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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2018/2019

Mathematical Analysis 2

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Code Completion Credits Range Language
B0B01MA2A Z,ZK 6 4+2 Czech
Lecturer:
Petr Hájek (guarantor)
Tutor:
Petr Hájek (guarantor), Jaroslav Tišer (guarantor), Josef Hekrdla, 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://math.feld.cvut.cz/hajek/teaching.html
Time-table for winter semester 2018/2019:
Time-table is not available yet
Time-table for summer semester 2018/2019:
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
Hájek P.
14:30–16:00
(lecture parallel1)
Dejvice
Posluchárna
roomT2:C4-364

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:A4-202a
Žukovec N.
12:45–14:15
(lecture parallel1
parallel nr.103)

Dejvice
Ucebna
roomT2:C4-364
Žukovec N.
14:30–16:00
(lecture parallel1
parallel nr.104)

Dejvice
Cvicebna
roomT2:C4-364
Žukovec N.
16:15–17:45
(lecture parallel1
parallel nr.105)

Dejvice
Cvicebna
Fri
roomT2:D2-256
Hájek P.
08:15–10:00
(lecture parallel1)
Dejvice
Posluchárna
Thu
roomT2:C3-54

11:00–12:30
(lecture parallel1
parallel nr.106)

Dejvice
Posluchárna
roomT2:C3-54
Hekrdla J.
12:45–14:15
(lecture parallel1
parallel nr.107)

Dejvice
Posluchárna
roomT2:C3-54
Hekrdla J.
14:30–16:00
(lecture parallel1
parallel nr.108)

Dejvice
Posluchárna
roomT2:C3-54
Hekrdla J.
16:15–17:45
(lecture parallel1
parallel nr.109)

Dejvice
Posluchárna
Fri
The course is a part of the following study plans:
Data valid to 2019-06-16
For updated information see http://bilakniha.cvut.cz/en/predmet5605406.html