 CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2021/2022

# Mathematics-Calculus m-D

Code Completion Credits Range Language
A8B01MCM Z,ZK 7 4P+2S Czech
The course cannot be taken simultaneously with:
Mathematics 2 (A3B01MA2)
Lecturer:
Petr Hájek, Jaroslav Tišer (guarantor)
Tutor:
Petr Hájek, Jaroslav Tišer (guarantor), Martin Křepela
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:

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

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

 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 2021/2022:
Time-table is not available yet
Time-table for summer semester 2021/2022:
 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 256 roomT4:D2-256Tišer J.09:15–10:45(lecture parallel1)DejvicePosluchárna 256roomT2:A4-204Křepela M.11:00–12:30(lecture parallel1parallel nr.101)DejviceUčebna
The course is a part of the following study plans:
Data valid to 2022-08-15
For updated information see http://bilakniha.cvut.cz/en/predmet2665506.html