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Methods of Numerical Mathematics I - NMAF013

Title:	Metody numerické matematiky I
Guaranteed by:	Department of Atmospheric Physics (32-KFA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2020
Semester:	winter
E-Credits:	3
Hours per week, examination:	winter s.:2/0, 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

Guarantor:	doc. Ing. Luděk Beneš, Ph.D. Mgr. Vladimír Fuka, Ph.D.
Teacher(s):	doc. Ing. Luděk Beneš, Ph.D. Mgr. Vladimír Fuka, Ph.D.
Classification:	Physics > Mathematics for Physicists

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Annotation -

The course, together with the Methods of Numerical Mathematics II, covers fundamentals of the numerical mathematics. The course is devoted to mathematical modelling and numerical solution of the ordinary and partial differential equations.

Last update: BENESL/MFF.CUNI.CZ (05.05.2008)

Aim of the course -

Fundamental of numerical methods.

Last update: BENESL/MFF.CUNI.CZ (05.05.2008)

Course completion requirements - Czech

Zkouška - viz sylabus

Last update: Mikšovský Jiří, doc. Mgr., Ph.D. (13.02.2019)

Literature -

A. Ralston: Základy numerické matematiky, Academia Praha 1973

E. Vitásek: Numerické metody, SNTL Praha 1987

R. J. LeVaque: Finite Difference Methods for Differential Equations

J.H. Ferzinger: Numerical Methods for Engineering Applications, Wiley1998

A. Quarteroni, A. Valli: Numerical Approximation of Partial Differential Equations, Springer 1997

Last update: BENESL/MFF.CUNI.CZ (05.05.2008)

Teaching methods -

Lecture.

Last update: BENESL/MFF.CUNI.CZ (05.05.2008)

Requirements to the exam -

Examination - sylabus.

Last update: BENESL/MFF.CUNI.CZ (05.05.2008)

Syllabus -

Numerical solution of Linear systems

Direct methods - Gauss elimination. LU decomposition

Iterative methods - -Jacobi, Gauss-Seidel methods, relaxation methods, conjugate gradient method. GMRES

Nonlinear equations and systems of nonlinear equations.
Approximation and interpolation

Least square method

Lagrange and Newton interpolations, spline functions.

Numerical integration: Newton-Cotes formulas, Riachardson

extrapolation, Romberg integration.

Numerical solution of ODR - Cauchy problem

Basic concept - approximation, stability, convergence, truncation error, global error.

One-step methods - Runge-Kutta methods, method based on Taylor series

Last update: BENESL/MFF.CUNI.CZ (05.05.2008)