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Course, academic year 2017/2018
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Fundamentals of Numerical Mathematics - NMNM201
Czech title: Základy numerické matematiky
Guaranteed by: Department of Numerical Mathematics (32-KNM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2017
Semester: winter
E-Credits: 8
Hours per week, examination: winter s.:4/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Guarantor: prof. RNDr. Vít Dolejší, Ph.D., DSc.
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
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: G_M (27.04.2012)

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: G_M (27.04.2012)

Examination according to the syllabus.

Syllabus -
Last update: prof. RNDr. Vít Dolejší, Ph.D., DSc. (29.09.2014)

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

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