Subject description - AD1B01MA2

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AD1B01MA2 Multidimensional Analysis 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 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:

(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 P 2
BKEEM_BO Common courses P 2
BKEEM2 Electrical Engineering and Management P 2
BKKYR1 Robotics V 2
BKKYR_BO Common courses V 2
BKKYR3 Systems and Control V 2
BKKYR2 Sensors and Instrumentation V 2
BKKME1 Communication Technology V 2
BKKME_BO Common courses V 2
BKKME4 Network and Information Technology V 2
BKKME3 Applied Electronics V 2
BKKME2 Multimedia Technology 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 18.9.2019 12:53:23, 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)