Sep 26, 2020   10:33 a.m. Edita

# Course syllabus B-MAT3E - Mathematics 3 (FEEIT - WS 2019/2020)

Information sheet          ECTS          Syllabus

Slovak          English

University:
Slovak University of Technology in Bratislava
Faculty:
Course unit code:
B-MAT3E
Course unit title:
Mathematics 3
Mode of delivery, planned learning activities and teaching methods:
 lecture 2 hours weekly (on-site method) 2 hours weekly (distance method) seminar 2 hours weekly (on-site method) 2 hours weekly (distance method)

Credits allocated:
6

Recommended semester/trimester:
Automotive Mechatronics - bachelor (compulsory), 3. semester
Electrical Engineering - bachelor (compulsory), 3. semester
Electrical Power Engineering - bachelor (compulsory), 3. semester
Nuclear and Physical Engineering - bachelor (compulsory), 3. semester
Level of study:
1.
Prerequisites for registration:

Assesment methods:
Three semestral tests (40 minutes) 20 points. For credit sum of two best evaluated tests (40% of total), written exam (120 minutes) 60 points (60% of total). Total evaluation - sum of points from tests and exam using official classification table.

Learning outcomes of the course unit:
The aim of the subject is to continue in last part of Calculus 2, namely in curve integrals from scalar and vector field, the use of Green theorem – change curve integral over the closed curve to double integral. The next goal is the knowledge from calculus of complex functions of comples variable. The methods of evalution complex integral over the curve. In the subject the student obtains knowledge about basic properties of ordinary differential equations of
second order and the methods od its solutions and about the Laplace transform and its use in solutions of initial value problems and electrical circuits.

Course contents:
The curve, line integral from scalar and vector field over the curve. Green’ s theorem, integral independent from the curve. The limit, continuity and the derivative of complex function of complex variable. Cauchy-Riemann’ s equations, analytic (holomorphic) and harmonic functions. Integral of a complex function of complex variable. Cauchy integral theorem, Cauchy integral theorem formula. Taylor series. Laurent series. Singular points, residues, Cauchy
residue theorem. Problems leading to ordinary differential equations of second order. Homogeneous linear differential equation of second order. Solution of linear differential equation of second order with constant coefficients. Nonhomogeneous linear differential equation of second order with constant coefficients. Laplace transform, basic
properties, inverse Laplace transform. Applications of Laplace transform in solutions of initial value problem for ordinary differential equations and electric circuits.

Basic:
 MARKO, Ľ. Matematická analýza online.  [online]. 2003. URL: http://aladin.elf.stuba.sk/~marko. BOCK, I. -- HORNIAČEK, J. Matematická analýza 3. Bratislava : Alfa, 1990. 344 p. ISBN 80-05-00433-8.

Recommended:
 Fisher, S.,D.: Complex variables, Wadsworth & Brooks, Pacific Grove, ISBN 0-534-13260-X, 1990 Lang, S.: Complex analysis, Springer Verlag, 1993

Language of instruction:
slovak or english

Notes:

Courses evaluation:
Assessed students in total: 124

ABC
D
EFX
5,6 %
5,6 %
10,5 %
24,2 %
44,4 %
9,7 %
Name of lecturer(s):
RNDr. Mária Kečkemétyová, PhD. (examiner, instructor) - slovak, english
doc. RNDr. Ľubomír Marko, PhD. (examiner, instructor, lecturer, person responsible for course) - slovak, english

Last modification:
6. 5. 2019
Supervisor: doc. RNDr. Ľubomír Marko, PhD. and programme supervisor

Last modification made by RNDr. Marian Puškár on 05/06/2019.

 Type of output: PDF output (PDF)Document RTF (RTF)XML format for IS (XML IL)