Apr 6, 2020   4:30 a.m. Irena
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Course syllabus 282102_BDP - Mathematics II (FME - SS 2019/2020)

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University: Slovak University of Technology in Bratislava
Faculty: Faculty of Mechanical Engineering
Course unit code: 282102_BDP
Course unit title: Mathematics II
Mode of delivery, planned learning activities and teaching methods:
lecture3 hours weekly (on-site method)
37 hours per semester of study (combined method)
seminar3 hours weekly (on-site method)

Credits allocated: 6
Recommended semester/trimester: Applied Mechanics and Mechatronics - bachelor (compulsory), 2. semester
Applied Mechanics and Mechatronics (in english language) - bachelor (compulsory), 2. semester
Automation and Informatics of Machines and Processes - bachelor (compulsory), 2. semester
Automobiles and Mobile Production Machines - bachelor (compulsory), 2. semester
Automobiles and Mobile Production Machines (in english language) - bachelor (compulsory), 2. semester
Environmental Manufacturing Technologies - bachelor (compulsory), 2. semester
Environmental Protection Technologies - bachelor (compulsory), 2. semester
Measurement and Quality Management in Mechnical Engineering - bachelor (compulsory), 2. semester
Measurement and Quality Management in Mechnical Engineering (in english language) - bachelor (compulsory), 2. semester
Operational Technician of Transport and Production Technology - bachelor (compulsory), 2. semester
Production Processes and Materials - bachelor (compulsory), 2. semester
Production Processes and Materials (in english language) - bachelor (compulsory), 2. semester
Thermal Power Engineering Machinery and Equipment - bachelor (compulsory), 2. semester
Level of study: 1.
Prerequisites for registration: none
Assesment methods:
Two written tests will be held during semester with 34 points at maximum, while one test will be solved as computer test using programe Mathematica. Student can obtain additional 1-6 points for activity on practical exercises during semester. Total score for final assessment from semester is 40 points. Assignments will be awarded for minimum of 15 points.
Student can attend one repetitory written test for 20 points maximum, assignments will be awarded for minimum of 15 points.
Subject is completed by passing exam, where student can obtain maximum 60 points, minimum 35 points.
Learning outcomes of the course unit:
Student will learn about basic concepts and properties of differential and integral calculus of functions in more variables and applications of presented methods of multivariable calculus for solution of optimization problems and for calculations of metric characteristics by means of multiple integrals. He/she will acquire basic knowledge on properties and solution methods for special types of ordinary differential equations of the first and second order.
Course contents:
Ordinary differential equations - basic concepts, special types and methods for solution of linear differential equations of the first, second, and higher orders.
Euclidean space - basic concepts and figures, vectors and their properties, equations of lines and planes and their metric and position rrelations, equations of quadratic surfaces
Important sets in the n-dimensional Euclidean space, special points in sets.
Function of two and more variables - domain of definition, graph of function, limit and continuity of function, partial derivatives.
Extremes of functions of two variables - local, constrained and global, investigation of extremes and appliction to calculation of optimisation problems.
Multiple integrals - basic properties, calculation and applications of double and triple integrals.
Mappings in the Euclidean plane and in the Euclidean space - transformations of Cartesian coordinate system to polar, cylindrical and spherical coordinate systems.
Calculation of double integrals by means of transformations to polar coordinates, triple integrals by means of transformation to cylindrical and spherical coodinates.
Recommended or required reading:
VELICHOVÁ, D. Matematika II, elektronická učebnica on-line.  [online]. 2007. URL: http://evlm.stuba.sk/~velichova/Matematika2/Kniha/kniha.html.
IVAN, J. Matematika 2. Bratislava : Alfa, 1989. 631 p. ISBN 80-05-00114-2.
HARMAN, B. -- DOBRAKOVOVÁ, J. -- ŠAMAJOVÁ, H. Matematika II: Základy teórie určitého integrálu. Bratislava : STU v Bratislave, 2003. 111 p. ISBN 80-227-1905-6.
KOLESÁROVÁ, A. -- BALÁŽ, V. Matematika II. Nakladateľstvo STU, 2011. 259 p. ISBN 978-80-227-3493-6.
KOLESÁROVÁ, A. -- KOVÁČOVÁ, M. -- ZÁHONOVÁ, V. Matematika II: Návody na cvičenia s programovým systémom MATHEMATICA. Bratislava : STU v Bratislave, 2002. 128 p. ISBN 80-227-1756-8.
GHORPADE, S R. -- LIMAYE, B V. A Course in Multivariable Calculus and Analysis. New York : Springer Science-Business Media, 2010. 475 p. ISBN 978-1-4419-1620-4.

Language of instruction: slovak or english
Courses evaluation:
Assessed students in total: 2357

4,5 %5,2 %13,2 %21,5 %44,3 %11,3 %
Name of lecturer(s): RNDr. Jana Gabková, PhD. (examiner, instructor) - slovak
Mgr. Monika Kováčová, PhD. (examiner, instructor) - slovak
Mgr. Peter Letavaj, PhD. (examiner, instructor) - slovak, english
Mgr. Milada Omachelová, PhD. (examiner, instructor) - slovak
Mgr. Monika Prášilová, PhD. (examiner, instructor) - slovak
RNDr. Daniela Richtáriková, PhD. (examiner, instructor) - slovak
doc. RNDr. Daniela Velichová, CSc. (examiner, instructor, lecturer, person responsible for course) - slovak, english
RNDr. Viera Záhonová, CSc. (examiner, instructor, lecturer) - slovak
Last modification: 11. 6. 2019
Supervisor: doc. RNDr. Daniela Velichová, CSc. and programme supervisor

Last modification made by Ing. Marianna Frajková on 06/11/2019.

Type of output: