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Fundamentals of Numerical Mathematics - NMNM201

Title:	Základy numerické matematiky
Guaranteed by:	Department of Numerical Mathematics (32-KNM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2016 to 2016
Semester:	winter
E-Credits:	8
Hours per week, examination:	winter s.:4/2, 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

Guarantor:	prof. RNDr. Miloslav Feistauer, DrSc., dr. h. c. prof. Ing. Miroslav Tůma, CSc.
Class:	M Bc. OM M Bc. OM > Povinné M Bc. OM > 2. ročník
Classification:	Mathematics > Numerical Analysis
Pre-requisite :	{One 1st year Analysis course}
Incompatibility :	NNUM105
Interchangeability :	NNUM105
Is pre-requisite for:	NMNM331
Is interchangeable with:	NNUM105

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: G_M (16.05.2012)

The first course of numerical analysis for students of General Mathematics.

Aim of the course -

Last update: prof. RNDr. Vít Dolejší, Ph.D., DSc. (08.06.2015)

To give a basic knowledge in numerical mathematics.

Literature -

Last update: doc. RNDr. Václav Kučera, Ph.D. (30.09.2019)

Stoer J., Bullirsch R.: Introduction to Numerical Analysis, Springer, l978

Teaching methods -

Last update: G_M (27.04.2012)

Lectures and tutorials in a lecture hall.

Requirements to the exam -

Last update: prof. RNDr. Vít Dolejší, Ph.D., DSc. (06.10.2017)

Examination according to the syllabus.

Syllabus -

Last update: prof. Ing. Miroslav Tůma, CSc. (09.10.2017)

Numerical methods of linear algebra. LU decomposition, elimination method, matrix iterative methods, power method .

Interpolation of functions. Lagrange and Hermite polynomials. Spline functions. Least-square approximation.

Qudrature formulas. Gaussian and Newton-Cotes formulas.

Solution of Nonlinear Equations.

Systems of linear difference equations, homogeneous, nohomogeneous systems, fundamental system of solutions, systems with constant coefficients.

Numerical solution of ordinary differential equations. a) One-step methods: Examples, general one-step methods, local discretization error, accumulated discretization error, convergence, consistency, error estimates, round-off errors, aposteriori error estimate, derivation of some formulae, Runge-Kutta methods. b) Multi-step methods, general framework, convergence, stability, consistency, order of the method, error estimates, derivation of some multi-step schemes.

Some optimization methods. Elements of convex analysis, steepest descent methods with constant and optimal step, convergence.

Entry requirements -

Last update: G_M (27.04.2012)

basic knowledge of calculus and linear algebra