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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2024/2025

Applied Numerical Methods

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Code Completion Credits Range Language
12ANM KZ 4 2+2 Czech
Course guarantor:
Jan Pšikal
Lecturer:
Jan Pšikal, Pavel Váchal, Alena Zavadilová
Tutor:
Jan Pšikal, Pavel Váchal, Alena Zavadilová
Supervisor:
Department of Laser Physics and Photonics
Synopsis:

For English version use code 12YNME1.

There are explained the basic principles of numerical mathematics important for numerical solving of problems important for physics and technology. Methods for solution of tasks very important for physicists (ordinary differential equations, random numbers) are included in addition to the basic numerical methods. Integrated computational environment MATLAB is used as a demonstration tool. The seminars are held in computer laboratory and PASCAL is used as a principle programming language and MATLAB is also used.

Requirements:
Syllabus of lectures:

For English version use code 12YNME1.

1.Numerical mathematics, truncation error, floating point representation of numbers, roundoff error

2.Correctness of problem, condition number, numerical stability; numerical libraries

3.Solution of linear equation systems - direct methods

4.Sparse matrices, iteration methods for linear equation systems; eigensystems

5.Interpolation and extrapolation, interpolation in more dimensions

6.Chebyshev approximation, Chebyshev polynomials, least square approximation

7.Evaluation of functions; sorting

8.Root finding and nonlinear set of equations

9.Search for extremes of functions

10.Numerical integration of functions

11.Random numbers and Monte Carlo integration

12.Ordinary differential equations - initial problem, stiff equations

13.Ordinary differential equations - boundary value problem

Syllabus of tutorials:

The seminars are held in computer laboratory and PASCAL is used as a principle programming language.

1. Floating point representation of numbers, roundoff error, condition number

2.Solution of linear equation systems - direct methods, condition number of matrix

3.Sparse matrices, iteration methods for linear equation systems; eigensystems

4.Interpolation and extrapolation, cubic spline

5.Chebyshev approximation, Chebyshev polynomials, least square approximation

6.Evaluation of functions

7.Root finding and nonlinear set of equations

8.Search for extremes of functions

9.Numerical integration of functions

10.Ordinary differential equations - initial problem, stiff equations

11.Ordinary differential equations - boundary value problem

Study Objective:

Knowledge:

Basic principles of numerical mathematics important for numerical solving of problems important for physics and technology including also ordinary differential equations.

Skills:

Usage of numerical mathematics for solving of practical problems, ability to choose routines from numerical libraries and to avoid most common errors.

Study materials:

Key references:

[1] W.H. Press, B.P. Flannery, S.A. Teukolsky, V. H. Vetterling: Numerical Recipes in Pascal (The art of scientific computation), Cambridge University Press, Cambridge 1989 (also versions for C and Fortran).

Recommended references:

[2] A. Ralston, P. Rabinowicz, A First Course in Numerical Analysis, McGraw-Hill 1965 (reprinted by Dover Publiícations, 2001)

[3] R.W. Hamming, Numerical Methods for Scientists and Engineers, 2nd edition, Dover Publiícations 1986

Equipment:

Computer laboratory with Pascal programming language and Matlab program.

Note:
Time-table for winter semester 2024/2025:
Time-table is not available yet
Time-table for summer semester 2024/2025:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2025-02-12
For updated information see http://bilakniha.cvut.cz/en/predmet8133106.html