MA002 Calculus

Faculty of Informatics
Autumn 2014
Extent and Intensity
2/2. 4 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
Teacher(s)
doc. Mgr. Peter Šepitka, Ph.D. (lecturer)
Mgr. Milan Bačík (seminar tutor)
Guaranteed by
prof. RNDr. Roman Šimon Hilscher, DSc.
Faculty of Informatics
Supplier department: Faculty of Science
Timetable
Tue 14:00–15:50 B204
  • Timetable of Seminar Groups:
MA002/01: Fri 8:00–9:50 A320, M. Bačík
Prerequisites
Basic knowledge from the calculus and multivariable calculus
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
Course objectives
This course extends the basic knowledge from mathematical analysis. It is devoted to the basic study of systems of linear differential equations, line integrals, the theory of complex functions of complex variable, and calculus of variations. 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
  • Systems of linear differential equations.
  • Line integral.
  • Analysis in complex domain.
  • Calculus of variations.
Literature
  • 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
  • https://www.math.muni.cz/~dosly/krivkovy_integral.pdf
  • KALAS, Josef. Analýza v komplexním oboru. 1. vyd. Brno: Masarykova univerzita, 2006, iv, 202. ISBN 8021040459. info
  • GEL'FAND, Izrail Moisejevič and Sergej Vasil'jevič FOMIN. Calculus of variations. Edited by Richard A. Silverman. Mineola, N. Y.: Dover Publications, 2000, vii, 232 s. ISBN 0-486-41448-5. info
  • SAGAN, Hans. Introduction to the calculus of variations. New York, N.Y.: Dover Publications, 1969, xvi, 449. ISBN 0486673669. info
Teaching methods
lectures (2 hours per week) + tutorial (2 hours per week)
Assessment methods
Exam: written (a multiple-choice test with the theory + a practical part), it takes 120 minutes. It is possible to get at most 100 points (30 points from the tutorial, 10 points from the test, and 60 points from the practical part). For the success it is needed to have at least 50 points to pass the exam but simultaneously it is necessary to reach at least 10 points from the tutorial and 4 points from the theory test.
Language of instruction
Czech
Further Comments
Study Materials
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 2010, Autumn 2011, Autumn 2012, Autumn 2013, Autumn 2015, Autumn 2016, Autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, Autumn 2021.
  • Enrolment Statistics (Autumn 2014, recent)
  • Permalink: https://is.muni.cz/course/fi/autumn2014/MA002