Information System of Masaryk University 

Course Information

F5330 Basic numerical methods

Faculty of Science
Autumn 2007

Extent and Intensity

1/1/0. 3 credit(s). Type of Completion: z (credit).

Teacher(s)

doc. RNDr. Jan Celý, CSc. (lecturer)
doc. RNDr. Jan Celý, CSc. (seminar tutor)

Supervisor

prof. RNDr. Josef Humlíček, CSc.
Department of Condensed Matter Physics - Physics Section - Faculty of Science
Contact Person: doc. RNDr. Jan Celý, CSc.

Timetable

Fri 11:00–11:50 F4,03017, Fri 12:00–12:50 Fs1,01017

Prerequisites

A knowledge of the programming (Pascal,Fortran, C,C++)

Course Enrollment Limitations

The course is also offered to the students of the fields other than those the course is directly associated with.

Fields of study the course is directly associated with

• Physics (programme PřF, B-FY)
• Biophysics (programme PřF, M-FY)
• Physics (programme PřF, M-FY)
• Physics (programme PřF, N-FY)

Course objectives

The course presents basic methods for solving systems of linear algebraic equations, for the matrix inversion, for the calculation of eigenvalues and eigenvectors of matrices, singular matrix decomposition and linear regression. Interpolation,splines.The solution of nonlinear equations.

Syllabus

• 1. Storage of numerical data in a computer. Errors in numerical algorithms, propagation of the errors. Stability of the algorthims. Ill-posed methods. 2. Systems of linear algebraic equations, direct and iterational metods. The Gauss elimination method, pivoting. LU decomposition. Systems with special matrices. The Choleski theorem and the Choleski method. The iteration methods, the Jacobi method, the Gauss-Seidel method. The problem of the convergence of the iteration methods. 3. Eigenvalues and eigenvectors of matrices. The Jacobi-method. The Householder transformation and the QL method. 4. Singular value decomposition and its applications. Linear regression. 5.Interpolation, splines 6. The solution of nonlinear equations

Literature

• MÍKA, Stanislav. Numerické metody algebry. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1982. 169 s. info
• HUMLÍČEK, J. Základní metody numerické matematiky. 1. vyd. Praha: Státní pedagogické nakladatelství, 1981. 171 s. info
• CELÝ, Jan. Programové moduly pro fyzikální výpočty. 1. vyd. Brno: Rektorát UJEP, 1985. 99 s. info
• PRESS, William H. Numerical recipes in C :the art of scientific computing. 2nd ed. Cambridge: Cambridge University Press, 1992. xxvi, 994. ISBN 0-521-43108-5. info
• MARČUK, Gurij Ivanovič. Metody numerické matematiky. 1. vyd. Praha: Academia, 1987. 528 s. info
• CELÝ, Jan. Řešení fyzikálních úloh na mikropočítačích. 1. vyd. Brno: Rektorát Masarykovy university, 1990. 108 s. ISBN 80-210-0126-7. info
• PANG, Tao. An introduction to computational physics. 2nd ed. Cambridge: Cambridge University Press, 2006. xv, 385 s. ISBN 0-521-82569-5. info

Assessment methods (v češtině)

přednáška, individální cvičení u počítače, předmět je ukončen zápočtem

Further comments (probably available only v češtině)

The course can also be completed outside the examination period.
The course is taught annually.

Listed among pre-requisites of other courses

• F6150 Advanced numerical methods
  F5330  
• F8370 Present-day methods in physical modelling
  F5330  

Teacher's information

Podrobnější informace lze nalézt také na www stránce monoceros.physics.muni.cz/~jancely

The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2008, Autumn 2009, Autumn 2010, autumn 2011, Autumn 2011 - acreditation, spring 2012 - acreditation, autumn 2012, autumn 2013.

---

• Enrollment Statistics (Autumn 2007, recent)
  
• Permalink: https://is.muni.cz/course/sci/autumn2007/F5330

---