Mathematical Analysis 1

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 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 B6B01MAA (mutually exclusive courses).

Course guarantor:

Josef Tkadlec

Lecturer:

Martin Křepela, Josef Tkadlec

Tutor:

Josef Dvořák, Miroslav Korbelář, Martin Křepela, Veronika Sobotíková, Josef Tkadlec

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 2024/2025:

	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	roomT2:C4-363 Tkadlec J. 12:45–14:15 (lecture parallel2 parallel nr.207) Dejvice roomT2:C4-363 Tkadlec J. 14:30–16:00 (lecture parallel2 parallel nr.206) Dejvice
Tue	roomT2:C2-85 Korbelář M. 11:00–12:30 (lecture parallel2 parallel nr.203) Dejvice roomT2:C2-85 Korbelář M. 12:45–14:15 (lecture parallel2 parallel nr.208) Dejvice roomT2:D3-209 Křepela M. 14:30–16:00 (lecture parallel2) Dejvice
Wed	roomT2:C3-51 Křepela M. 09:15–10:45 (lecture parallel2 parallel nr.204) Dejvice roomT2:C3-51 Křepela M. 11:00–12:30 (lecture parallel2 parallel nr.205) Dejvice roomT4:D2-256 Křepela M. 16:15–17:45 (lecture parallel2) Dejvice roomT2:C4-78 09:15–10:45 (lecture parallel2 parallel nr.209) Dejvice
Thu	roomT2:C2-85 Tkadlec J. 09:15–10:45 (lecture parallel2 parallel nr.201) Dejvice roomT2:C2-85 Tkadlec J. 11:00–12:30 (lecture parallel2 parallel nr.202) Dejvice
Fri	roomT2:D3-309 Křepela M. 11:00–12:30 (lecture parallel2) Dejvice

Time-table for summer semester 2024/2025:

	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	roomT2:C3-54 Sobotíková V. 12:45–14:15 (lecture parallel1 parallel nr.102) Dejvice T2:C3-54roomT2:C3-54 14:30–16:00 (lecture parallel1 parallel nr.101) Dejvice T2:C3-54
Tue	roomT2:C3-51 Sobotíková V. 09:15–10:45 (lecture parallel1 parallel nr.111) Dejvice roomT2:C4-155 Sobotíková V. 11:00–12:30 (lecture parallel1 parallel nr.112) Dejvice
Wed	roomT4:D2-256 Tkadlec J. 11:00–12:30 (lecture parallel1) Dejvice
Thu	roomT2:C3-52 Dvořák J. 12:45–14:15 (lecture parallel1 parallel nr.106) Dejvice roomT2:C3-52 Dvořák J. 14:30–16:00 (lecture parallel1 parallel nr.107) Dejvice
Fri	roomT2:D3-309 Tkadlec J. 09:15–10:45 (lecture parallel1) Dejvice roomT2:C4-155 Tkadlec J. 12:45–14:15 (lecture parallel1 parallel nr.109) Dejvice roomT2:C4-155 Tkadlec J. 14:30–16:00 (lecture parallel1 parallel nr.110) Dejvice

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 2016 (compulsory course in the program)