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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

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Page updated 6.12.2019 17:52:32, 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)