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Course, academic year 2023/2024
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Numerical Methods for Theoretical Physicists II - NTMF058
Title: Numerické metody pro teoretické fyziky II
Guaranteed by: Institute of Theoretical Physics (32-UTF)
Faculty: Faculty of Mathematics and Physics
Actual: from 2022
Semester: summer
E-Credits: 5
Hours per week, examination: summer s.:2/1, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Teaching methods: full-time
Additional information:
Guarantor: doc. RNDr. Martin Čížek, Ph.D.
doc. RNDr. Karel Houfek, Ph.D.
Comes under: Doporučené přednášky 1/2
Annotation -
Last update: doc. RNDr. Karel Houfek, Ph.D. (18.05.2022)
Continuation of the course NTMF057. Numerical methods for solving initial and boundary value problems in physics, iterative methods of numerical linear algebra, Monte Carlo method. For the first year of the master study of theoretical physics.
Course completion requirements - Czech
Last update: doc. RNDr. Karel Houfek, Ph.D. (11.06.2019)

Ústní zkouška a udělení zápočtu, který student dostane za vypracovanání úlohy zadané v poslední třetině semestru.

Literature -
Last update: doc. RNDr. Karel Houfek, Ph.D. (18.05.2022)

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery: Numerical Recipes: The Art of Scientific Computing 3rd ed, Cambridge 2007,

L. N. Trefethen, D. Bau III: Numerical Linear Algebra, Siam 1997.

L. N. Trefethen: Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations, 1996,

S. E. Koonin: Computational Physics, Benjamin, Menlo Park 1986.

Requirements to the exam -
Last update: doc. RNDr. Martin Čížek, Ph.D. (16.10.2017)

Oral exam. Before coming to exam, student must solve one practical programming task selected from the list provided in the last weeks of semester. Oral exam consists of two questions. First question is to describe the theory considering the selected practical task. The second question will be selected from the topics coverd by sylabus of the lecture.

Syllabus -
Last update: T_UTF (17.05.2012)
Numerical solution of partial differential equations
differential scheme, order of accuracy and stability, formulation and solution of initial and boundary value problems, finite element method

Iterative methods in numerical linear algebra
basic methods (Jacobi, Gauss-Seidel, overrelaxation), gradient methods, multigrid

Monte Carlo method
central limit theorem, application to integration, Metropolis algorithm

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