Course detail

Numerical Methods

FP-nmePAcad. year: 2026/2027

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

5

Mode of study

Not applicable.

Guarantor

doc. Mgr. Veronika Novotná, Ph.D.

Department

Institute of Informatics (ÚI)

Entry knowledge

Mathematics 1

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 for selected problems.

Study aids

See Literature

Prerequisites and corequisites

Not applicable.

Basic literature

JACQUES, Ian, 2023. Mathematics for economics and business. Tenth edition. Harlow, England: Pearson. ISBN 978-1-292-19166-9. (EN)
V. Novotná, B. Půža: Výpočetní metody. Vysoké učení technické v Brně, Fakulta podnikatelská, 2015. ISBN 978-80-214-5248-0. (CS)

Recommended reading

Krejsa, M., Algoritmizace inženýrských výpočtů, učební texty, VŠB-TU Ostrava, 2024. (CS)
M. SOLTYS. An introduction to the analysis of algorithms. 3rd edition. New Jersey: World Scientific, 2018. ISBN 978-981-3235-908. (EN)

Classification of course in study plans

  • Programme BAK-MIn Bachelor's 2 year of study, winter semester, compulsory

Type of course unit

 

Lecture

13 hours, optionally

Teacher / Lecturer

doc. Mgr. Veronika Novotná, Ph.D.

Syllabus

Graphs (undirected, directed and rated, Dijkstra's shortest path algorithm, Kruskal's algorithm)
Solution of nonlinear equations - interval bisection method, tangent method
Solution of linear systems
Interpolation of functions
Approximate functions
Numerical integration and differentiation
Numerical solution of differential equations

Exercise

26 hours, compulsory

Teacher / Lecturer

doc. Mgr. Veronika Novotná, Ph.D.

Syllabus

  1. The concept of algorithm and algorithm complexity, introduction to thePS Diagram program
  2. A cycle with a condition at the beginning and end of the cycle, sorting algorithms
  3. Graphs
  4. Solution of nonlinear equations - interval bisection method
  5. Solution of nonlinear equations - tangent method
  6. Solution of linear systems
  7. Polynomials, roots of polynomials, Horner scheme
  8. Interpolation of functions
  9. Approximation of functions
  10. Numerical integration
  11. Numerical derivative
  12. Numerical solution of differential equations
  13. Differential equations

Self-study

52 hours, optionally

Teacher / Lecturer

doc. Mgr. Veronika Novotná, Ph.D.

Individual preparation for an ending of the course

40 hours, optionally

Teacher / Lecturer

doc. Mgr. Veronika Novotná, Ph.D.