Subject description - A8B01MCM

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A8B01MCM Mathematics-Calculus m-D
Roles:P Extent of teaching:4P+2S
Department:13101 Language of teaching:CS
Guarantors:Tišer J. Completion:Z,ZK
Lecturers:Bohata M., Tišer J. Credits:7
Tutors:Bohata M. Semester:L

Web page:

https://moodle.fel.cvut.cz/course/view.php?id=6317

Anotation:

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.

Study targets:

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.

Content:

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.

Course outlines:

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.

Exercises outline:

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.

Literature:

[1] Stewart J.: 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

Requirements:

https://moodle.fel.cvut.cz/course/view.php?id=6317

Keywords:

Partial derivatives, Lagrange multipliers, mulidimensional integrals, Gauss, Green and Stokes Theorems.

Subject is included into these academic programs:

Program Branch Role Recommended semester
BPOES_2020 Common courses P 2
BPOES Common courses P 2

Page updated 26.3.2025 17:51:06, semester: Z,L/2025-6, Z,L/2024-5, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)
Responsible person: prof. Ing. Jiří Jakovenko, Ph.D.