Subject description - B4B01NUM

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B4B01NUM Numerical Analysis
Roles:PO, PZ, PV Extent of teaching:2P+2C
Department:13101 Language of teaching:CS
Guarantors:Navara M. Completion:Z,ZK
Lecturers:Navara M. Credits:6
Tutors:Navara M., Němeček A. Semester:Z

Anotation:

The course introduces to basic numerical methods of interpolation and approximation of functions, numerical differentiation and integration, solution of transcendent equations and systems of linear equations. Emphasis is put on estimation of errors, practical skills with the methods and demonstration of their properties using Maple and computer graphics.

Study targets:

Practical use of numerical methods, also in non-standard situations, where a modification of the task is needed.

Course outlines:

 1 Overview of the subject of Numerical Analysis. 2 Sources of errors in numerical computations. 3 Approximation of functions, polynomial interpolation. 4 Errors of polynomial interpolation and their estimation. 5 Hermite interpolating polynomial. Splines. 6 Least squares approximation. 7 Basic root-finding methods. 8 Iteration method, fixed point theorem. 9 Basic theorem of algebra, root separation and finding roots of polynomials, 10 Solution of systems of linear equations. 11 Numerical differentiation. 12 Numerical integration (quadrature); error estimates and stepsize control. 13 Gaussian and Romberg integration.

Exercises outline:

 1 Instruction on work in laboratory and Maple. 2 Individual work - training in Maple. 3 Polynomial interpolation, estimation of errors. 4 Individual work on assessment tasks. 5 Individual work on assessment tasks. 6 Least squares approximation. 7 Individual work on assessment tasks. 8 Root-finding methods, root separation. 9 Individual work on assessment tasks. 10 Solution of systems of linear equations. 11 Numerical differentiation. 12 Numerical differentiation and integration, modification of tasks. 13 Individual work on assessment tasks; assessment.

Literature:

 [1] Press, W. H., Flannery, B. P., Teukolsky, S. A., Vetterling, W. T.: Numerical Recipes (The Art of Scientific Computing), Cambridge University Press, Cambridge, 2002, ISBN 0-521-75033-4. [2] Knuth, D. E., The Art of Computer Programming, Addison Wesley, Boston, 1997. [3] Maple User Manuals and Programming Guides, Maplesoft, a division of Waterloo Maple Inc. (http://www.maplesoft.com/documentation_center/)

Requirements:

Linear Algebra, Calculus.

Note:

 Form: classical lectures, work on computer in the laboratory (Maple).

Webpage:

http://math.feld.cvut.cz/nemecek/nummet.html

Keywords:

Interpolation, approximation of functions, numerical differentiation, numerical integration, solution of equations, solution of systems of linear equations.

Subject is included into these academic programs:

 Program Branch Role Recommended semester BPOI1_2018 Artificial Intelligence and Computer Science PZ 3 BPBIO_2018 Common courses PV 4 BPOI1_2016 Computer and Information Science PO 3 BPOI_BO_2016 Common courses PO 3

 Page updated 6.8.2020 17:51:45, semester: Z,L/2020-1, L/2019-20, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)