FI:MA002 Calculus III - Course Information

MA002 Calculus III

Extent and Intensity

3/0. 3 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).

Teacher(s)

prof. Alexander Lomtatidze, DrSc. (lecturer)
doc. Mgr. Petr Zemánek, Ph.D. (seminar tutor)

Guaranteed by

doc. RNDr. Bedřich Půža, CSc.
Faculty of Informatics

Timetable

Mon 17:00–19:50 G123

Prerequisites

! M002 Calculus III || MB001 Calculus II
Completion of courses Mathematical Analysis I and Mathematical Analysis II.

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

• Applied Informatics (programme FI, N-AP)
• Information Technology Security (programme FI, N-IN)
• Bioinformatics (programme FI, N-AP)
• Information Systems (programme FI, N-IN)
• Informatics (eng.) (programme FI, D-IN4)
• Informatics (programme FI, D-IN4)
• Parallel and Distributed Systems (programme FI, N-IN)
• Computer Graphics (programme FI, N-IN)
• Computer Networks and Communication (programme FI, N-IN)
• Computer Systems and Technologies (eng.) (programme FI, D-IN4)
• Computer Systems and Technologies (programme FI, D-IN4)
• Computer Systems (programme FI, N-IN)
• Embedded Systems (eng.) (programme FI, N-IN)
• Embedded Systems (programme FI, N-IN)
• Service Science, Management and Engineering (eng.) (programme FI, N-AP)
• Service Science, Management and Engineering (programme FI, N-AP)
• Social Informatics (programme FI, B-AP)
• Theoretical Informatics (programme FI, N-IN)
• Upper Secondary School Teacher Training in Informatics (programme FI, N-SS) (2)
• Artificial Intelligence and Natural Language Processing (programme FI, N-IN)
• Image Processing (programme FI, N-AP)

Course objectives

The course that presents not obligatory part of mathematical analysis. It is devoted to study of series, line integrals,a basic of the theory of complex functions of complex variable and elementary methods of the solution of differential equations. 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

• Functional series, uniform convergence.
• Power series, radius of convergence.
• Fourier series.
• Dependence of integrals on parameters.
• Implicit functions.
• Line integral, Green's formula.
• Complex functions of complex variable.
• Cauchy's theorem, residua.
• First order differential equations, direction field, initial conditions.
• Higher order linear differential equations, equations with constant coefficients.

Literature

• NOVÁK, Vítězslav and Zuzana DOŠLÁ. Nekonečné řady (Infinite series). 1. vyd. Brno: Masarykova univerzita v Brně, 1998, 120 pp. skripta. ISBN 80-210-1949-2. info
• 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
• RÁB, Miloš. Zobrazení a Riemannův integrál v En. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 97 s. info

Teaching methods

lectures

Assessment methods

Teaching: lecture 3 hours a week. Exam: written.

Language of instruction

Czech

Further comments (probably available only in Czech)

The course is taught annually.

• Enrolment Statistics (Autumn 2011, recent)
  
• Permalink: https://is.muni.cz/course/fi/autumn2011/MA002