Course Details

Mathematics 5 (M)

Academic Year 2024/25

CA003 course is not part of any programme in the faculty

Course Guarantor

Institute

Language of instruction

Czech

Credits

4 credits

Semester

winter

Forms and criteria of assessment

course-unit credit and examination

Offered to foreign students

Not to offer

Course on BUT site

Lecture

13 weeks, 2 hours/week, elective

Syllabus

1. Mathematical modelling. Deterministic and stochastic models. Errors in numerice calculations. 2. Lagrangean and Hermitean interpolation of functions. Interpolation functions, especially polynomials and splines. 3. Numerical solution of linear and nonlinear algebraic equations and their systems. 4. Numerical derivatives and quadrature. 5. Formulation and numerical solution of direct problems with differential and integral equations. 6. Finite difference, element and volume methods for stationary problems. 7. Methods of lines and discretization in time (Rothe sequences) for nonstationary problems. 8. Statistical tests, variance analysis, fuzzy models. 9. Linear regression analysis. Least squares method. 10. Nonlinear regression analysis. 11. Sensitivity analysis. Application to uncertainty transfer and estimates of durability of building structures. 12. Inverse analysis. Application to determination of material parameters from experiments. 13. Application to significant engineering problems.

Exercise

13 weeks, 1 hours/week, compulsory

Syllabus

Follows directly particular lectures: 1. Mathematical modelling. Deterministic and stochastic models. Errors in numerice calculations. 2. Lagrangean and Hermitean interpolation of functions. Interpolation functions, especially polynomials and splines. 3. Numerical solution of linear and nonlinear algebraic equations and their systems. 4. Numerical derivatives and quadrature. 5. Formulation and numerical solution of direct problems with differential and integral equations. 6. Finite difference, element and volume methods for stationary problems. 7. Methods of lines and discretization in time (Rothe sequences) for nonstationary problems. 8. Statistical tests, variance analysis, fuzzy models. 9. Linear regression analysis. Least squares method. 10. Nonlinear regression analysis. 11. Sensitivity analysis. Application to uncertainty transfer and estimates of durability of building structures. 12. Inverse analysis. Application to determination of material parameters from experiments. 13. Application to significant engineering problems.