M5520 Mathematical Analysis 5

Faculty of Science
Autumn 2018
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
Mon 17. 9. to Fri 14. 12. Tue 12:00–13:50 M2,01021
  • Timetable of Seminar Groups:
M5520/01: Mon 17. 9. to Fri 14. 12. Thu 10:00–11:50 M2,01021, P. Liška
M5520/02: Mon 17. 9. to Fri 14. 12. Thu 8:00–9:50 M4,01024, P. Liška
Prerequisites (in Czech)
M4502 Mathematical Analysis 4
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
The main objective is to understand basic notions, results and techniques of computations and applications of some "advanced" areas of mathematical analysis involving autonomous systems of differential equations, difference equations, metric spaces and Fourier series.
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
  • Autonomous systems of differential equations.
  • Difference and summation calculus.
  • Linear first order difference equations.
  • Linear second order difference equations with constant coefficients.
  • Applications of difference equations.
  • Metric spaces, Banach fixed point theorem and its applications.
  • Fourier series.
Literature
  • PRÁGEROVÁ, Alena. Diferenční rovnice. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1971, 115 s. URL info
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady. 3. vyd. Brno: Masarykova univerzita, 2013, iv, 113. ISBN 9788021064164. info
  • DOŠLÁ, Zuzana and Ondřej DOŠLÝ. Metrické prostory : teorie a příklady. 3. vyd. Brno: Masarykova univerzita, 2006, viii, 90. ISBN 8021041609. info
  • KALAS, Josef and Miloš RÁB. Obyčejné diferenciální rovnice. 1. vyd. Brno: Masarykova univerzita, 1995, 207 s. ISBN 8021011300. 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 2013, Autumn 2014, Autumn 2016, Autumn 2020.
  • Enrolment Statistics (Autumn 2018, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2018/M5520