Subject description - A3B01MA2

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A3B01MA2 Mathematics 2 Extent of teaching:4+2
Guarantors:  Roles:P,V Language of
teaching:
CS
Teachers:  Completion:Z,ZK
Responsible Department:13101 Credits:7 Semester:L

Anotation:

The subject covers an introduction to the differential and integral calculus in several variables and basic relations between curve and surface integrals. Other part contains 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. Basic convergence tests for series.
2. Series of functions, the Weierstrass test. Power series.
3. Standard Taylor expansions. Fourier series.
4. Functions of more variables, limit, continuity.
5. Directional and partial derivatives - gradient.
6. Derivative of a composition of function, higher order derivatives.
7. Jacobiho matrix. Local extrema.
8. Extrema with constraints. Lagrange multipliers.
9. Double and triple integral - Fubini theorem and theorem on substitution.
10. Path integral and its applications.
11. Surface integral and its applications.
12. The Gauss, Green, and Stokes theorems.
13. Potential of vector fields.

Exercises outline:

1. Basic convergence tests for series.
2. Series of functions, the Weierstrass test. Power series.
3. Standard Taylor expansions. Fourier series.
4. Functions of more variables, limit, continuity.
5. Directional and partial derivatives - gradient.
6. Derivative of a composition of function, higher order derivatives.
7. Jacobiho matrix. Local extrema.
8. Extrema with constraints. Lagrange multipliers.
9. Double and triple integral - Fubini theorem and theorem on substitution.
10. Path integral and its applications.
11. Surface integral and its applications.
12. The Gauss, Green, and Stokes theorems.
13. Potential of vector fields.

Literature:

1. J. Stewart.: Calculus, Seventh Edition, Brooks/Cole, 2012, 1194 p.
2. L. Gillman, R. H. McDowell, Calculus, W.W.Norton & Co.,New York, 1973
3. S. Lang, Calculus of several variables, Springer Verlag, 1987

Requirements:

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

Subject is included into these academic programs:

Program Branch Role Recommended semester
BPKYR1 Robotics P 2
BPKYR_BO Common courses P 2
BPKYR3 Systems and Control P 2
BPKYR2 Sensors and Instrumentation P 2
BPOI1 Computer Systems V 2
BPOI_BO Common courses V 2
BPOI3 Software Systems V 2
BPOI2 Computer and Information Science 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 V 2
BPEEM_BO Common courses V 2
BPEEM2 Electrical Engineering and Management V 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 27.5.2019 07:53:08, 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)