# Subject description - AE4B01NUM

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AE4B01NUM Numerical Analysis
Roles:PO, V Extent of teaching:2+2c
Department:13101 Language of teaching:EN
Guarantors:  Completion:Z,ZK
Lecturers:  Credits:6
Tutors:  Semester:Z

Anotation:

The course introduces to basic numerical methods of interpolation and approximation of functions, numerical differentiation and integration, solution of transcendent and ordinary differential 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:

Basic methods of approximation, numerical differentiation and integration, numerical solution to algebraic, transcendent and differential equations.

Course outlines:

 1 Overview of the subject of Numerical Analysis 2 Approximation of functions, polynomial interpolation 3 Errors of polynomial interpolation and their estimation 4 Hermite interpolating polynomial. Splines 5 Least squares approximation 6 Basic root-finding methods 7 Iteration method, fixed point theorem 8 Basic theorem of algebra, root separation and finding roots of polynomials 9 Solution of systems of linear equations 10 Numerical differentiation 11 Numerical integration (quadrature); error estimates and stepsize control 12 Gaussian and Romberg integration 13 One-step methods of solution of ODE's 14. Multistep methods of solution of ODE's

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 Least squares approximation 6 Individual work on assessment tasks 7 Root-finding methods, root separation 8 Individual work on assessment tasks 9 Solution of systems of linear equations 10 Numerical differentiation 11 Numerical differentiation and integration, modification of tasks 12 Individual work on assessment tasks 13 Solution of ODE's 14. 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, 1990. [2] Knuth, D. E., The Art of Computer Programming, Addison Wesley, Boston, 1997.

Requirements:

The first two courses of bachelor studies, mathematics and programming.

Webpage:

http://cmp.felk.cvut.cz/~navara/nm/eindex.htm

Subject is included into these academic programs:

 Program Branch Role Recommended semester BEKME1 Communication Technology V 3 BEKME5 Komunikace a elektronika V 3 BEKME_BO Common courses V 3 BEKME4 Network and Information Technology V 3 BEKME3 Applied Electronics V 3 BEKME2 Multimedia Technology V 3 BEEEM1 Applied Electrical Engineering V 3 BEEEM_BO Common courses V 3 BEEEM2 Electrical Engineering and Management V 3 BEKYR1 Robotics V 3 BEKYR_BO Common courses V 3 BEKYR3 Systems and Control V 3 BEKYR2 Sensors and Instrumentation V 3 BEOI2 Computer and Information Science PO 3

 Page updated 14.6.2021 19:52:31, semester: L/2021-2, L/2020-1, Z,L/2022-3, Z/2021-2, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)