Course detail
Mathematics
FAST-DAB038Acad. year: 2023/2024
Mathematical approaches to the analysis of engineering problems, namely ordinary and partial differential equations, directed to numerical calculations.
Language of instruction
Czech
Number of ECTS credits
4
Mode of study
Not applicable.
Guarantor
Department
Institute of Mathematics and Descriptive Geometry (MAT)
Entry knowledge
Knowledge of engineering mathematics at the level of engineering study of civil engineering at FCE BUT.
Rules for evaluation and completion of the course
Extent and forms are specified by guarantor’s regulation updated for every academic year.
Aims
Not applicable.
Study aids
Not applicable.
Prerequisites and corequisites
Not applicable.
Basic literature
DALÍK J., PŔIBYL O., VALA J.: Numerické metody 2 (pro doktorandy). FAST VUT v Brně 2010. (CS)
DALÍK J.: Numerické metody. CERM Brno 1997. (CS)
VALA J.: Numerická matematika. FAST VUT v Brně 2021. (CS)
DALÍK J.: Numerické metody. CERM Brno 1997. (CS)
VALA J.: Numerická matematika. FAST VUT v Brně 2021. (CS)
Recommended reading
Not applicable.
Classification of course in study plans
- Programme DPC-GK Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DPA-GK Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DPC-GK Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DKA-GK Doctoral 1 year of study, summer semester, compulsory-optional
Type of course unit
Lecture
39 hod., optionally
Teacher / Lecturer
Syllabus
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.