Course detail

Numerical Methods

FP-NUMAcad. year: 2023/2024

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)

Entry knowledge

Not applicable.

Rules for evaluation and completion of the course

Credit requirements:

Passing two control tests and achieving at least 55% of the points. In case of absence, it is possible to complete one of the assignments in the credit week. One of the written assignments can be corrected during the credit week.
Awarding credit is a necessary condition for taking the exam.

The exam is written and lasts 1 hour. If the student does not achieve at least 50% of the total number of attainable points,  the entire exam are graded "F" (at ECTS).

Individual study plan:
Credit requirements:
Passing the comprehensive control test and achieving at least 55% of the points.

The exam is written and lasts 1 hour. If the student does not achieve at least 50% of the total number of attainable points,  the entire exam are graded "F" (at ECTS).

 

Participation in exercises is controlled.

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.

Study aids

Viz. literature

Prerequisites and corequisites

Not applicable.

Basic literature

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

Recommended reading

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

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 hod., 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. Characterization of calculation methods, errors and their classification, convergence and stability, repetition of the course of the function,
3. Solving nonlinear equations
4. Solving linear systems
5. Roots of polynomials, use of Horner's scheme
6. Summary of the material covered
7. Interpolation and approximation of functions
8. Numerical integration and derivation
9. Numerical solution of differential equations
10. Graphs (undirected, directed and evaluated, Dijkstra's shortest path algorithm, Kruskal's algorithm)
11. Differential equation
12. Summary of the material covered
13. Monte Carlo methods

Exercise

26 hod., compulsory

Teacher / Lecturer

Natálie Rontóová, Ph.D.

Syllabus

1. The concept of an algorithm and the complexity of an algorithm, familiarization with the PS Diagram program

2. Cycle with a condition at the beginning and at the end of the cycle, sorting algorithms

3. Characterization of calculation methods, repetition of the course of the function,

4. Solving nonlinear equations - interval bisection method

5. Solving nonlinear equations - method of tangents

6. Solving linear systems

7. Roots of polynomials, use of Horner's scheme,

8. Interpolation of functions

9. Approximation of functions - method of least squares, Taylor's series

10. Numerical integration and derivation

11. Numerical solution of differential equations

12. Graphs (undirected, directed and evaluated, Dijkstra's shortest path algorithm, Kruskal's algorithm)

13. Differential equationstar_border​

Elearning

eLearning: currently opened course