Mathematics A2I - MS710P53

• Title: Matematika A2
• Guaranteed by: Institute of Applied Mathematics and Information Technologies (31-710)
• Faculty: Faculty of Science
• Actual: from 2012 to 2012
• Semester: summer
• E-Credits: 8
• Examination process: summer s.:
• Hours per week, examination: summer s.:4/4, C+Ex [HT]
• Capacity: 150
• Min. number of students: unlimited
• 4EU+: no
• Virtual mobility / capacity: no
• State of the course: taught
• Language: Czech
• Note: enabled for web enrollment
• Guarantor: RNDr. Naděžda Krylová, CSc.
• Teacher(s): RNDr. Naděžda Krylová, CSc.
• Incompatibility : MS710P04B, MUMP001
• Interchangeability : MS710P04B
• Is incompatible with: MB162P05, MS710P54, MS710P55
• Is pre-requisite for: MC260P35N

Annotation

English

As a continuation of the course from the previous term S710P04A the main focus will be improper integral, series and the calculus of functions of several variables.

Last update: FORSTOVA/NATUR.CUNI.CZ (06.05.2011)

Czech

Navazuje na výuku v předchozím semestru. Jsou probrány nevlastní integrály a řady. Dále se studuje diferenciální a integrální počet funkcí více proměnných.

Last update: Krylová Naděžda, RNDr., CSc. (17.02.2021)

Literature

J. Štěpánek: Matematika pro přírodovědce I, II. Univerzita Karlova, Praha 1990.

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

A. Klíč a kolektiv: Matematika I. VŠCHT, Praha 1998.

D. Turzík a kolektiv: Matematika II. VŠCHT, Praha 1998.

Kolektiv autorů: Sbírka příkladů z matematiky. VŠCHT, Praha 1992.

Vojtěch Jarník: Diferenciální počet I. Academia, Praha 1963.

Vojtěch Jarník: Integrální počet I. Academia, Praha 1963.

Last update: Krylová Naděžda, RNDr., CSc. (17.02.2021)

Syllabus

1. Improper integrals.

2. 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.

3. 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.

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

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

Last update: FORSTOVA/NATUR.CUNI.CZ (06.05.2011)