FAST-DAB038Acad. year: 2020/2021
Mathematical approaches to the analysis of engineering problems, namely ordinary and partial differential equations, directed to numerical calculations.
Institute of Mathematics and Descriptive Geometry (MAT)
Learning outcomes of the course unit
Knowledge of engineering mathematics at the level of engineering study of civil engineering at FCE BUT.
Recommended optional programme components
Recommended or required reading
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
Language of instruction
1. Errors in numerical calculations. Numerical methods for one nonlinear equation in one unknown
2. Basic principles of iterative methods. The Banach fixed-point theorem.
3. Norms of vectors and of matrices, eigenvalues and eigenvectors of matrices. Iterative methods for systems of linear algebraic equations– part I.
4. Iterative methods for linear algebraic equations – part II. Iterative methods for systems of nonlinear equations.
5. Direct methods for systems of linear algebraic equations, LU-decomposition. Systems of linear algebraic equations with special matrice – part I.
6. Systems of linear algebraic equations with special matrices – part II. The methods based on the minimization of a quadratic form.
7. Computing inverse matrices and determinants, the stability and the condition number of a matrix.
8. Eigenvalues of matrices – the power method. Basic principles of interpolation.
9. Polynomial interpolation.
10. Interpolation by means of splines. Orthogonal polynoms.
11. Approximation by the discrete least squares.
12. Numerical differentiation, Richardson´s extrapolation. Numerical integration of functions in one variables – part I.
13. Numerical integration of functions in one variables – part II. Numerical integration of functions in two variables.
Specification of controlled education, way of implementation and compensation for absences
Extent and forms are specified by guarantor’s regulation updated for every academic year.
Classification of course in study plans
- Programme DKC-GK Doctoral, 1. year of study, summer semester, 4 credits, compulsory-optional
- Programme DPA-GK Doctoral, 1. year of study, summer semester, 4 credits, compulsory-optional
- Programme DKA-GK Doctoral, 1. year of study, summer semester, 4 credits, compulsory-optional
- Programme DPC-GK Doctoral, 1. year of study, summer semester, 4 credits, compulsory-optional
Type of course unit
39 hours, optionally
Teacher / Lecturer