MA002 Calculus III

Faculty of Informatics
Autumn 2010
Extent and Intensity
3/0. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
prof. Alexander Lomtatidze, DrSc. (lecturer)
prof. RNDr. Luboš Brim, CSc. (assistant)
Guaranteed by
doc. RNDr. Bedřich Půža, CSc.
Faculty of Informatics
Contact Person: prof. Alexander Lomtatidze, DrSc.
Timetable
Tue 8:00–10:50 B003
Prerequisites
! M002 Calculus III || MB001 Calculus II
Completion of courses Mathematical Analysis I and Mathematical Analysis II.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 26 fields of study the course is directly associated with, display
Course objectives
The course that presents not obligatory part of mathematical analysis. It is devoted to study of series, line integrals,a basic of the theory of complex functions of complex variable and elementary methods of the solution of differential equations. At the end of the course students should be able to: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements and to explain methods of their proofs; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected problems from the topics of the course.
Syllabus
  • Functional series, uniform convergence.
  • Power series, radius of convergence.
  • Fourier series.
  • Dependence of integrals on parameters.
  • Implicit functions.
  • Line integral, Green's formula.
  • Complex functions of complex variable.
  • Cauchy's theorem, residua.
  • First order differential equations, direction field, initial conditions.
  • Higher order linear differential equations, equations with constant coefficients.
Literature
  • NOVÁK, Vítězslav and Zuzana DOŠLÁ. Nekonečné řady (Infinite series). 1. vyd. Brno: Masarykova univerzita v Brně, 1998, 120 pp. skripta. ISBN 80-210-1949-2. info
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice (Ordinary differential equations). 1st ed. Brno: Masarykova univerzita Brno, 1995, 207 pp. ISBN 80-210-1130-0. info
  • RÁB, Miloš. Zobrazení a Riemannův integrál v En. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 97 s. info
Teaching methods
lectures
Assessment methods
Teaching: lecture 3 hours a week. Exam: written.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is also listed under the following terms Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2011, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, Autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, Autumn 2021.
  • Enrolment Statistics (Autumn 2010, recent)
  • Permalink: https://is.muni.cz/course/fi/autumn2010/MA002