convergence.

12. Introduction to differential equations.

13. Other topics of mathematical analysis.

Study Objective:

The aim of the course is to introduce students to basics of differential and integral calculus of functions of one variable.

Study materials:

[1] J. Stewart, Single variable calculus, Seventh Edition, Brooks/Cole, 2012, ISBN 0538497831.

Note:

Further information:

https://moodle.fel.cvut.cz/courses/B0B01MA1

Time-table for winter semester 2026/2027:

	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	roomKN:A-311 Dvořák J. 12:45–14:15 (lecture parallel2 parallel nr.202) Karlovo nám. roomKN:A-311 Dvořák J. 16:15–17:45 (lecture parallel2 parallel nr.203) Karlovo nám. roomKN:A-311 Dvořák J. 14:30–16:00 (lecture parallel2 parallel nr.205) Karlovo nám.
Tue	roomKN:A-311 Habala P. 09:15–10:45 (lecture parallel2 parallel nr.208) Karlovo nám. roomKN:A-311 Habala P. 11:00–12:30 (lecture parallel2 parallel nr.201) Karlovo nám.
Wed	roomT2:C3-51 Berkman P. 11:00–12:30 (lecture parallel2 parallel nr.206) Dejvice roomT2:C3-51 Berkman P. 12:45–14:15 (lecture parallel2 parallel nr.204) Dejvice roomT4:D2-256 Velebil J. 16:15–17:45 (lecture parallel2) Dejvice
Thu	room 09:15–10:45 (lecture parallel2 parallel nr.207) roomT2:C4-364 11:00–12:30 (lecture parallel2 parallel nr.209) Dejvice roomT2:D3-309 Velebil J. 14:30–16:00 (lecture parallel2) Dejvice
Fri

Time-table for summer semester 2026/2027:

Time-table is not available yet

The course is a part of the following study plans:

Electrical Engineering, Power Engineering and Management - Applied Electrical Engineering 2016 (compulsory course in the program)
Electrical Engineering, Power Engineering and Management - Electrical Engineering and Management (compulsory course in the program)
Cybernetics and Robotics 2016 (compulsory course in the program)
Open Informatics - Computer Science 2016 (compulsory course in the program)
Open Informatics - Internet of Things 2016 (compulsory course in the program)
Open Informatics - Software 2016 (compulsory course in the program)
Open Informatics - Computer Games and Graphics 2016 (compulsory course in the program)
Electrical Engineering, Power Engineering and Management (compulsory course in the program)
Open Informatics (compulsory course in the program)
Open Informatics (compulsory course in the program)
Open Informatics - Artificial Intelligence and Computer Science 2018 (compulsory course in the program)
Open Informatics - Internet of Things 2018 (compulsory course in the program)
Open Informatics - Software 2018 (compulsory course in the program)
Open Informatics - Computer Games and Graphics 2018 (compulsory course in the program)
Cybernetics and Robotics 2021 (compulsory course in the program)
Open Informatics (compulsory course in the program)
Open Informatics - Artificial Intelligence and Computer Science 2025 (compulsory course in the program)
Open Informatics - Internet of Things 2025 (compulsory course in the program)
Open Informatics - Software 2025 (compulsory course in the program)
Open Informatics - Computer Games and Graphics 2025 (compulsory course in the program)