 CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2021/2022

# Numerical Methods 1

Code Completion Credits Range Language
12NME1 Z,ZK 4 2+2 Czech
Lecturer:
Pavel Váchal
Tutor:
Pavel Váchal, Martin Jirka, Sebastian Lorenz, Jan Vábek, Petr Valenta
Supervisor:
Department of Physical Electronics
Synopsis:

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 principle programming language as a demonstration tool. The seminars are held in computer laboratory.

Requirements:
Syllabus of lectures:

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 and system MATLAB is applied for demonstrations.

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:

 W.H. Press, B.P. Flannery, S.A. Teukolsky, V. H. Vetterling: Numerical Recipes in C++ (The art of scientific computing), Cambridge University Press, Cambridge, 3rd edition 2007 (also versions for C, 2nd edition 1993 and Fortran, 2nd edition 1993) (available at http://www.numerical.recipes/oldverswitcher.html).

Recommended references:

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

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

Equipment:

Computer laboratory with Matlab program.

Note:
Further information:
Slajdy k přednáškám na http://kfe.fjfi.cvut.cz/~limpouch/numet/lecnum.html
Time-table for winter semester 2021/2022:
Time-table is not available yet
Time-table for summer semester 2021/2022:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2022-08-09
For updated information see http://bilakniha.cvut.cz/en/predmet1915206.html