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Course, academic year 2023/2024
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Numerical Methods for Theoretical Physicists I - NTMF057
Title: Numerické metody pro teoretické fyziky I
Guaranteed by: Institute of Theoretical Physics (32-UTF)
Faculty: Faculty of Mathematics and Physics
Actual: from 2022
Semester: winter
E-Credits: 5
Hours per week, examination: winter 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.
Annotation -
Last update: doc. RNDr. Karel Houfek, Ph.D. (18.05.2022)
Numerical methods and their application to solution of the equations of mathematical physics. The course covers the basic requirements from numerical mathematics for the final examination of theoretical physics. Recommended in the first year of master study of theoretical physics, or in the last year of the bachelor study of 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,

E. Isaacson, H. B. Keller: Analysis of Numerical Methods, Dover 1966.

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

E. Vitásek: Numerické metody, SNTL Praha 1987.

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: CIZEK (16.05.2005)

Basic numerical methods and application to solutions of problems of mathematical physics.

1) Error, precision, stability.

2) Interpolation, extrapolation, reprezentation, derivation and integration of function.

3) Roots of function, fixed point theorem and axceleration of convergence.

4) Minimalization a maximalization.

5) Solution of ordinary differential equations. Boundary- and initial-value problems.

6) Linear algebra: matrix inversion and diagonalization.

8) Integral equations.

9) Fast Fourier transform.

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