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B0B01MA2	Mathematical Analysis 2
Roles:	P	Extent of teaching:	4P+2S
Department:	13101	Language of teaching:	CS
Guarantors:	Tišer J.	Completion:	Z,ZK
Lecturers:	Hájek P.	Credits:	7
Tutors:	Hájek P., Korbelář M., Pospíšil K.	Semester:	L,Z

Web page:

https://moodle.fel.cvut.cz/courses/B0B01MA2

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.

Content:

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.

Course outlines:

1.		Functions of more variables, limit, continuity.
2.		Directional and partial derivatives - gradient.
3.		Derivative of a composition of function, higher order derivatives.
4.		Jacobiho 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 theorems.
10.		Potential of vector fields.
11.		Basic convergence tests for series.
12.		Series of functions, the Weierstrass test. Power series.
13.		Standard Taylor expansions. Fourier series.

Exercises outline:

1.		Functions of more variables, limit, continuity.
2.		Directional and partial derivatives - gradient.
3.		Derivative of a composition of function, higher order derivatives.
4.		Jacobiho 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 theorems.
10.		Potential of vector fields.
11.		Basic convergence tests for series.
12.		Series of functions, the Weierstrass test. Power series.
13.		Standard Taylor expansions. Fourier series.

Literature:

[1]		Stewart J.: Calculus, Seventh Edition, Brooks/Cole, 2012, 1194 p., ISBN 0-538-49781-5.
[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:

https://moodle.fel.cvut.cz/course/view.php?id=6317

Keywords:

Partial derivatives, Lagrange multipliers, mulidimensional integrals, Gauss, Green and Stokes Theorems.

Subject is included into these academic programs:

Program	Branch	Role	Recommended semester
BPOI1_2016	Computer and Information Science	P	3
BPOI_BO_2016	Common courses	P	3
BPOI4_2016	Computer Games and Graphics	P	3
BPOI3_2016	Software	P	3
BPOI2_2016	Internet of Things	P	3
BPBIO_2018	Common courses	P	2
BPOI_BO_2018	Common courses	P	3
BPOI4_2018	Computer Games and Graphics	P	3
BPOI3_2018	Software	P	3
BPOI2_2018	Internet of Things	P	3
BPOI1_2018	Artificial Intelligence and Computer Science	P	3
BPEEM1_2016	Applied Electrical Engineering	P	2
BPEEM_BO_2016	Common courses	P	2
BPEEM2_2016	Electrical Engineering and Management	P	2
BPEK_2016	Common courses	P	2
BPKYR_2021	Common courses	P	2
BPKYR_2016	Common courses	P	2

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Page updated 6.10.2024 17:51:16, semester: Z,L/2024-5, Z/2025-6, L/2023-4, Send comments about the content to the Administrators of the Academic Programs

Proposal and Realization: I. Halaška (K336), J. Novák (K336)