# 230-0226/05 – Numerical Methods (NM)

 Gurantor department Department of Mathematics Credits 2 Subject guarantor doc. Ing. Martin Čermák, Ph.D. Subject version guarantor doc. Ing. Martin Čermák, Ph.D. Study level undergraduate or graduate Requirement Optional Year Semester summer Study language Czech Year of introduction 2019/2020 Year of cancellation Intended for the faculties HGF, FAST Intended for study types Follow-up Master, Bachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
CER365 doc. Ing. Martin Čermák, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Graded credit 0+3
Part-time Graded credit 0+16

### 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.

### Way of continuous check of knowledge in the course of semester

Individually developed program for classified credit.

### Other requirements

There are no other requirements on students

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

1. Problematics of numerical computing. Sources and types of errors. Conditionality of problems and algorithms. 2. Basic work with MATLAB. 3. Scrips and functions in MATLAB. 4. Fundamentals of programming in MATLAB. 5. Methods for solving algebraic and transcendental equations. The bisection method, the iterative method for solving equations. 6. The Newton method, the Regula-Falsi (False-Position) method, the combined method. 7. Solving systems of linear equations. Direct solution methods. Iterative methods (the Jacobi method, the Seidel method). Matrix norms. 8. Interpolation and approximation of functions. Approximation – the least-square method. Lagrange interpolation polynomials. 9. Newton interpolation polynomials. Spline-function interpolation. 10. Numerical integration. Newton-Cotes quadrature formulas. Composed quadrature formulas. Error estimation. 11. The Richardson extrapolation. 12. Initial value problems for ordinary differential equations. One-step methods. The Euler method. Error estimation using the half-step method. 13. The Runge-Kutta methods. Estimation of the approximation error. 14. Reserve.

### Conditions for subject completion

Full-time form (validity from: 2019/2020 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Graded credit Graded credit 100  51
Mandatory attendence parzicipation: 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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### Occurrence in study plans

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2019/2020 (B0731A010004) Architecture and Construction P Czech Ostrava Optional study plan
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### Occurrence in special blocks

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