M5520 Mathematical Analysis 5

Faculty of Science
Autumn 2013
Extent and Intensity
2/2/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Zuzana Došlá, DSc. (lecturer)
Mgr. Petr Liška, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Eduard Fuchs, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 14:00–15:50 M5,01013
  • Timetable of Seminar Groups:
M5520/01: Fri 8:00–9:50 M6,01011, P. Liška
Prerequisites (in Czech)
M4502 Mathematical Analysis 4
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
The main objective is to understand basic notions, results and techniques of computations and applications of some "advanced" areas of mathematical analysis involving multiple integrals, Fourier series and difference equations.
After passing the course, the student will be able:
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.
Syllabus
  • Integral calculus for functions of more variables.
  • Riemann integral in E2 a E3.
  • Methods of calculus, transformation to polar, cylindric and sferic coordinates.
  • Geometric interpretations of integrals.
  • Fourier series.
  • Difference and summation calculus.
  • Linear first order difference equations.
  • Linear second order difference equations with constant coefficients.
  • Applications of difference equations in combinatorics.
Literature
  • KALAS, Josef and Jaromír KUBEN. Integrální počet funkcí více proměnných (Integral calculus of functions of several variables). 1st ed. Brno: Masarykova univerzita, 2009, 278 pp. ISBN 978-80-210-4975-8. info
  • RÁB, Miloš. Zobrazení a Riemannův integrál v En. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 97 s. info
  • DULA, Jiří and Jiří HÁJEK. Cvičení z matematické analýzy : Riemannův integrál. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 84 s. info
  • PRÁGEROVÁ, Alena. Diferenční rovnice. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1971, 115 s. URL info
Teaching methods
lectures and class exercises
Assessment methods
Lectures 2 hours a week, class exercises 2 hours a week. Examination both in written and oral form. The written test contains usually 8 questions evaluated by 20 points, the oral part 2 questions. 50% of correct answers from the written test and the knowledge of the basic concept of both oral questions are needed to pass.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011 - acreditation, Autumn 2012, Autumn 2014, Autumn 2016, Autumn 2018, Autumn 2020.
  • Enrolment Statistics (Autumn 2013, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2013/M5520