M5520 Mathematical Analysis 5

Faculty of Science
Autumn 2011 - acreditation

The information about the term Autumn 2011 - acreditation is not made public

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)
RNDr. Bc. Jiří Rosenberg (seminar tutor)
Guaranteed by
doc. RNDr. Eduard Fuchs, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites (in Czech)
M4502 Mathematical Analysis 3
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 of Functions of Two or More Variables.
  • Riemann integral in E2 and E3.
  • Computation methods, transformation into polar, cylindrical and spherical coordinates.
  • Geometric applications.
  • Fourier series, general theory.
  • Trigonometric system and corresponding Fourier series.
  • Point-wise and uniform convergence of Fourier series.
  • Difference of functions and difference equations.
  • Linear difference equations of the first order.
  • Linear difference equations of the second order.
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
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady. Vyd. 1. Brno: Masarykova univerzita, 1998, 113 s. ISBN 8021019492. 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.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught every week.
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 2012, Autumn 2013, Autumn 2014, Autumn 2016, Autumn 2018, Autumn 2020.