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# Course detail

## Numerical methods I

Course unit code: FAST-DA61
Type of course unit: optional
Level of course unit: Doctoral (3rd cycle)
Year of study: 1
Semester: summer
Number of ECTS credits:
 Learning outcomes of the course unit: Not applicable.
 Mode of delivery: 20 % face-to-face, 80 % distance learning
 Prerequisites: Basics of linear algebra and vector calculus. Basics of the theory of one- and more-functions (limit, continuous functions, graphs of functions, derivative, partial derivative). Basics of the integral calculus of one- and two-functions.
 Co-requisites: Not applicable.
 Recommended optional programme components: Not applicable.
 Course contents (annotation): Errors in numerical calculations and numerical methods for one nonlinear equation in one unknown. Iterative methods. The Banach fixed-point theorem. Iterative methods for the systems of linear and nonlinear equations. Direct methods for the systems of linear algebraic equations, matrix inversion, eigenvalues and eigenvectors of matrices. Interpolation and approximation of functions. Splines. Numeric differentiation and integration. Extrapolation to the limit.
 Recommended or required reading: HOROVÁ, I., ZELINKA, J.: Numerické metody. Masarykova univerzita v Brně 2004MIKA, S.: Numerické metody algebry. SNTL Praha 1982PŘIKRYL, P., BRANDNER, M.: Numerické metody II. ZČU Plzeň 2000
 Planned learning activities and teaching methods: Not applicable.
 Assesment methods and criteria linked to learning outcomes: Not applicable.
 Language of instruction: Czech
 Work placements: 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.
 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.

Type of course unit:

Lecture: 39 hours, optionally prof. Ing. Jiří Vala, CSc.

The study programmes with the given course