1. SylabUZ
2. Wydział Informatyki, Elektrotechniki i Automatyki
3. semestr zimowy 2020/2021
4. Automatyka i robotyka - Program Erasmus pierwszego stopnia
5. Numerical methods

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Numerical methods - opis przedmiotu

Cel przedmiotu

• to familiarize students with the basic numerical methods used in engineering calculations

• forming understanding among students that it is necessary to correctly perform computer calculations that guarantee acceptable errors

• shaping basic skills of a practical application of numerical methods in computer calculations - using the Matlab package

Wymagania wstępne

Zapisz zmiany

Mathematical analysis, Linear algebra with analytical geometry

Zakres tematyczny

Computer arithmetic: fixed and the floating-point representation of numbers, calculation errors in the floating-point arithmetic, stability, and correctness of a numerical algorithm, conditioning of a numerical task).

Solving nonlinear equations: bisection method, falsi rule, secant and tangent methods, multiple zeros, systems of nonlinear equations.

Solving problems of linear algebra: exact methods for solving systems of linear equations: Gauss method, pivoting, triangular distribution, Thomas method, Cholesky-Banachiewicz method; iterative methods: Jordan, Gauss-Seidel, determination of determinants and inverse matrix, spectral problem.

Interpolation: definition and classification of methods, polynomial interpolation: Lagrange interpolation formula, Newton interpolation formula; trigonometric interpolation, interpolation with spline functions, cubic spline.

Approximation: discrete and continuous mean square approximation, triangular families of orthogonal polynomials in approximation.

Quadratures: a complex pattern of rectangles and triangles, Newton-Cotes quadrature, Gaussian quadrature, numerical integration of integrals with improper boundaries, and with singular points inside the integration interval, integration of multidimensional functions.

Ordinary differential equations: Euler method, Rung-Kutta methods. Introduction to boundary problem methods and partial differential equations.

Matlab engineering calculations environment.

Metody kształcenia

Lecture: traditional lecture

Laboratory: lab exercises

Efekty uczenia się i metody weryfikacji osiągania efektów uczenia się

Opis efektu	Symbole efektów	Metody weryfikacji	Forma zajęć

Warunki zaliczenia

Lecture – the main condition to get a pass is a sufficient mark in a written exam.
Laboratory – the passing condition is to obtain positive marks from all laboratory exercises to be planned during the semester.

Calculation of the final grade: lecture 50% + laboratory 50%

Literatura podstawowa

1. Stachurski M.: Metody numeryczne w programie Matlab, Mikom, Warszawa, 2003.
2. Zalewski A., Cegieła R.: MATLAB: obliczenia numeryczne i ich zastosowania, Poznań, 2002.
3. Fortuna Z., Macukow B., Wąsowski J.: Metody numeryczne, WNT, Warszawa, 1995

Literatura uzupełniająca

1. Wanat K.: Algorytmy numeryczne, Helion, Gliwice, 1994
2. Bjorck A., Dahlquist G.: Metody numeryczne, PWN, Warszawa, 198

Uwagi

Zmodyfikowane przez dr hab. inż. Wojciech Paszke, prof. UZ (ostatnia modyfikacja: 05-05-2020 07:40)