Czech

4

Not applicable.

Institute of Mathematics and Descriptive Geometry (MAT)

Following the aim of the course, students will receive the basic orientaion in numerical and statistical methods needed in material engineering and in related engineering applications.

Basic knowledge of numerical mathematics, probability and statistics, applied to technical problems.

Not applicable.

Not applicable.

Requirements for successful completion of the subject are specified by guarantor’s regulation updated for every academic year.

1. Mathematical modelling. Deterministic and stochastic models, uncertain and vague systems. Errors in numerical calculations.
2. Interpolation. Lagrange and Hermite interpolation of a function. Interpolat-ing functions, especially polynomials and splines.
3. Testing of dependencies. Stochastic functions and correlations. Testing of randomness, conformity and remoteness. Software STATISTICA.
4. Linear regression analysis. Approximation of a function using the least square method. Linear regression.
5. Nonlinear regression analysis. Solving nonlinear algebraic equations and their systems. General regression.
6. Statistical tests. Testing of various distributions. Testing of parameters with one or two random parameters for problems with 1 and 2 random choices.
7. Numerical analysis of technical problems. Fundamentals of numerical dif-ferentiation and integration. Formulation and numerical analysis of direct problems with differential and integral equations. Methods of finite differ-ences, elements and volumes. Software packages for the analysis of technical problems, namely ANSYS a COMSOL.
8. Applications. Using numerical methods for deterministic problems of techni-cal practice: static and dynamic response of a construction, heat and sound propagation.
9. Transfer of uncertainties. Formulation, analysis and numerical solution of direct problems with uncertain parameters.
10. Applications. Reliability of constructions. Estimates of durability using the methods of building mechanics.
11. Identification of parameters. Formulation, analysis and numerical solution of inverse problems.
12. Applications. Uncertainties in laboratory measurements. Model example of a measurement and evaluation of thermal technical material characteristics.
13. Vague problems. Cluster analysis, quantitative, qualitative and binary clus-tering. Fuzzy sets and their application in cluster analysis. Fuzzy regulators in technological processes.

Seminars are scheduled according to lectures.

Not applicable.

Students will obtain the basic knowledge of numerical mathematics, probability and statistics, applied to technical problems, especially from material engineering.

Extent and forms are specified by guarantor’s regulation updated for every academic year.

Not applicable.

Not applicable.

REKTORYS, K. a kol.: Přehled užité matematiky. SNTL, Praha, 1988. (CS)
BUDÍNSKÝ, B., CHARVÁT, J.: Matematika II. SNTL, Praha, 1990. (CS)
LANG, S.: Calculus of Several Variables. Springer, 1996. (EN)
Dalík, Josef: Numerické metody. CERM Brno, ISBN 80-214-0646-1, 1997.

Not applicable.

13 hours, obligation not entered