PřF:F5330 Basic numerical methods - Course Information

F5330 Basic numerical methods

Extent and Intensity

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

Teacher(s)

doc. Mgr. Jiří Chaloupka, Ph.D. (lecturer)
doc. Mgr. Jiří Chaloupka, Ph.D. (seminar tutor)

Guaranteed by

prof. RNDr. Josef Humlíček, CSc.
Department of Condensed Matter Physics – Physics Section – Faculty of Science
Contact Person: doc. 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 Enrolment Limitations

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

fields of study / plans the course is directly associated with

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

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. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1982, 169 s. info
• HUMLÍČEK, Josef. Základní metody numerické matematiky. Vyd. 1. 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 0521431085. info
• MARČUK, Gurij Ivanovič. Metody numerické matematiky. Vyd. 1. Praha: Academia, 1987, 528 s. URL info
• CELÝ, Jan. Řešení fyzikálních úloh na mikropočítačích. 1. vyd. Brno: Rektorát Masarykovy university, 1990, 108 s. ISBN 8021001267. info
• PANG, Tao. An introduction to computational physics. 2nd ed. Cambridge: Cambridge University Press, 2006, xv, 385. ISBN 0521825695. 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 of instruction

Czech

Follow-Up Courses

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

Further Comments

Study Materials
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  

Teacher's information

http://www.physics.muni.cz/~chaloupka/F5330/

• Enrolment Statistics (Autumn 2012, recent)
  
• Permalink: https://is.muni.cz/course/sci/autumn2012/F5330