Course detail
Mathematics 3
FP-MA3_MAcad. year: 2018/2019
It is part of the theoretical basis of the field and follows the subjects Mathematics 1 and 2. It is the basis of theory and application of endless series, differential equations, selected integral transformations and the basics of mathematical optimization.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Department
Learning outcomes of the course unit
Prerequisites
Co-requisites
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
- Active participation in the seminar, attendance at the seminar is compulsory,
- fulfillment of individual tasks and written assignments,
-Solving control tests and gaining more than 50% points.
The examination has a written and an oral part, with the written part of the exam.
The written part lasts 2 hours.
If the student fails to reach at least 50% of the total number of points achieved, the written part and the whole examination are assessed as "F" (unsatisfactory) and the student does not go to the oral part.
The oral part follows a written one, the duration of which does not normally exceed 10 minutes. Its main purpose is to clarify the classification. During the oral part the student has the opportunity to get acquainted with the specific evaluation of individual tasks. The oral exam also serves to resolve any uncertainties in the written part. If there are reasons for the examiner, student, additional questions may be asked. Students have the right to request preparation time for their preparation.
Course curriculum
2. Power series (sum, radius of convergence, properties)
3. Application of power series (approximate calculations of function values, integral and differential equations)
4. Fourier series (sum, properties, applications)
5. Rational lesion function in the complex field (complex roots and singularity, decomposition on partial fragments)
6. Laplace transform (definition, properties, inverse Laplace transform)
7. Use of L-transformation to solve ODR
8. Differential equations
9. Z-transformation (definition, properties, inverse Z-transformation, use to solve differential equations)
10. Fourier transform (definitions, properties, applications)
11. Mathematical optimization (convex sets and functions, mathematical programming tasks)
12. Linear programming (the role of LP and its properties, the basics of the simplex method, duality, Farkas theorem)
Work placements
Aims
Specification of controlled education, way of implementation and compensation for absences
Recommended optional programme components
Prerequisites and corequisites
Basic literature
DUPAČOVÁ, J., LACHOUT, P . Úvod do optimalizace. Vyd. 1. Praha: Matfyzpress, 2011, 81 s. ISBN 978-80-7378-176-7.
KROPÁČ J., KUBEN J.: Fukce gama a beta, transformace Laplaceova, Z a Fourierova, 3.vydání, VA v Brně, 2002 (CS)
Recommended reading
JURA, P.: Signály a systémy. Elektronické skriptum, část I, II, III, druhé opravené vydání, 2010 (CS)
WISNIEWSKI, M.: Introductory mathematical methods in economics. First edition. McGraw-Hill, London 1991, 257s, ISBN 0-07-707407-6
Classification of course in study plans
Type of course unit
Lecture
Teacher / Lecturer
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Exercise
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Syllabus