Subject description - AE1B01MA2

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AE1B01MA2 Multidimensional Analysis Extent of teaching:2+2
Guarantors:  Roles:P,V Language of
teaching:
EN
Teachers:  Completion:Z,ZK
Responsible Department:13101 Credits:6 Semester:L

Anotation:

The aim of the course is to introduce students to basics of differential and integral calculus of functions of more variables and to basics of series of numbers and functions.

Course outlines:

1. Functions of more variables: Limit, continuity.
2. Directional and partial derivative - gradient.
3. Derivative of a composition of functions, higher order derivatives.
4. Jacobi 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 theorem. Potential of a vector field.
10. Basic convergence tests for series of numbers.
11. Series of functions, the Weirstrasse test.
12. Power series, radius of convergence. Taylor series.
13. Fourier series.

Exercises outline:

1. Functions of more variables: Limit, continuity.
2. Directional and partial derivative - gradient.
3. Derivative of a composition of functions, higher order derivatives.
4. Jacobi 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 theorem. Potential of a vector field.
10. Basic convergence tests for series of numbers.
11. Series of functions, the Weirstrasse test.
12. Power series, radius of convergence. Taylor series.
13. Fourier series.

Literature:

1. L. Gillman, R. H. McDowell, Calculus, W. W. Norton & Co., New York, 1973.
2. S. Lang, Calculus of several variables, Springer Verlag, 1987.

Requirements:

Požadavky viz http://math.feld.cvut.cz/hajek/zkouska-priklad.pdf

Webpage:

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

Subject is included into these academic programs:

Program Branch Role Recommended semester
BEKME1 Communication Technology V 2
BEKME5 Komunikace a elektronika V 2
BEKME_BO Common courses V 2
BEKME4 Network and Information Technology V 2
BEKME3 Applied Electronics V 2
BEKME2 Multimedia Technology V 2
BEEEM1 Applied Electrical Engineering P 2
BEEEM_BO Common courses P 2
BEEEM2 Electrical Engineering and Management P 2
BEKYR1 Robotics V 2
BEKYR_BO Common courses V 2
BEKYR3 Systems and Control V 2
BEKYR2 Sensors and Instrumentation V 2
BEOI1 Computer Systems V 2
BEOI_BO Common courses V 2
BEOI3 Software Systems V 2
BEOI2 Computer and Information Science V 2


Page updated 24.6.2019 17:52:59, semester: Z,L/2020-1, L/2018-9, Z,L/2019-20, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)