Mar 28, 2020   8:01 p.m. Soňa
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Course syllabus 282212_BDP - Differential Equations (FME - SS 2019/2020)


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University: Slovak University of Technology in Bratislava
Faculty: Faculty of Mechanical Engineering
Course unit code: 282212_BDP
Course unit title: Differential Equations
Mode of delivery, planned learning activities and teaching methods:
lecture2 hours weekly (on-site method)
20 hours per semester of study (combined method)

 
Credits allocated: 2
 
Recommended semester/trimester: Applied Mechanics and Mechatronics - bachelor (optional), 4. semester
Applied Mechanics and Mechatronics (in english language) - bachelor (optional), 4. semester
Automation and Informatics of Machines and Processes - bachelor (optional), 4. semester
Automobiles and Mobile Production Machines - bachelor (optional), 4. semester
Environmental Manufacturing Technologies - bachelor (optional), 4. semester
Environmental Protection Technologies - bachelor (optional), 4. semester
Measurement and Quality Management in Mechnical Engineering - bachelor (optional), 4. semester
Operational Technician of Transport and Production Technology - bachelor (optional), 4. semester
Production Processes and Materials - bachelor (optional), 4. semester
Thermal Power Engineering Machinery and Equipment - bachelor (optional), 4. semester
Level of study: 1.
Prerequisites for registration: none
 
Assesment methods:
Two written test will be offered during semester, each with 25 points score, while it is necessary to receive 14 points in minimum from both. To receive assignments it is necessary to receive 28 points at minimum.
 
Learning outcomes of the course unit:
Student will get basic knowledge of the concept and properties of Laplace transformation and will learn how to apply it to solution of differential equations. He/she will extend skills in solving boundary values for ordinary differential equations of the second order and will apply it to finding eigen-values and eigen-vectors of given problems. He/she will be acknowledged with classification of partial differential equations of order 2 and with respective mathematical models in natural and technical sciences. He/she is able to determine boundary, initial and mixed boundary problems for basic types of equations. He/she will learn how to solve these problems by means of orthogonal series and by means of Fourier method.
 
Course contents:
Laplace transformation (definition, properties, image iof transformation). Inverse transformation. Applications for solution of differential equations.
Solution of boundary problems for ordinary differential equation of order 2 with constant coefficients. Respective eigen-values and eigen-vectors for given problem. Sturm-Liouville problem.
Classification of partial differential equations of order 2 and respective models in natural and technical sciences. Laplace and Poisson equation. Vibrating string and membrane, wave equation and heat conduction equation.
Solution of problems by means of Fourier method, Fourier (orthogonal) and power series and by means of finite elements´ method.
 
Recommended or required reading:
Basic:
ROVDER, J. Vybrané state z matematiky: Funkcie komplexnej premennej. Laplaceova transformácia. Parciálne diferenciálne rovnice 2.rádu. Bratislava : SVŠT v Bratislave, 1986. 209 p.
REKTORYS, K. Variační metódy v inženýrskych problémech a v problémech matematické fyziky. Praha : SNTL, 1974. 600 p.
REKTORYS, K. Metoda časové diskretizace a parciální diferenciální rovnice. Praha : SNTL, 1985. 361 p.

Recommended:
IVAN, J. Matematika 1. Bratislava : Alfa, 1986. 704 p.
IVAN, J. Matematika 2. Bratislava : Alfa, 1989. 631 p.
REKTORYS, K. Přehled užité matematiky. Praha : SNTL, 1981. 1139 p.

 
Language of instruction: slovak or english
 
Notes:
 
Courses evaluation:
Assessed students in total: 59

ZFX
100,0 %0 %
Name of lecturer(s): RNDr. Jana Gabková, PhD. (examiner, instructor, lecturer)
RNDr. Daniela Richtáriková, PhD. (examiner, instructor, lecturer, person responsible for course) - slovak, english
doc. RNDr. Daniela Velichová, CSc. (examiner, lecturer) - slovak, english
 
Last modification: 12. 6. 2019
Supervisor: RNDr. Daniela Richtáriková, PhD. and programme supervisor


Last modification made by Ing. Marianna Frajková on 06/12/2019.

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