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Course, academic year 2017/2018
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Numerical Mathematics - NMAI042
Czech title: Numerická matematika
Guaranteed by: Department of Numerical Mathematics (32-KNM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2015
Semester: summer
E-Credits: 6
Hours per week, examination: summer s.:2/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Guarantor: doc. RNDr. Jiří Felcman, CSc.
Class: Informatika Bc.
Classification: Mathematics > Numerical Analysis
Annotation -
Last update: T_KNM (17.05.2008)

The first course of numerical analysis for students of computer science. Topics: approximaton of continuous functions, numerical qudrature, differentiation and methods for solving ordinary differential equations, methods of numerical linear algebra - decomposition of matrices, solving systems of linear equations, eigenvalue problem. Introduction to numerical methods for solving partial differential equations.
Aim of the course -
Last update: T_KNM (17.05.2008)

The course gives students a knowledge of fundamentals of numerical mathematics.

Literature - Czech
Last update: FELCMAN/MFF.CUNI.CZ (11.02.2009)

Felcman J.: (2009). Numerická matematika, učební text k přednášce.

Feistauer, M., Felcman, J., and Straškraba, I. (2003). Mathematical and Com-

putational Methods for Compressible Flow. Oxford University Press, Oxford.

Higham, N. (1989). The accuracy of solutions to triangular systems. SIAM J.

Appl. Math., 26(5), 1252?1265.

Quarteroni, A., Sacco, R., and Saleri, F. (2004). Numerical Mathematics (2nd

edn), Volume 37 of Texts in Applied Mathematics. Springer, Berlin. ISBN

0-387-98959-5.

Segethová, J. (2000). Základy numerické matematiky. Karolinum, Praha.

Ueberhuber, W. (2000). Numerical Computation 1, 2: Methods, Software, and

Analysis. Springer, Berlin.

Teaching methods -
Last update: T_KNM (17.05.2008)

Lectures and tutorials in a lecture hall.

Requirements to the exam -
Last update: T_KNM (17.05.2008)

Examination according to the syllabus.

Syllabus -
Last update: T_KNM (17.05.2008)

Aproximations of functions in R, Lagrange interpolation polynomial, error of Lagrange interpolation, cubic spline, construction of natural cubic spline.

Numerical integration of functions, Newton-Cotes formulae, composed Newton-Cotes formulae, Romberg quadrature, Gauss quadrature.

Methods for solution of nonlinear equations, Newton method, proof of convergence of Newton method, method of successive approximations for nonlinear equations, roots of polynomial, Horner scheme.

Systems of linear equations, condition number of matrices, Gauss' elimination, LU decomposition, influence of rounding errors, Cholesky decomposition, QR decomposition, iterative methods for the solution of systems of linear equations.

Computation of matrix eigenvalues.

Numerical integration of ordinary differential equations. One-step methods, Runge-Kutta methods.

Gradient methods.

Entry requirements -
Last update: T_KNM (17.05.2008)

There are no special entry requirements.

 
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