Subject description - A1B01MA2

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A1B01MA2 Multidimensional Analysis Extent of teaching:2+2
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

Subject is included into these academic programs:

Program Branch Role Recommended semester
BPOI1 Computer Systems V 2
BPOI_BO Common courses V 2
BPOI3 Software Systems V 2
BPOI2 Computer and Information Science V 2
BPKYR1 Robotics V 2
BPKYR_BO Common courses V 2
BPKYR3 Systems and Control V 2
BPKYR2 Sensors and Instrumentation V 2
BPKME1 Communication Technology V 2
BPKME5 Komunikace a elektronika V 2
BPKME_BO Common courses V 2
BPKME4 Network and Information Technology V 2
BPKME3 Applied Electronics V 2
BPKME2 Multimedia Technology V 2
BPEEM1 Applied Electrical Engineering P 2
BPEEM_BO Common courses P 2
BPEEM2 Electrical Engineering and Management P 2
BMI(ECTS) Manager Informatics V 2
BWM(ECTS) Web and Multimedia V 2
BIS(ECTS) Intelligent Systems V 2
BSI(ECTS) Software Engineering V 2


Page updated 22.5.2019 15:01:10, semester: Z,L/2020-1, L/2019-20, Z,L/2018-9, Z/2019-20, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)