Course Details
Mathematics 5 (M)
Academic Year 2023/24
CA003 course is part of 1 study plan
N-P-C-SI (N) / M Winter Semester 1st year
Interpolation and approximation of functions. Numerical solution of algebraic equations and their systems. Numerical derivatives and quadrature. Variance analysis, regression analysis. Numerical solution of stationary and non-stationary boundary and initial problems for differential equations with applications to civil engineering. Direct, sensitivity and inverse problems.
Course Guarantor
Institute
Objective
Students will obtain the basic knowledge of numerical mathematics, probability and statistics, applied to technical problems, especially from material engineering.
Knowledge
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.
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.
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.
Prerequisites
Basic knowledge of numerical mathematics, probability and statistics, applied to technical problems.
Language of instruction
Czech
Credits
4 credits
Semester
winter
Forms and criteria of assessment
course-unit credit and examination
Specification of controlled instruction, the form of instruction, and the form of compensation of the absences
Extent and forms are specified by guarantor’s regulation updated for every academic year.
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.