Course detail

Numerical Methods

FP-NUMAcad. year: 2022/2023

Students will become familiar with the analysis of basic problems of numerical mathematics and suitable algorithms for their solution. The introductory part of the course is intended for familiarization with algorithm designs, data abstraction and their implementation so that students think about the use of computing resources algorithmically and thus be able to effectively use program resources for data processing in the future.
Subsequently, the student will be introduced to some numerical methods (approximation of functions, solution of nonlinear equations, approximate determination of derivative and integral, solution of differential equations) suitable for modeling various problems of economic practice.

Language of instruction

Czech

Number of ECTS credits

6

Mode of study

Not applicable.

Guarantor

doc. Mgr. Veronika Novotná, Ph.D.

Department

Institute of Informatics (ÚI)

Learning outcomes of the course unit

Not applicable.

Prerequisites

Not applicable.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Credit requirements:
Preparation and submission of a seminar paper, which will be graded at least "E". Assignment of the seminar work will be published in the news and on e-learning.

The exam is written and lasts 1 hour. If the student does not achieve at least 60% of the total number of attainable points, the written part and the entire exam are graded "F".

Individual study plan:
Credit requirements:
Preparation and submission of a seminar paper, which will be graded at least "E". Assignment of the seminar paper will be published in the news and on e-learning.

The exam is written and lasts 1 hour. If the student does not achieve at least 60% of the total number of attainable points, the written part and the entire exam are graded "F".

Course curriculum

An overview of the general principles and types of calculation methods used in applications of differential and integral calculus, linear algebra and differential equations with an emphasis on the issue of their errors, convergence and stability of calculations:

 

The concept of an algorithm and the complexity of an algorithm (algorithm, basic properties, flow diagram, cycles with a constant number of repetitions, with a condition at the beginning and end of the cycle)
Characterization of calculation methods, errors and their classification, convergence and stability, repetition of the course of the function,
Solving nonlinear equations
Solving linear systems
Roots of polynomials, use of Horner's scheme, interpolation
Approximation of functions
Numerical integration and derivation
Numerical solution of differential equations
Graph theory I (introduction – undirected, directed and graded graphs)
Graph Theory II (Dijkstra's shortest path algorithm, Kruskal's algorithm)
Differential equation
Monte Carlo methods
Final summary

Work placements

Not applicable.

Aims

Pochopit obecné principy a typy výpočetních metod spolu s problémy jejich konvergence a stability. Znát zdroje chyb, jejich klasifikaci a provádět odhady chyb. Zvládnout efektivní přibližné metody řešení algebraických a transcendentních rovnic, soustav lineárních a nelineárních rovnic, základní metody aproximace funkcí, přibližné metody výpočtu určitých integrálů a metody Monte Carlo pro vybrané problémy.

Specification of controlled education, way of implementation and compensation for absences

Participation in exercises is controlled.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

V. Novotná, B. Půža: Výpočetní metody. Vysoké učení technické v Brně, Fakulta podnikatelská, 2015. ISBN 978-80-214-5248-0.
Maroš, B., Marošová, M.: Základy numerické matematiky. Skriptum FSI VUT Brno, 1997.
Horová, I.: Numerické metody. Skriptum PřF MU Brno, 2004, ISBN 80-210-3317-7

Recommended reading

SOLTYS, Michael. An introduction to the analysis of algorithms. 3rd edition. New Jersey: World Scientific, 2018. ISBN 978-981-3235-908.
Krejsa, M., Algoritmizace inženýrských výpočtů, učební texty v obrazovkové verzi i ve verzi pro tisk, VŠB-TU Ostrava, 2011.

eLearning

eLearning: currently opened course

Classification of course in study plans

  • Programme BAK-MIn Bachelor's, 1. year of study, summer semester, compulsory

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

doc. Mgr. Veronika Novotná, Ph.D.

Syllabus

1. The concept of an algorithm and the complexity of an algorithm (algorithm, basic properties, flowchart, cycles with a constant number of repetitions, with a condition at the beginning and end of the cycle)
2. Graphs (undirected, directed and graded, Dijkstra's shortest path algorithm, Kruskal's algorithm)
3. Characterization of calculation methods, errors and their classification, convergence and stability
4. Solving nonlinear equations
5. Roots of polynomials, use of Horner's scheme
6. Solving linear systems
7. Interpolation
8. Approximation of functions
9. Numerical integration and derivation
10. Numerical solution of differential equations
11. Differential equation
12. Monte Carlo methods.
13. Final summary

Exercise

26 hours, optionally

Teacher / Lecturer

Natálie Rontóová, Ph.D.

Syllabus

1. The concept of an algorithm and the complexity of an algorithm (algorithm, basic properties, flowchart, cycles with a constant number of repetitions, with a condition at the beginning and end of the cycle)
2. Graphs (undirected, directed and graded, Dijkstra's shortest path algorithm, Kruskal's algorithm)
3. Characterization of calculation methods, errors and their classification, convergence and stability
4. Solving nonlinear equations
5. Roots of polynomials, use of Horner's scheme
6. Solving linear systems
7. Interpolation
8. Approximation of functions
9. Numerical integration and derivation
10. Numerical solution of differential equations
11. Differential equation
12. Monte Carlo methods.
13. Final summary

eLearning

eLearning: currently opened course