Numerical Methods for Scientists and Engineers
- Jiří Limpouch (guarantor), Pavel Váchal
- Jiří Limpouch (guarantor), Pavel Váchal, Alena Zavadilová
- Department of Physical Electronics
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.
- 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:
Basic principles of numerical mathematics important for numerical solving of problems important for physics and technology including also ordinary differential equations.
Usage of numerical mathematics for solving of practical problems, ability to choose routines from numerical libraries and to avoid most common errors.
- Study materials:
 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).
 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
Computer laboratory with Pascal programming language and Matlab program.
- Time-table for winter semester 2020/2021:
- Time-table is not available yet
- Time-table for summer semester 2020/2021:
- Time-table is not available yet
- The course is a part of the following study plans:
- BS Jaderná chemie (compulsory course of the specialization)