Mathematical Analysis 2

Code	Completion	Credits	Range	Language
B0B01MA2	Z,ZK	7	4P+2S	Czech

Vztahy:

It is not possible to register for the course B0B01MA2 if the student is concurrently registered for or has already completed the course B0B01MA2A (mutually exclusive courses).

It is not possible to register for the course B0B01MA2 if the student is concurrently registered for or has previously completed the course B0B01MA2A (mutually exclusive courses).

Garant předmětu:

Jaroslav Tišer

Lecturer:

Petr Hájek

Tutor:

Petr Hájek, Miroslav Korbelář, Karel Pospíšil

Supervisor:

Department of Mathematics

Synopsis:

The subject covers an introduction to the

differential and integral calculus in

several variables and basic relations between curve and surface integrals.

Other part contains function series and power series with application to Taylor and

Fourier series.

Requirements:

https://moodle.fel.cvut.cz/course/view.php?id=6317

Syllabus of lectures:

1. Functions of more variables, limit, continuity.

2. Directional and partial derivatives - gradient.

3. Derivative of a composition of function, higher order derivatives.

4. Jacobiho matrix. Local extrema.

5. Extrema with constraints. Lagrange multipliers.

6. Double and triple integral - Fubini theorem and theorem on substitution.

7. Path integral and its applications.

8. Surface integral and its applications.

9. The Gauss, Green, and Stokes theorems.

10. Potential of vector fields.

11. Basic convergence tests for series.

12. Series of functions, the Weierstrass test. Power series.

13. Standard Taylor expansions. Fourier series.

Syllabus of tutorials:

1. Functions of more variables, limit, continuity.

2. Directional and partial derivatives - gradient.

3. Derivative of a composition of function, higher order derivatives.

4. Jacobiho matrix. Local extrema.

5. Extrema with constraints. Lagrange multipliers.

6. Double and triple integral - Fubini theorem and theorem on substitution.

7. Path integral and its applications.

8. Surface integral and its applications.

9. The Gauss, Green, and Stokes theorems.

10. Potential of vector fields.

11. Basic convergence tests for series.

12. Series of functions, the Weierstrass test. Power series.

13. Standard Taylor expansions. Fourier series.

Study Objective:

The aim of the course is to introduce students to basics of differential and integral calculus of functions of more variables and theory of series.

Study materials:

[1] Stewart J.: Calculus, Seventh Edition, Brooks/Cole, 2012, 1194 p., ISBN 0-538-49781-5.

[2] L. Gillman, R. H. McDowell, Calculus, W.W.Norton & Co.,New York, 1973

[3] S. Lang, Calculus of several variables, Springer Verlag, 1987

Note:

Further information:

https://moodle.fel.cvut.cz/courses/B0B01MA2

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:C4-364 Korbelář M. 09:15–10:45 (lecture parallel1 parallel nr.109) Dejvice CvicebnaroomT2:C4-365 Korbelář M. 11:00–12:30 (lecture parallel1 parallel nr.101) Dejvice CvičebnaroomT2:C3-54 Korbelář M. 12:45–14:15 (lecture parallel1 parallel nr.102) Dejvice T2:C3-54roomT2:C3-135 Hájek P. 16:15–17:45 (lecture parallel1) Dejvice T2:C3-135 roomT2:D3-209 Hájek P. 16:15–17:45 (lecture parallel1) Dejvice T2:D3-209
Tue
Wed
Thu	roomT2:C4-364 Korbelář M. 09:15–10:45 (lecture parallel1 parallel nr.103) Dejvice CvicebnaroomT2:C4-78 Korbelář M. 11:00–12:30 (lecture parallel1 parallel nr.104) Dejvice T2:C4-78roomT2:C3-51 Korbelář M. 16:15–17:45 (lecture parallel1 parallel nr.105) Dejvice T2:C3-51 roomT2:D3-309 Hájek P. 12:45–14:15 (lecture parallel1) Dejvice T2:D3-309
Fri

Time-table for summer semester 2024/2025:

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)
Medical electronics and bioinformatics (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)