Logo ČVUT
CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

Mathematical Analysis 2

Login to KOS for course enrollment Display time-table
Code Completion Credits Range Language
B0B01MA2A Z,ZK 6 4P+2S Czech
The course cannot be taken simultaneously with:
Mathematical Analysis 2 (B0B01MA2)
Lecturer:
Jaroslav Tišer (guarantor)
Tutor:
Jaroslav Tišer (guarantor), Martin Bohata, Josef Hekrdla, Martin Křepela, Paola Vivi, Natalie Žukovec
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. Basic convergence tests for series.

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

3. Standard Taylor expansions. Fourier series.

4. Functions of more variables, limit, continuity.

5. Directional and partial derivatives - gradient.

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

7. Jacobiho matrix. Local extrema.

8. Extrema with constraints. Lagrange multipliers.

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

10. Path integral and its applications.

11. Surface integral and its applications.

12. The Gauss, Green, and Stokes theorems.

13. Potential of vector fields.

Syllabus of tutorials:

1. Basic convergence tests for series.

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

3. Standard Taylor expansions. Fourier series.

4. Functions of more variables, limit, continuity.

5. Directional and partial derivatives - gradient.

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

7. Jacobiho matrix. Local extrema.

8. Extrema with constraints. Lagrange multipliers.

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

10. Path integral and its applications.

11. Surface integral and its applications.

12. The Gauss, Green, and Stokes theorems.

13. Potential of vector fields.

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 & Co.,New York, 1973

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

Note:
Further information:
https://moodle.fel.cvut.cz/courses/B0B01MA2A
Time-table for winter semester 2019/2020:
Time-table is not available yet
Time-table for summer semester 2019/2020:
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:D2-256
Tišer J.
14:30–16:00
(lecture parallel1)
Dejvice
T2:D2-256
roomT2:C4-364
Tišer J.
Křepela M.

16:15–17:45
(lecture parallel1
parallel nr.101)

Dejvice
Cvicebna
roomT2:C4-364

18:00–19:30
(lecture parallel1
parallel nr.102)

Dejvice
Cvicebna
Tue
roomT2:C3-51
Křepela M.
Tišer J.

12:45–14:15
(lecture parallel1
parallel nr.103)

Dejvice
T2:C3-51
roomT2:C3-51
Křepela M.
Tišer J.

14:30–16:00
(lecture parallel1
parallel nr.104)

Dejvice
T2:C3-51
roomT2:A4-202a
Žukovec N.
16:15–17:45
(lecture parallel1
parallel nr.105)

Dejvice
Ucebna
Fri
roomT2:D2-256
Tišer J.
08:15–10:00
(lecture parallel1)
Dejvice
T2:D2-256
roomT2:A4-204
Tišer J.
Křepela M.

11:00–12:30
(lecture parallel1
parallel nr.110)

Dejvice
Učebna
Thu
roomT2:C4-78
Bohata M.
11:00–12:30
(lecture parallel1
parallel nr.106)

Dejvice
T2:C4-78
roomT2:C4-78
Bohata M.
12:45–14:15
(lecture parallel1
parallel nr.107)

Dejvice
T2:C4-78
roomT2:A4-203b
Vivi P.
14:30–16:00
(lecture parallel1
parallel nr.108)

Dejvice
Učebna
roomT2:C3-54

16:15–17:45
(lecture parallel1
parallel nr.109)

Dejvice
T2:C3-54
Fri
The course is a part of the following study plans:
Data valid to 2020-07-07
For updated information see http://bilakniha.cvut.cz/en/predmet5605406.html