## Numerical Methods

### Studijní plán: Aplikovaná informatika - platný pro studenty, kteří započali studium od ZS 2013/2014

Předmět Numerical Methods (xNUMa) Katedra matematiky (KM) doc. RNDr. Ivana Pultarová, Ph.D. Anglicky 3
Prezenční studium
Přednáška1 h
Cvičení2 h
Studijní plán Typ Sem. Kred. Ukon.
Aplikovaná informatika - platný pro studenty, kteří započali studium od ZS 2013/2014 P 3 3 kr. ZA
Erasmus - Cestovní ruch - příjezd na krátkodobý studijní pobyt PV 3 kr. KZ
Erasmus - Finance a řízení - příjezd na krátkodobý studijní pobyt PV 3 kr. KZ
Počítačové systémy - platný pro studenty, kteří započali studium od ZS 2013/2014 P 3 3 kr. ZA

#### Sylabus

• Taylor expansion, polynomial substitution, approximation of irrational numbers, evaluation of polynomials, Horner scheme.
• Numerical solution of nonlinear problems (bisection m., regula falsi m., tangent and secant m.), numerical optimization (Nelder-Mead method).
• Direct methods of numerical solution of systems of linear equations, conditioning and stability, vector and matrix norms.
• Iterative methods for solution of systems of linear equations.
• Interpolation polynomials, Lagrange and Newton methods.
• Least squares approximations.
• Numerical quadrature, rectangle, trapezoidal and Simpson rules.
• Numerical derivative.
• Numerical solution of differential equations, initial and boundary problems. Euler method. Finite difference method.

#### Doporučená literatura

• Jeffrey R. Chasnov, Introduction to Numerical Methods, Lecture notes for MATH 3311 (http://www.math.ust.hk/~machas/numerical-methods.pdf)
• Kendall E. Atkinson, An Introduction to Numerical Analysis, John Wiley & Sons 1988, (http://math.science.cmu.ac.th/docs/qNA2556/ref_na/Katkinson.pdf)
• Douglas N. Arnold, A Concise Introduction to Numerical Analysis (http://www.ima.umn.edu/~arnold/597.00-01/nabook.pdf)

#### Anotace

This course provides students with basic knowledge in numerical methods which are frequently used in scientific and applied computation. Several fields of numerical mathematics are covered: interpolation and approximation of numbers and functions, including the least squares method, nonlinear root finding, solving systems of linear equations, numerical integration and numerical solution of differential equations, both initial and boundary value problems. Simple relevant algorithms are presented during the lectures or developed during exercises in some appropriate programming language.

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