Course: Numerical Methods

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Course title Numerical Methods
Course code KMA/NM
Organizational form of instruction Lecture + Tutorial
Level of course Bachelor
Year of study 2
Semester Summer
Number of ECTS credits 5
Language of instruction Czech, English
Status of course Compulsory, Compulsory-optional, Optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Daněk Josef, Doc. Ing. Ph.D.
  • Brandner Marek, Doc. Ing. Ph.D.
  • Kopincová Hana, Ing. Ph.D.
  • Tomiczková Světlana, RNDr. Ph.D.
Course content
1. Problems of numerical mathematics, ill-conditioned and well-conditioned problems, stability of algorithms, computational software. 2. Methods for root finding and methods for solution of nonlinear sets of equations. 3. Direct methods for solving linear algebraic equations. 4. Iterative methods for solving linear algebraic equations. 5. Gradient methods for solving linear algebraic equations. 6. Methods for solving eigenvalue problems. 7. Approximation of functions. 8. L2 approximation, discrete Fourier transform. 9. Numerical differentiation 10. Numerical integration. 11. Numerical methods for ordinary differential equations - one-step methods. 12. Numerical methods for ordinary differential equations - multi-step methods.

Learning activities and teaching methods
Interactive lecture, Lecture supplemented with a discussion, Lecture with practical applications, Discussion, Students' portfolio
  • Preparation for formative assessments (2-20) - 20 hours per semester
  • Preparation for an examination (30-60) - 48 hours per semester
  • Contact hours - 65 hours per semester
prerequisite
professional knowledge
aplikovat základní poznatky z lineární algebry (maticový počet, soustavy lineárních algebraických rovnic)
aplikovat základní poznatky z oblasti matematické analýzy (diferenciální a integrální počet)
aplikovat základní znalosti z oblasti matematické analýzy (posloupnosti, řady)
professional skills
řešit soustavy lineárních algebraických rovnic (pomocí přímých metod)
řešit úlohy s posloupnostmi a řadami
stanovit derivace a integrály elementárních funkcí
popsat, vysvětlit a aplikovat vlastnosti elementárních funkcí jedné reálné proměnné
general eligibility
N/A
N/A
learning outcomes
professional knowledge
formulovat úlohu, posoudit její korektnost a podmíněnost
popsat a vysvětlit metody numerického derivování a integrování
popsat a vysvětlit numerické metody pro aproximaci funkcí
popsat a vysvětlit numerické metody pro řešení nelineárních rovnic a jejich soustav
popsat a vysvětlit numerické metody pro řešení počátečních úloh pro obyčejné diferenciální rovnice
popsat a vysvětlit přímé a iterační metody pro řešení soustav lineárních algebraických rovnic
professional skills
posoudit podmíněnost a stabilitu numerických algoritmů
aplikovat numerické metody na praktické úlohy
analyzovat chyby a problémy konvergence numerických metod
algoritmizovat numerické metody
general eligibility
N/A
N/A
N/A
teaching methods
professional knowledge
Lecture supplemented with a discussion
Lecture with practical applications
professional skills
Students' portfolio
Individual study
Practicum
Self-study of literature
general eligibility
Textual studies
Individual study
Task-based study method
assessment methods
professional knowledge
Oral exam
professional skills
Test
Individual presentation at a seminar
Seminar work
general eligibility
Seminar work
Individual presentation at a seminar
Oral exam
Test
Recommended literature
  • Benda, Josef; Černá, Růžena. Numerická matematika : doplňkové skriptum. Vyd. 2. Praha : Vydavatelství ČVUT, 2000. ISBN 80-01-02156-4.
  • Gershenfeld, Neil. The nature of mathematical modeling. 1st pub. Cambridge : Cambridge University Press, 1999. ISBN 0-521-57095-6.
  • Chapra, Steven C.; Canale, Raymond P. Numerical methods for engineers. 2nd ed. New York : McGraw-Hill Book Company, 1990. ISBN 0-07-100412-2.
  • Míka, Stanislav; Brandner, Marek. Numerické metody I. 1. vyd. Plzeň : Západočeská univerzita, 2000. ISBN 80-7082-619-3.
  • Muzikářová, Hana; Voříšek, Jan. Úvod do numerické matematiky. Vyd. 1. Praha : Vysoká škola ekonomická, 1995. ISBN 80-7079-449-6.
  • Přikryl, Petr; Brandner, Marek. Numerické metody II. 1. vyd. Plzeň : Západočeská univerzita, 2000. ISBN 80-7082-699-1.
  • Ralston, Anthony. Základy numerické matematiky. 2. vyd. Praha : Academia, 1978.
  • Samarskij, Aleksandr Andrejevič; Nikolajev, Jevgenij Sergejevič. Numerické řešení velkých řídkých soustav : celost. vysokošk. příručka pro stud. matematicko-fyz. a přírodověd. fakult. 1. vyd. Praha : Academia, 1985.
  • Vitásek, Emil. Numerické metody. 1. vyd. Praha : SNTL, 1987.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Applied Sciences Computations and Design (2014) Special and interdisciplinary fields 2 Summer
Faculty of Applied Sciences Systems for Identification, Security and Communication (2015) Special and interdisciplinary fields 2 Summer
Faculty of Applied Sciences Financial Informatics and Statistics (2016) Economy 2 Summer
Faculty of Applied Sciences Financial Informatics and Statistics (1) Economy 2 Summer
Faculty of Applied Sciences Computer Modelling (2014) Special and interdisciplinary fields 2 Summer
Faculty of Applied Sciences Intelligent Man-Machine Communication (2016) Special and interdisciplinary fields 2 Summer
Faculty of Applied Sciences Information Technologies (2012) Informatics courses 2 Summer
Faculty of Applied Sciences Mathematics for Business Studies (2016) Mathematics courses 2 Summer
Faculty of Applied Sciences Financial Informatics and Statistics (2016) Economy 2 Summer
Faculty of Applied Sciences Computations and Design (1) Special and interdisciplinary fields 2 Summer
Faculty of Applied Sciences Intelligent Man-Machine Communication (2015) Special and interdisciplinary fields 2 Summer
Faculty of Applied Sciences Computer Control of Systems and Processes (2015) Special and interdisciplinary fields 2 Summer
Faculty of Applied Sciences Land-use Planning (2016) Special and interdisciplinary fields 2 Summer
Faculty of Applied Sciences Information Technologies (2013) Informatics courses 2 Summer
Faculty of Applied Sciences Computer Systems (2016) Electrical engineering, telecommunication and IT 2 Summer
Faculty of Applied Sciences Mathematics for Business Studies (2015) Mathematics courses 2 Summer
Faculty of Applied Sciences Mathematics for Business Studies (2011) Mathematics courses 2 Summer
Faculty of Applied Sciences Computations and Design (2017) Special and interdisciplinary fields 2 Summer
Faculty of Applied Sciences Systems for Identification, Security and Communication (2017) Special and interdisciplinary fields 2 Summer
Faculty of Applied Sciences Computer Systems (2017) Electrical engineering, telecommunication and IT 2 Summer
Faculty of Applied Sciences Intelligent Man-Machine Communication (2017) Special and interdisciplinary fields 2 Summer
Faculty of Applied Sciences Applied and Engineering Physics (2017) Special and interdisciplinary fields 2 Summer
Faculty of Applied Sciences Mathematics and its Applications (2015) Mathematics courses 2 Summer
Faculty of Applied Sciences Mathematics for Science (2012) Mathematics courses 2 Summer
Faculty of Applied Sciences Mathematics for Business Studies (2017) Mathematics courses 2 Summer
Faculty of Applied Sciences Cybernetics and Control Engineering (2017) Special and interdisciplinary fields 2 Summer
Faculty of Applied Sciences Computer Systems (2017) Electrical engineering, telecommunication and IT 2 Summer
Faculty of Applied Sciences Systems for Identification, Security and Communication (2016) Special and interdisciplinary fields 2 Summer
Faculty of Applied Sciences Applied and Engineering Physics (2016) Special and interdisciplinary fields 2 Summer
Faculty of Applied Sciences Applied and Engineering Physics (2012) Special and interdisciplinary fields 2 Summer
Faculty of Applied Sciences Information Technologies (2015) Informatics courses 2 Summer
Faculty of Applied Sciences Geomatics (2017) Construction industry, geodesy and cartography 2 Summer
Faculty of Applied Sciences Mathematics and its Applications (2017) Mathematics courses 2 Summer
Faculty of Applied Sciences Financial Informatics and Statistics (2017) Economy 2 Summer
Faculty of Applied Sciences Mathematics and its Applications (2017) Mathematics courses 2 Summer
Faculty of Applied Sciences Computer Systems (2016) Electrical engineering, telecommunication and IT 2 Summer
Faculty of Applied Sciences Computer Systems (2012) Electrical engineering, telecommunication and IT 2 Summer
Faculty of Applied Sciences Cybernetics and Control Engineering (2016) Special and interdisciplinary fields 1 Summer
Faculty of Applied Sciences Information Technologies (2016) Informatics courses 2 Summer
Faculty of Applied Sciences Geomatics (2017) Construction industry, geodesy and cartography 2 Summer
Faculty of Applied Sciences Geomatics (2016) Construction industry, geodesy and cartography 2 Summer
Faculty of Applied Sciences Computer Modelling (2017) Special and interdisciplinary fields 2 Summer
Faculty of Applied Sciences Mathematics and Management (2011) Mathematics courses 2 Summer
Faculty of Applied Sciences Cybernetics and Control Engineering (2017) Special and interdisciplinary fields 1 Summer
Faculty of Applied Sciences Information Technologies (2017) Informatics courses 2 Summer
Faculty of Applied Sciences Financial Informatics and Statistics (2017) Economy 2 Summer
Faculty of Applied Sciences Computer Control of Systems and Processes (2016) Special and interdisciplinary fields 2 Summer
Faculty of Applied Sciences Computer Control of Systems and Processes (2012) Special and interdisciplinary fields 2 Summer
Faculty of Applied Sciences Cybernetics and Control Engineering (2016) Special and interdisciplinary fields 2 Summer
Faculty of Applied Sciences Information Technologies (2016) Informatics courses 2 Summer
Faculty of Applied Sciences Information Technologies (2017) Informatics courses 2 Summer
Faculty of Applied Sciences Computer Systems (2013) Electrical engineering, telecommunication and IT 2 Summer
Faculty of Applied Sciences General Mathematics (2012) Mathematics courses 2 Summer
Faculty of Applied Sciences Mathematics for Business Studies (2017) Mathematics courses 2 Summer
Faculty of Applied Sciences Scientific Computing and Modelling (2011) Mathematics courses 2 Summer
Faculty of Applied Sciences General Mathematics (2012) Mathematics courses 2 Summer
Faculty of Applied Sciences Computer Control of Systems and Processes (2017) Special and interdisciplinary fields 2 Summer
Faculty of Applied Sciences Systems for Identification, Security and Communication (2012) Special and interdisciplinary fields 2 Summer
Faculty of Applied Sciences Computer Modelling (2016) Special and interdisciplinary fields 2 Summer
Faculty of Applied Sciences Computations and Design (2016) Special and interdisciplinary fields 2 Summer
Faculty of Applied Sciences Geomatics (2016) Construction industry, geodesy and cartography 2 Summer
Faculty of Applied Sciences Land-use Planning (2017) Special and interdisciplinary fields 2 Summer
Faculty of Applied Sciences Intelligent Man-Machine Communication (2012) Special and interdisciplinary fields 2 Summer
Faculty of Applied Sciences Cybernetics and Control Engineering (2013) Special and interdisciplinary fields 2 Summer
Faculty of Applied Sciences Mathematics and its Applications (2016) Mathematics courses 2 Summer
Faculty of Applied Sciences Cybernetics and Control Engineering (2012) Special and interdisciplinary fields 1 Summer
Faculty of Applied Sciences Financial Informatics and Statistics (2007) Economy 2 Summer
Faculty of Applied Sciences Mathematics for Business Studies (2016) Mathematics courses 2 Summer
Faculty of Applied Sciences Mathematics and its Applications (2016) Mathematics courses 2 Summer
Faculty of Applied Sciences Mathematics and its Applications (2015) Mathematics courses 2 Summer