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BE5B01MA2	Calculus 2
Roles:	P	Extent of teaching:	4P+2S
Department:	13101	Language of teaching:	EN
Guarantors:	Habala P.	Completion:	Z,ZK
Lecturers:	Vivi P.	Credits:	7
Tutors:	Vivi P.	Semester:	L

Web page:

https://math.fel.cvut.cz/en/people/vivipaol/BE5B01MA2.html

Anotation:

The subject covers an introduction to the differential and integral calculus in several variables and basic relations between curve and surface integrals. Fourier series are also introduced.

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.		Real plane, three dimensional analytic geometry, vector functions.
2.		Functions of several variables: limits, continuity.
3.		Directional and partial derivative, tangent plane, gradient.
4.		Derivative of a composition of functions, higher order derivatives.
5.		Local extrema, Lagrange multipliers.
6.		Double integral, Fubini's Theorem. Polar coordinates.
7.		Triple integrals. Cylindrical and spherical coordinates. Change of variables in multiple integrals.
8.		Space curves. Line integrals.
9.		Potential of a vector field. Fundamental Theorem for line integrals. Green's Theorem.
10.		Parametric surfaces and their area. Surface integrals.
11.		Curl and divergence. Gauss, and Stokes theorem and their applications.
12.		Fourier series.
13.		Sine and cosine Fourier series.

Exercises outline:

1.		Real plane, three dimensional analytic geometry, vector functions.
2.		Functions of several variables: limits, continuity.
3.		Directional and partial derivative, tangent plane, gradient.
4.		Derivative of a composition of functions, higher order derivatives.
5.		Local extrema, Lagrange multipliers.
6.		Double integral, Fubini's Theorem. Polar coordinates.
7.		Triple integrals. Cylindrical and spherical coordinates. Change of variables in multiple integrals.
8.		Space curves. Line integrals.
9.		Potential of a vector field. Fundamental Theorem for line integrals. Green's Theorem.
10.		Parametric surfaces and their area. Surface integrals.
11.		Curl and divergence. Gauss, and Stokes theorem and their applications.
12.		Fourier series.
13.		Sine and cosine 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

http://math.feld.cvut.cz/vivi/

Requirements:

http://math.feld.cvut.cz/vivi/BE5B01MA2.pdf

Subject is included into these academic programs:

Program	Branch	Role	Recommended semester
BEECS	Common courses	P	2
BPEECS_2018	Common courses	P	2

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Page updated 18.4.2024 17:51:04, semester: L/2023-4, Z/2024-5, Z/2023-4, Send comments about the content to the Administrators of the Academic Programs

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