Numerical Mathematics - NMAX042
Title: Numerická matematika
Guaranteed by: Student Affairs Department (32-STUD)
Faculty: Faculty of Mathematics and Physics
Actual: from 2020
Semester: summer
E-Credits: 6
Hours per week, examination: summer s.:2/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Is provided by: NMAI042
Guarantor: doc. RNDr. Jiří Felcman, CSc.
Class: Informatika Bc.
Classification: Mathematics > Numerical Analysis
Pre-requisite : {NXXX014, NXXX015, NXXX016, NXXX017, NXXX018, NXXX022, NXXX023, NXXX024, NXXX025, NXXX033}
Incompatibility : NMAI042
Interchangeability : NMAI042
Is incompatible with: NMAI042
Is interchangeable with: NMAI042
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Annotation -
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.
Last update: T_KNM (17.05.2008)
Aim of the course -

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

Last update: T_KNM (17.05.2008)
Course completion requirements -

It is necessary to obtain the course-credit before passing the exam.

To get the course-credit, one needs to obtain 12 points. The points will be awarded for:

  • active presence at the practicals (1 point per presence). This option may change in case of covid restrictions.
  • doing the Matlab homeworks (max 2 points for one homework, there will be four Matlab homeworks during the semester)
  • a written exam (max 12 points). There is a possibility of one additional attempt.

Last update: Pozza Stefano, Dr., Ph.D. (01.02.2022)
Literature -

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.

Last update: Kučera Václav, doc. RNDr., Ph.D. (29.10.2019)
Teaching methods -

Lectures and tutorials in a lecture hall.

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

The exam is written and oral, possibly in the form of distance testing and distance interview. The examination requirements are given by the topics in the syllabus, in the extent to which they they were taught in course.

Last update: Felcman Jiří, doc. RNDr., CSc. (30.04.2020)
Syllabus -

Approximations 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, Gauss quadrature.

Methods for solving nonlinear equations, Newton method, proof of convergence of Newton method, method of successive approximations for nonlinear equations, roots of polynomials, 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 - the conjugate gradient method, the steepest descent method.

Last update: Pozza Stefano, Dr., Ph.D. (31.01.2022)
Entry requirements -

There are no special entry requirements.

Last update: T_KNM (17.05.2008)