Subject description - AD2B01MA3

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AD2B01MA3 Multidimensional Calculus Extent of teaching:14+6
Guarantors:  Roles:P,V Language of
teaching:
CS
Teachers:  Completion:Z,ZK
Responsible Department:13101 Credits:6 Semester:L

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:

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

Webpage:

(kombinované studium)http://math.feld.cvut.cz/vivi/AD0B01MA2.htm

Subject is included into these academic programs:

Program Branch Role Recommended semester
BKOI1 Computer Systems V 2
BKOI_BO Common courses V 2
BKOI3 Software Systems V 2
BKOI2 Computer and Information Science V 2
BKEEM1 Applied Electrical Engineering V 2
BKEEM_BO Common courses V 2
BKEEM2 Electrical Engineering and Management V 2
BKKME1 Communication Technology P 2
BKKME5 Komunikace a elektronika P 2
BKKME_BO Common courses P 2
BKKME4 Network and Information Technology P 2
BKKME3 Applied Electronics P 2
BKKME2 Multimedia Technology P 2
BKKYR1 Robotics V 2
BKKYR_BO Common courses V 2
BKKYR3 Systems and Control V 2
BKKYR2 Sensors and Instrumentation V 2
BIS(ECTS)-D Intelligent Systems V 2
BKSTMWM Web and Multimedia V 2
BKSTMSI Software Engineering V 2
BKSTMMI Manager Informatics V 2
BKSTMIS Intelligent Systems V 2
BKSTM_BO Common courses V 2
BSI(ECTS)-D Software Engineering V 2
BWM(ECTS)-D Web and Multimedia V 2
BMI(ECTS)-D Manager Informatics V 2


Page updated 12.11.2019 17:52:15, 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)