Course detail
Numerical methods 1
FAST-DAB030Acad. year: 2021/2022
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)
Learning outcomes of the course unit
Not applicable.
Prerequisites
Knowledge of engineering mathematics at the level of engineering study of civil engineering at FCE BUT.
Co-requisites
Not applicable.
Planned learning activities and teaching methods
Not applicable.
Assesment methods and criteria linked to learning outcomes
Not applicable.
Course curriculum
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.
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.
Work placements
Not applicable.
Aims
Understanding the main priciples of numeric calculation and the factors influencing calculation. Solving selected basic problems of numerical analysis, using iteration methods to solve the f(x)=0 equation and systems of linear algebraic equations using calculation algorithms. Learning how to approximate eigenvalues and eigenvectors of matrices. Learning about the basic problems in interpolation and approximation of functions. Getting acquainted with the principles of numeric differentiation and knowing how to numerically approximate integrals of one- and two-functions.
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.
Recommended optional programme components
Not applicable.
Prerequisites and corequisites
Not applicable.
Basic literature
Not applicable.
Recommended reading
Not applicable.
Classification of course in study plans
- Programme DPA-M Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DPC-M Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DPA-K Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DPC-K Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DPA-V Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DPC-V Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DPA-S Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DPC-S Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DPA-E Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DPC-E 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-M Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DKC-M Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DKA-K Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DKC-K Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DKA-V Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DKC-V Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DKA-S Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DKC-S Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DKA-E Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DKC-E Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DKA-GK Doctoral 1 year of study, summer semester, compulsory-optional
- Programme DKC-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.