Subject description - AE2B01MA3

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AE2B01MA3 Multidimensional Calculus Extent of teaching:2+2
Guarantors:  Roles:P,V Language of
teaching:
EN
Teachers:  Completion:Z,ZK
Responsible Department:13101 Credits:6 Semester:Z

Anotation:

The course covers an introduction to differential and integral calculus in several variables and basic relations between curve and surface integrals. We also introduce 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.

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. Double and triple integral - Fubini theorem and theorem on substitution.
6. Path integral and its applications.
7. Surface integral and its applications.
8. The Gauss, Green, and Stokes theorem. Potential of a vector field.
9. Basic convergence tests for series of numbers.
10. Series of functions, the Weirstrasse test.
11. Power series, radius of convergence.
12. Standard expansions of elementary functions. 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. Double and triple integral - Fubini theorem and theorem on substitution.
6. Path integral and its applications.
7. Surface integral and its applications.
8. The Gauss, Green, and Stokes theorem. Potential of a vector field.
9. Basic convergence tests for series of numbers.
10. Series of functions, the Weirstrasse test.
11. Power series, radius of convergence.
12. Standard expansions of elementary functions. 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:

The requirement for receiving the credit is an active participation in the tutorials. http://math.feld.cvut.cz/vivi/AE2B01MA3.pdf

Webpage:

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

Subject is included into these academic programs:

Program Branch Role Recommended semester
BEEEM1 Applied Electrical Engineering V 2
BEEEM_BO Common courses V 2
BEEEM2 Electrical Engineering and Management V 2
BEKME1 Communication Technology P 2
BEKME5 Komunikace a elektronika P 2
BEKME_BO Common courses P 2
BEKME4 Network and Information Technology P 2
BEKME3 Applied Electronics P 2
BEKME2 Multimedia Technology 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 12:52:41, 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)