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:
[1] 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:
[2] A. Ralston, P. Rabinowicz, A First Course in Numerical Analysis, McGrawHill 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 Matlab program.
 Note:
 Further information:
 Slajdy k přednáškám na http://kfe.fjfi.cvut.cz/~limpouch/numet/lecnum.html
 Timetable for winter semester 2021/2022:
 Timetable is not available yet
 Timetable for summer semester 2021/2022:
 Timetable is not available yet
 The course is a part of the following study plans:

 BS Matematické inženýrství  Aplikované matematickostochastické metody (compulsory elective course)
 BS Informatická fyzika (compulsory elective course)
 BS Aplikace softwarového inženýrství (compulsory course of the specialization)
 BS jaderné inženýrství B (compulsory course of the specialization)
 BS Jaderné inženýrství C (compulsory course of the specialization)
 BS Dozimetrie a aplikace ionizujícího záření (compulsory elective course)
 BS Experimentální jaderná a částicová fyzika (compulsory elective course)
 BS Radiologická technika (compulsory course of the specialization)
 BS Inženýrství pevných látek (compulsory elective course)
 BS Diagnostika materiálů (compulsory elective course)
 BS Fyzika a technika termojaderné fúze (compulsory elective course)
 BS Fyzikální elektronika (compulsory elective course)
 Bc Laser Technology and Instrumentation (compulsory course of the specialization)