CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2023/2024

# Mathematical Analysis 2

Code Completion Credits Range Language
B0B01MA2A Z,ZK 6 4P+2S Czech
Vztahy:
It is not possible to register for the course B0B01MA2A if the student is concurrently registered for or has already completed the course B0B01MA2 (mutually exclusive courses).
It is not possible to register for the course B0B01MA2A if the student is concurrently registered for or has previously completed the course B0B01MA2 (mutually exclusive courses).
The requirement for course B0B01MA2A can be fulfilled by substitution with the course BE5B01MA2.
Garant předmětu:
Petr Hájek, Jaroslav Tišer
Lecturer:
Jaroslav Tišer
Tutor:
Martin Bohata, Martin Křepela, Zdeněk Mihula, Karel Pospíšil, Veronika Sobotíková, Jaroslav Tišer
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:
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. J. Stewart.: Calculus, Seventh Edition, Brooks/Cole, 2012, 1194 p., ISBN 0-538-49781-5.

2. L. Gillman, R. H. McDowell: Calculus, W.W.Norton &amp; Co.,New York, 1973

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

Note:
Further information:
https://moodle.fel.cvut.cz/course/view.php?id=6317
Time-table for winter semester 2023/2024:
Time-table is not available yet
Time-table for summer semester 2023/2024:
 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 roomT4:D2-256Tišer J.14:30–16:00(lecture parallel1)DejvicePosluchárna 256roomT2:C4-364Tišer J.16:15–17:45(lecture parallel1parallel nr.101)DejviceCvicebnaroom18:00–19:30(lecture parallel1parallel nr.102) roomT2:C3-51Křepela M.12:45–14:15(lecture parallel1parallel nr.103)DejviceT2:C3-51roomT2:C3-51Sobotíková V.14:30–16:00(lecture parallel1parallel nr.104)DejviceT2:C3-51roomT2:C3-54Sobotíková V.16:15–17:45(lecture parallel1parallel nr.105)DejviceT2:C3-54 roomT4:D2-256Tišer J.09:15–10:45(lecture parallel1)DejvicePosluchárna 256roomT2:C4-459Tišer J.11:00–12:30(lecture parallel1parallel nr.110)DejviceLaborator počítače roomT2:C4-78Pospíšil K.11:00–12:30(lecture parallel1parallel nr.106)DejviceT2:C4-78roomT2:C4-78Pospíšil K.12:45–14:15(lecture parallel1parallel nr.107)DejviceT2:C4-78roomT2:C4-36514:30–16:00(lecture parallel1parallel nr.108)DejviceCvičebnaroomT2:C3-54Pospíšil K.16:15–17:45(lecture parallel1parallel nr.109)DejviceT2:C3-54 roomT2:C3-135Pospíšil K.16:15–17:45(lecture parallel1parallel nr.109)DejviceT2:C3-135
The course is a part of the following study plans:
Data valid to 2024-07-15
Aktualizace výše uvedených informací naleznete na adrese https://bilakniha.cvut.cz/en/predmet5605406.html