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Mathematics C2 - MS710P14

Title:	Matematika C2
Czech title:	Matematika C2
Guaranteed by:	Institute of Applied Mathematics and Information Technologies (31-710)
Faculty:	Faculty of Science
Actual:	from 2023
Semester:	summer
E-Credits:	5
Examination process:	summer s.:
Hours per week, examination:	summer s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	6
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech
Note:	enabled for web enrollment

Guarantor:	RNDr. Hana Hladíková, Ph.D.
Teacher(s):	RNDr. Hana Hladíková, Ph.D.

Opinion survey results Examination dates SS schedule

Annotation -

Last update: RNDr. Hana Hladíková, Ph.D. (26.11.2019)

Is a continuation of the course MatC, the main focus will be improper integral, series and the calculus of functions of several variables.

Literature - Czech

Last update: RNDr. Hana Hladíková, Ph.D. (26.11.2019)

Základní literatura:

Kotvalt, V.: Základy matematiky pro přírodovědné obory. Karolinum, 2008.

Štědrý, M.: Sbírka úloh k matematice pro geografy. Karolinum, 2006.

N. Krylová, M. Štědrý: Sbírka příkladů z matematiky I. PřF UK, Praha 1994.

D. Turzík a kolektiv: Matematika II ve strukturovaném studiu II. VŠCHT, Praha 2014 (také 2005, 2002, 1998).

Budínský, B.: Analytická a diferenciální geometrie. SNTL, 1983

J. Hamhalter, J. Tišer: Diferenciální počet funkcí více proměnnných. Skripta ČVUT, 2005.

J. Hamhalter, J. Tišer: Integrální počet funkcí více proměnnných. Skripta ČVUT, 2005.

Syllabus -

Last update: RNDr. Hana Hladíková, Ph.D. (26.11.2019)

Differential calculus of several variables: the metric space En, vector-valued function of several variables, limits and continuity, partial derivatives and differentials, chain rules, the gradient, directional derivatives, Taylor´s theorem, extreme values, differentiation of implicit functions.

Multiple integral: double and triple integrals, evaluation - iterated integrals, integration in polar, cylindrical and spherical coordinates, applications.

Calculus of vector fields: vector fields, basic curves and surfaces in the space, conservative vector fields and potencial functions, applications of line integrals.

Sequences and serier: convergence properties of sequences, infinit series of constants, nonnegative series - the integral, the comparison and the ratio tests, alternating series and absolute convergence, power series, Taylor series.