Numerical Methods for Scientists and Engineers
Code  Completion  Credits  Range  Language 

12NMEA  KZ  3  2+2  Czech 
 Garant předmětu:
 Pavel Váchal
 Lecturer:
 Pavel Váchal, Alena Zavadilová
 Tutor:
 Pavel Váchal, Alena Zavadilová
 Supervisor:
 Department of Laser Physics and Photonics
 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 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:

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, 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 Pascal programming language and Matlab program.
 Note:
 Timetable for winter semester 2023/2024:
 Timetable is not available yet
 Timetable for summer semester 2023/2024:
 Timetable is not available yet
 The course is a part of the following study plans:

 BS Jaderná chemie (compulsory course of the specialization)
 Jaderná chemie (compulsory course in the program)