Course detail

# Numerical methods 1

Mathematical approaches to the analysis of engineering problems, namely ordinary and partial differential equations, directed to numerical calculations.

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.

Recommended optional programme components

Not applicable.

Not applicable.

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.

Classification of course in study plans

• Programme DKC-S Doctoral, 1. year of study, summer semester, 4 credits, compulsory-optional
• Programme DPA-S Doctoral, 1. year of study, summer semester, 4 credits, compulsory-optional
• Programme DKA-S Doctoral, 1. year of study, summer semester, 4 credits, compulsory-optional
• Programme DPC-S Doctoral, 1. year of study, summer semester, 4 credits, compulsory-optional
• Programme DPA-E Doctoral, 1. year of study, summer semester, 4 credits, compulsory-optional
• Programme DKA-E Doctoral, 1. year of study, summer semester, 4 credits, compulsory-optional
• Programme DPC-E Doctoral, 1. year of study, summer semester, 4 credits, compulsory-optional
• Programme DKC-E 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
• 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-M Doctoral, 1. year of study, summer semester, 4 credits, compulsory-optional
• Programme DKA-M Doctoral, 1. year of study, summer semester, 4 credits, compulsory-optional
• Programme DKC-M Doctoral, 1. year of study, summer semester, 4 credits, compulsory-optional
• Programme DPA-M Doctoral, 1. year of study, summer semester, 4 credits, compulsory-optional
• Programme DPC-K Doctoral, 1. year of study, summer semester, 4 credits, compulsory-optional
• Programme DPA-K Doctoral, 1. year of study, summer semester, 4 credits, compulsory-optional
• Programme DKC-K Doctoral, 1. year of study, summer semester, 4 credits, compulsory-optional
• Programme DKA-K Doctoral, 1. year of study, summer semester, 4 credits, compulsory-optional
• Programme DPA-V Doctoral, 1. year of study, summer semester, 4 credits, compulsory-optional
• Programme DKC-V Doctoral, 1. year of study, summer semester, 4 credits, compulsory-optional
• Programme DPC-V Doctoral, 1. year of study, summer semester, 4 credits, compulsory-optional
• Programme DKA-V Doctoral, 1. year of study, summer semester, 4 credits, compulsory-optional

#### Type of course unit

Lecture

39 hours, optionally

Teacher / Lecturer