SubjectsSubjects(version: 901)
Course, academic year 2021/2022
  
Numerical Mathematics - NMAI042
Title: Numerická matematika
Guaranteed by: Department of Numerical Mathematics (32-KNM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2020
Semester: summer
E-Credits: 5
Hours per week, examination: summer s.:2/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
Virtual mobility / capacity: no
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
Incompatibility : NMAX042
Interchangeability : NMAX042
Is incompatible with: NMAI017, NMAX042
Is interchangeable with: NMAX042, NMAI017
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.

Course completion requirements -
Last update: Stefano Pozza, Dr., Ph.D. (01.02.2022)

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.

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

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: doc. RNDr. Jiří Felcman, CSc. (30.04.2020)

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.

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

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.

Entry requirements -
Last update: T_KNM (17.05.2008)

There are no special entry requirements.

 
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