# Course Information

česky | in English

## F5330 Basic numerical methods

Faculty of Science
autumn 2012
Extent and Intensity
1/1/0. 3 credit(s). Type of Completion: z (credit).
Teacher(s)
Mgr. Jiří Chaloupka, Ph.D. (lecturer)
Mgr. Jiří Chaloupka, Ph.D. (seminar tutor)
Supervisor
prof. RNDr. Josef Humlíček, CSc.
Department of Condensed Matter Physics - Physics Section - Faculty of Science
Contact Person: Mgr. Jiří Chaloupka, Ph.D.
Supplier department: Department of Condensed Matter Physics - Physics Section - Faculty of Science
Timetable
Tue 10:00–10:50 F4,03017, Tue 11:00–11:50 F4,03017
Prerequisites
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
Course objectives
The course presents to students knowledge on basic numerical methods of calculus and linear algebra.

After successful passing of the course the students should be able to
- list and describe basic numerical methods lectured
- successfully apply these methods for solving a specified problem.
Syllabus
• 1. number representation in a computer, errors in numerical calculations, stability of the algorithms, ill-posed problems
• 2. solution of nonlinear equations with a single variable (bisection, secant method, Ridders' method, Newton-Raphson method)
• 3. minimization and maximalization in one dimension
• 4. interpolating polynomials
• 5. numerical quadrature (classical rules, Romberg quadrature, improper integrals, multidimensional integrals)
• 6. initial value problems for ordinary differetial equations and their systems (Euler's method, methods of Runge-Kutta type)
• 7. linear systems of equations (Gaussian elimination method, LU decomposition, Cholesky decomposition, iterative methods for sparse matrices)
• 8. eigenvalues and eigenvectors of matrices (Jacobi method)
• 9. systems of nonlinear equations (Newton-Raphson method)
• 10. boundary value problems for ordinary differential equations
• 11. partial differential equations (Laplace equation, heat conduction)
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
Teaching methods
Lecture + individual work on PC.
Assessment methods
Requirements for credit: knowledge on topics presented in the lectures + discussion of worked out programs.
Language in which the course is taught
Czech
Follow-Up Courses
Study Materials
The course can also be completed outside the examination period.
The course is taught annually.
Listed among pre-requisites of other courses
Teacher's information
http://www.physics.muni.cz/~chaloupka/F5330/
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 2007, Autumn 2008, Autumn 2009, Autumn 2010, autumn 2011, Autumn 2011 - acreditation, spring 2012 - acreditation, autumn 2013.
• Enrollment Statistics (autumn 2012, recent)