University of Pardubice
Study programmes & Course catalogue
for academic year 2016/2017
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Course: Applied Mathematics

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Course title Applied Mathematics
Course code KID/PAMAP
Organizational form of instruction Lecture + Tutorial
Level of course Master
Year of study 1
Semester Winter
Number of ECTS credits 5
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Kulička Jiří, Mgr. Ph.D.
  • Míča Ondřej, Ing.
Course content
Principle of iteration methods, recurrent errors and their classification, estimation arithmetic operation errors. Conditional and numerical solution stability, number condition, ill conditioning. Approximation of functions using least squares methods, (principle, classes of the function, orthogonality and independence of systems) Construction of orthogonal system of polynomials and calculation of the approximation polynomial. Trigonometric Polynomial Approximation. Interpolating polynomial - generally true problem, error estimation of interpolation, Lagrange and Newton interpolating polynomial; equidistant knots sequence. Hermit interpolating polynomial. Methods for solving equations (the Banach fixed point theorem and its proof). Error estimate of kth iteration; determination of the contracted function from derivation. Newton method, secant method and regula falsi. Numerical solution of linear equations systems (LU decomposition). Gaussian elimination algorithm, Gauss-Jordan method, method of iteration for systems of linear equations (Jacobi, Gauss-Seidl). Convergence of stationary iteration methods Relaxation method. Numerical integration, Numerical derivation, error estimate; methods for solving differential equations. Euler's method and different modification for solutions to a ordinary differential equations. Runge-Kutta method.

Learning activities and teaching methods
Monologic (reading, lecture, briefing), Skills training
Learning outcomes
The student will be introduced to the mathematical basis theory of technical operations and their implementation in specialized software.
The graduate can pass judgment on basic numerical method and suggest their application.
Prerequisites
unspecified

Assessment methods and criteria
Oral examination, Written examination

Giving a credit confirms that a student has attended the lessons to the extent required and fulfilled all the qualified requirements. Conditions for obtaining a credit will be provided by the lecturer. Format, content and length of the exam are determined in accordance with the Study and Examination Rules of the University of Pardubice.
Recommended literature
  • Atkinson, Kendall E.. Elementary numerical analysis. Hoboken: John Wiley & Sons, 2004. ISBN 0-471-43337-3.
  • Chapra, S.C., Canale, R.P. Numerical methods for engineers. 2006. ISBN 007-124429-8.
  • Kulička, Jiří. Elementární algoritmy aplikované matematiky : studijní opora. Pardubice: Univerzita Pardubice, 2014. ISBN 978-80-7395-846-6.
  • Prouza, L. st. - Prouza, L. ml. Matematické základy finančních operací. Univerzita Pardubice, 2000.
  • Rektorys, K. a kol. Přehled užité matematiky. Praha: Prometheus, 2000.
  • Vitásek, E. Numerické metody. Praha, SNTL, 1987.


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
Faculty: Faculty of Transport Engineering Study plan (Version): Electrical Engineering and Electronic Systems in Transport (2014) Category: Transportation and communications 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Transport Engineering Study plan (Version): Transport Means: Road Vehicles (2016) Category: Transportation and communications 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Transport Engineering Study plan (Version): Transport Means: Rail Vehicles (2014) Category: Transportation and communications 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Transport Engineering Study plan (Version): Transport Technology and Control (2016) Category: Transportation and communications 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Transport Engineering Study plan (Version): Transport Means: Rail Vehicles (2016) Category: Transportation and communications 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Transport Engineering Study plan (Version): Transport Means: Rail Vehicles (2013) Category: Transportation and communications 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Transport Engineering Study plan (Version): Transport Technology and Control (2013) Category: Transportation and communications 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Transport Engineering Study plan (Version): Transport Management, Marketing and Logistics (2016) Category: Transportation and communications 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Transport Engineering Study plan (Version): Transport Means: Environmental Protection in Transport (2016) Category: Transportation and communications 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Transport Engineering Study plan (Version): Electrical Engineering and Electronic Systems in Transport (2013) Category: Transportation and communications 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Transport Engineering Study plan (Version): Transport Management, Marketing and Logistics (2014) Category: Transportation and communications 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Transport Engineering Study plan (Version): Transport Means: Environmental Protection in Transport (2015) Category: Transportation and communications 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Transport Engineering Study plan (Version): Electrical Engineering and Electronic Systems in Transport (2016) Category: Transportation and communications 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Transport Engineering Study plan (Version): Applied Informatics in Transport (2014) Category: Informatics courses 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Transport Engineering Study plan (Version): Transport Technology and Control (2014) Category: Transportation and communications 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Transport Engineering Study plan (Version): Applied Informatics in Transport (2016) Category: Informatics courses 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Transport Engineering Study plan (Version): Transport Management, Marketing and Logistics (2013) Category: Transportation and communications 1 Recommended year of study:1, Recommended semester: Winter
Faculty: Faculty of Transport Engineering Study plan (Version): Transport Means: Road Vehicles (2014) Category: Transportation and communications 1 Recommended year of study:1, Recommended semester: Winter
University of Pardubice, date of update: 02.11.2024 23:51. Data created for academic year 2016/2017