PřF:M5520 Mathematical Analysis 5 - Course Information

M5520 Mathematical Analysis 5

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)
Mgr. Jakub Krnáč (assistant)

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 M4,01024

• Timetable of Seminar Groups:

M5520/01: Thu 16:00–17:50 prace doma, 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

there are 11 fields of study the course is directly associated with, display

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.

Learning outcomes

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.

• Enrolment Statistics (recent)
  
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