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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2016/2017

Calculus 2

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Code Completion Credits Range Language
BE5B01MA2 Z,ZK 7 4+2
Lecturer:
Paola Vivi
Tutor:
Paola Vivi
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. Fourier series are also introduced.

Requirements:

http://math.feld.cvut.cz/vivi/BE5B01MA2.pdf

Syllabus of lectures:

1. Real plane, three dimensional analytic geometry, vector functions.

2. Functions of several variables: limits, continuity.

3. Directional and partial derivative, tangent plane, gradient.

4. Derivative of a composition of functions, higher order derivatives.

5. Local extrema, Lagrange multipliers.

6. Double integral, Fubini's Theorem. Polar coordinates.

7. Triple integrals. Cylindrical and spherical coordinates. Change of variables in multiple integrals.

8. Space curves. Line integrals.

9. Potential of a vector field. Fundamental Theorem for line integrals. Green's Theorem.

10. Parametric surfaces and their area. Surface integrals.

11. Curl and divergence. Gauss, and Stokes theorem and their applications.

12. Fourier series.

13. Sine and cosine Fourier series.

Syllabus of tutorials:

1. Real plane, three dimensional analytic geometry, vector functions.

2. Functions of several variables: limits, continuity.

3. Directional and partial derivative, tangent plane, gradient.

4. Derivative of a composition of functions, higher order derivatives.

5. Local extrema, Lagrange multipliers.

6. Double integral, Fubini's Theorem. Polar coordinates.

7. Triple integrals. Cylindrical and spherical coordinates. Change of variables in multiple integrals.

8. Space curves. Line integrals.

9. Potential of a vector field. Fundamental Theorem for line integrals. Green's Theorem.

10. Parametric surfaces and their area. Surface integrals.

11. Curl and divergence. Gauss, and Stokes theorem and their applications.

12. Fourier series.

13. Sine and cosine 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. L. Gillman, R. H. McDowell, Calculus, W.W.Norton & Co.,New York, 1973

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

http://math.feld.cvut.cz/vivi/

Note:
Further information:
http://math.feld.cvut.cz/vivi/
Time-table for winter semester 2016/2017:
Time-table is not available yet
Time-table for summer semester 2016/2017:
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:A4-202b
Vivi P.
12:45–14:15
(lecture parallel1)
Dejvice
Učebna
Tue
Fri
Thu
roomT2:A4-202b
Vivi P.
09:15–10:45
(lecture parallel1)
Dejvice
Učebna
roomT2:A4-202b
Vivi P.
11:00–12:30
(lecture parallel1
parallel nr.101)

Dejvice
Učebna
Fri
The course is a part of the following study plans:
Data valid to 2017-09-24
For updated information see http://bilakniha.cvut.cz/en/predmet4355906.html