Course Details

Numerical methods 1

DAB030 course is part of 24 study plans

Ph.D. full-t. program DPC-S compulsory-elective Summer Semester 1st year 4 credits

Ph.D. full-t. program DPC-M compulsory-elective Summer Semester 1st year 4 credits

Ph.D. full-t. program DPC-K compulsory-elective Summer Semester 1st year 4 credits

Ph.D. full-t. program DPC-V compulsory-elective Summer Semester 1st year 4 credits

Ph.D. full-t. program DPC-E compulsory-elective Summer Semester 1st year 4 credits

Ph.D. full-t. program DPC-GK compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program DKC-S compulsory-elective Summer Semester 1st year 4 credits

Ph.D. full-t. program DPA-S compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program DKC-V compulsory-elective Summer Semester 1st year 4 credits

Ph.D. full-t. program DPA-V compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program DKC-M compulsory-elective Summer Semester 1st year 4 credits

Ph.D. full-t. program DPA-M compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program DKC-K compulsory-elective Summer Semester 1st year 4 credits

Ph.D. full-t. program DPA-K compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program DKC-E compulsory-elective Summer Semester 1st year 4 credits

Ph.D. full-t. program DPA-E compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program DKC-GK compulsory-elective Summer Semester 1st year 4 credits

Ph.D. full-t. program DPA-GK compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program DKA-GK compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program DKA-S compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program DKA-M compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program DKA-K compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program DKA-V compulsory-elective Summer Semester 1st year 4 credits

Ph.D. combi. program DKA-E compulsory-elective Summer Semester 1st year 4 credits

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

Course Guarantor

prof. Ing. Jiří Vala, CSc.

Institute

Institute of Mathematics and Descriptive Geometry

Learning outcomes

The aim of the course is to give students the overview of modern mathematical approaches to the analysis of engineering problems, to be able to apply them to concrete problems of their disciplines.

Prerequisites

Knowledge of engineering mathematics at the level of engineering study of civil engineering at FCE BUT.

Corequisites

Not required.

Planned educational activities and teaching methods

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.

Forms and criteria of assessment

Evaluatiopn of work of specific tasks.

Objective

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 instruction, the form of instruction, and the form of compensation of the absences

Vymezení kontrolované výuky a způsob jejího provádění stanoví každoročně aktualizovaná vyhláška garanta předmětu.

Lecture

3 hours/week, 13 weeks, elective

Syllabus of lectures

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.