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Numerical Methods

* Exchange students do not have to consider this information when selecting suitable courses for an exchange stay.

Course Unit Code230-0226/05
Number of ECTS Credits Allocated2 ECTS credits
Type of Course Unit *Optional
Level of Course Unit *Second Cycle
Year of Study *
Semester when the Course Unit is deliveredWinter, Summer Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech
Prerequisites and Co-Requisites Course succeeds to compulsory courses of previous semester
Name of Lecturer(s)Personal IDName
CER365doc. Ing. Martin Čermák, Ph.D.
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.
Learning Outcomes of the Course Unit
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;

Course Contents
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.
Recommended or Required Reading
Required Reading:
Abhishek, G.: Numerical Methods Using MATLAB. Springer Nature 2014, ISBN 9781484201558.
Kučera, R.: Numerické metody. VŠB-TU Ostrava 2007, na www.studopory.vsb.cz, mdg.vsb.cz/M,ISBN 80-248-1198-7.
Vondrák, V., Pospíšil, L.: Numerické metody 1. VŠB-TU Ostrava 2011, na http://mi21.vsb.cz/modul/numericke-metody-1
Kubíček, M., Dubcová, M., Janovská, D.: Numerické metody a algoritmy. Vydavatelství VŠCHT 2008, ISBN 9788070805589.
Abhishek, G.: Numerical Methods Using MATLAB. Springer Nature 2014, ISBN 9781484201558.
Recommended Reading:
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.
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
Planned learning activities and teaching methods
Lectures, Tutorials
Assesment methods and criteria
Task TitleTask TypeMaximum Number of Points
(Act. for Subtasks)
Minimum Number of Points for Task Passing
Graded creditGraded credit100 51