## F5330 Basic numerical methods

Faculty of Science
Autumn 2020
Extent and Intensity
1/1/0. 3 credit(s). Type of Completion: z (credit).
Taught online.
Teacher(s)
Mgr. Jiří Chaloupka, Ph.D. (lecturer)
prof. Mgr. Dominik Munzar, Dr. (lecturer)
Mgr. Jiří Chaloupka, Ph.D. (seminar tutor)
Guaranteed by
prof. Mgr. Dominik Munzar, Dr.
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
Thu 9:00–9:50 Pouze distančně
• Timetable of Seminar Groups:
F5330/01: Thu 10:00–10:50 Pouze distančně
Prerequisites
Knowledge of very basic programming in some high-level programming language (for example Python, C, C++, Java, Fortran, Pascal)
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
Course objectives
The course presents to students knowledge on basic numerical methods of calculus and linear algebra. An emphasis is put on the applications of these methods in physics, these applications are illustrated by a number of examples.
Learning outcomes
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 specific problem;
- analyze the reliability of the selected method depending on the problem inputs and identify the sources of numerical errors;
- learn to utilize suitable software to perform numerical simulations of physical systems.
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 0521431085. 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 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