714-0253/01 – Numerical Methods (NM)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits4
Subject guarantorRNDr. Jana Staňková, Ph.D.Subject version guarantorRNDr. Jana Staňková, Ph.D.
Study levelundergraduate or graduateRequirementOptional
Year1Semesterwinter
Study languageCzech
Year of introduction2015/2016Year of cancellation
Intended for the facultiesFASTIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
STA50 RNDr. Jana Staňková, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2

Subject aims expressed by acquired skills and competences

The first part of this course is dedicated to finding numerical solutions of mathematical problems. These problems can arise from other courses as well as from practice. The main emphasis lays in explanation of fundamental principles of numerical methods and of their general properties. The students learn how to decide which numerical procedure is a suitable tool for solving a specific problem. An important ingredient of the course is algorithmic implementation of the learned numerical methods. The students learn how to use existing software specialized for numerical computations, too. The graduate of this course should be able: * to recognize problems solvable by numerical procedures and to find an appropriate numerical method; * to decide whether the obtained numerical solution is accurate enough and, if it is not the case, to assess the reasons of inaccuracies; * to propose an algorithmic procedure to solving a problem and to choose a suitable software for its realization;

Teaching methods

Lectures
Tutorials

Summary

The first part of this course deals with selected issues in numerical computations (including sources and types of numerical errors, conditionality of certain problems and algorithms), with methods for solving algebraic and transcendent equations, with solving systems of linear equations, with interpolation and approximation of functions, with numerical computations of integrals, and with Cauchy problems for ordinary differential equations.

Compulsory literature:

Kučera, R.: Numerické metody. VŠB-TU Ostrava 2007, na www.studopory.vsb.cz, mdg.vsb.cz/M,ISBN 80-248-1198-7.

Recommended literature:

Harshbarger, Ronald; Reynolds, James: Calculus with Applications, D.C. Heath and Company 1990, ISBN 0-669-21145-1

Way of continuous check of knowledge in the course of semester

E-learning

Další požadavky na studenta

There are no other requirements on students

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

. Problematics of numerical computing . Sources and types of errors. Conditionality of problems and algorithms. 2. Methods for solving algebraic and transcendental equations. The bisection method, the iterative method for solving equations. 3. The Newton method, the Regula-Falsi (False-Position) method, the combined method. 4. Solving systems of linear equations. Direct solution methods. Iterative methods (the Jacobi method, the Seidel method). Matrix norms. 5. Interpolation and approximation of functions. Approximation – the least-square method. Lagrange interpolation polynomials. 6. Newton interpolation polynomials. Spline-function interpolation. 7. Numerical integration. Newton-Cotes quadrature formulas. Composed quadrature formulas. Error estimation. 8. The Richardson extrapolation. 9. Initial value problems for ordinary differential equations. One-step methods. The Euler method. Error estimation using the half-step method. 10. The Runge-Kutta methods. Estimation of the approximation error.

Conditions for subject completion

Full-time form (validity from: 2015/2016 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 20  5
        Examination Examination 80  51
Mandatory attendence parzicipation:

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Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2017/2018 (N3607) Civil Engineering (3607T035) Geotechnics P Czech Ostrava 1 Optional study plan
2017/2018 (N3607) Civil Engineering (3607T013) Municipal Engineering and Construction P Czech Ostrava 1 Optional study plan
2016/2017 (N3607) Civil Engineering (3607T035) Geotechnics P Czech Ostrava 1 Optional study plan
2016/2017 (N3607) Civil Engineering (3607T013) Municipal Engineering and Construction P Czech Ostrava 1 Optional study plan
2015/2016 (N3607) Civil Engineering (3607T013) Municipal Engineering and Construction P Czech Ostrava 1 Optional study plan
2015/2016 (N3607) Civil Engineering (3607T035) Geotechnics P Czech Ostrava 1 Optional study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner