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.