Course detail

Numerical Methods

FP-NUMAcad. year: 2024/2025

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 50% 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 30 minutes. The exam is written and lasts 30 minutes. The classification is based on 0.75 times the points obtained during the semester and the points obtained in the written part of the exam (classification according to 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 30 minutes. The points obtained during the semester and the points obtained in the written part of the exam are added together for classification (classification according to ECTS: less than 50 points = F... 90 and more points = A).

Participation in exercises is controlled.

Aims

Understand the general principles and types of computational methods, along with the issues of their convergence and stability. Know the sources of errors, their classification, and perform error estimation. Master effective approximate methods for solving algebraic and transcendental equations, systems of linear and nonlinear equations, basic methods of function approximation, approximate methods for calculating definite integrals, and Monte Carlo methods for selected problems.

Study aids

See 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 algorithm and algorithm complexity
2. Graphs (undirected, directed and rated, Dijkstra's shortest path algorithm, Kruskal's algorithm)
3. Solving nonlinear equations
4. Solving linear systems
5. Roots of polynomials, using Horner's scheme
6. Summary of the material covered
7. Numerical integration and differentiation
8. Interpolation and approximation of functions
9. Working with AI
10. Numerical solution of differential equations
11. Differential equations
12. Summary of the material covered
13. Numerical methods in practice

Exercise

26 hod., compulsory

Teacher / Lecturer

Natálie Rontóová, Ph.D.

Syllabus

1. The concept of algorithm and algorithm complexity, introduction to the PS Diagram program
2. Cycle with a condition at the beginning and end of the cycle, sorting algorithms
3. Sorting algorithms, graphs
4. Solving nonlinear equations - interval bisection method
5. Solving nonlinear equations - tangent method
6. Solving linear systems
7. Roots of polynomials, use of Horner's scheme,
8. Numerical integration and derivative
9. Interpolation of functions
10. Working with AI
11. Consultation
12. Numerical solution of differential equations
13. Repetition

Elearning

eLearning: currently opened course