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F5330 Basic numerical methods
Faculty of Scienceautumn 2013
- 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.
Dodavatelské pracoviště: Department of Condensed Matter Physics - Physics Section - Faculty of Science - 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.
- Follow-Up Courses
- Further Comments
- The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week. - Listed among pre-requisites of other courses
- Teacher's information
- http://www.physics.muni.cz/~chaloupka/F5330/
- Enrollment Statistics (autumn 2013, recent)
- Permalink: https://is.muni.cz/course/sci/autumn2013/F5330
Other references:
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