Czech

4

Not applicable.

Institute of Mathematics and Descriptive Geometry (MAT)

Not applicable.

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

Not applicable.

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations -lectures, seminars.

Successful completion of the scheduled tests and submission of solutions to problems assigned by the teacher for home work. Unless properly excused, students must attend all the workshops. The result of the semester examination is given by the sum of maximum of 70 points obtained for a written test and a maximum of 30 points from the seminar.

1. Mathematical modelling. Deterministic and stochastic models, uncertain and vague systems. Errors in numerical calculations.
2. Interpolation. Lagrange and Hermite interpolation of a function. Interpolating 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, compulsory

Follows directly particular lectures.

1. Mathematical modelling. Deterministic and stochastic models, uncertain and vague systems. Errors in numerical calculations.
2. Interpolation. Lagrange and Hermite interpolation of a function. Interpolating 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.