# 230-0226/01 – Numerical Methods (NM)

 Gurantor department Department of Mathematics Credits 4 Subject guarantor doc. Ing. Martin Čermák, Ph.D. Subject version guarantor RNDr. Jana Staňková, Ph.D. Study level undergraduate or graduate Requirement Optional Year 1 Semester winter Study language Czech Year of introduction 2018/2019 Year of cancellation 2020/2021 Intended for the faculties FAST Intended for study types Follow-up Master
Instruction secured by
CER365 doc. Ing. Martin Čermák, Ph.D.
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;

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:

Abhishek, G.: Numerical Methods Using MATLAB. Springer Nature 2014, ISBN 9781484201558.

### Recommended literature:

Boháč, Z.,Častová, N.: Základní numerické metody. Skriptum VŠB, Ostrava 1985. Přikryl, P.: Numerické metody matematické analýzy. MVŠT, SNTL 1985. Ralston, A.: Základy numerické matematiky. Academia 1973. Harshbarger, Ronald; Reynolds, James: Calculus with Applications, D.C. Heath and Company 1990, ISBN 0-669-21145-1 Görner, V., Nedoma, P. Programový systém MATLAB, ČVUT Praha, 1991 MATLAB Reference Guide, Mass. 01760, 1994.

### Other requirements

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: 2018/2019 Winter semester, validity until: 2020/2021 Summer semester)
Min. number of pointsMax. počet pokusů
Credit and Examination Credit and Examination 100 (100) 51
Credit Credit 20  5
Examination Examination 80 (80) 30 3
Písemná zkouška Written examination 60  25
Ústní zkouška Oral examination 20  5
Mandatory attendence participation: At least 70% attendance at the exercises. Absence, up to a maximum of 30%, must be excused and the apology must be accepted by the teacher (the teacher decides to recognize the reason for the excuse).

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Conditions for subject completion and attendance at the exercises within ISP: Mandatory participation in the course is not required. Other conditions for subject completion will respect the individual needs of the student.

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### Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2018/2019 (N3607) Civil Engineering (3607T035) Geotechnics P Czech Ostrava 1 Optional study plan
2018/2019 (N3607) Civil Engineering (3607T013) Municipal Engineering and Construction P Czech Ostrava 1 Optional study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

### Assessment of instruction

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