1. SylabUZ
2. Wydział Mechaniczny
3. semestr zimowy 2019/2020
4. WM - oferta ERASMUS - Program Erasmus
5. Numerical Methods

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Numerical Methods - opis przedmiotu

Cel przedmiotu

• familiarize students with the basic aspects of numerical mathematics to solve common problems,

• familiarize students with the basic algorithms to solve these tasks,

• education students' ability to use Matlab to issues of engineering calculations.

Wymagania wstępne

Zapisz zmiany

Mastery of knowledge and skills in the subject Elements of Algebra and Mathematical Analysis

Zakres tematyczny

Lecture: Computer Arithmetic (Fixed and floating point representation of numbers, calculation errors in floating-point arithmetic, atabilność and accuracy of numerical algorithms, numerical conditioning task). Solving nonlinear equations (bisection method, regulatory falsi, secant and tangent method). Solving linear algebra (exact method for solving systems of linear equations: Gauss method, pivoting, triangular distribution method, Thomas-Banachiewicz Cholesky method, iterative methods: Jordan, Gauss-Seidel, setting benchmarks and matrix inverse spectral problem). Interpolation (definition and classification methods, polynomial interpolation: Lagrange interpolation formula, Newton's interpolation formula, spline interpolation, splines 3 degrees). Approximation (mean square approximation discrete and continuous, triangular families of orthogonal polynomials in approximation). Quadrature (pattern of rectangles and triangles, Newton-Cotes quadrature, Gauss quadrature, numerical integration of the limits of improper integrals and singular points within the interval of integration, integration of multidimensional functions). Ordinary differential equations (Euler's method, Runge-Kutta methods). Introduction to the methods of boundary and partial differential equations.

Environmental engineering calculations Matlab (system resources, environmental programming, graphical tools, and editing). Floating-point arithmetic (numerical experiments, errors of calculation procedures and the accumulation and transfer of numerical instability). Solving equations (equations of nonlinear systems of linear equations, systems of a van der Monde, testing algorithms, Newton and Newtona_Raphsona). Data Processing (interpolation method, method of approximation of mean method, spectral analysis, Fast Fourier Transform). Ordinary differential equations, initial and boundary issues. Elementary finite element techniques and testing them on the basis of certain issues.

Metody kształcenia

Lecture: Lecture conventional

Laboratory: The laboratory exercises on which a students solve tasks from list.

Efekty uczenia się i metody weryfikacji osiągania efektów uczenia się

Opis efektu	Symbole efektów	Metody weryfikacji	Forma zajęć

Warunki zaliczenia

Grading lecture

The pass of the lecture is to provide a positive evaluation of the test.

Grading of the laboratory

Evaluation of the laboratory is based on two tests making in a half and on the end semester.

Literatura podstawowa

1. Stachurski M., Metody Numeryczne w programie MATLAB. Wydawnictwo MIKOM Warszawa 2003.

2. Zalewski A.. Cegieła R., MATLAB – obliczenia numeryczne i ich zastosowania. Wydawnictwo Nakom. Poznań 2001.

3. Fortuna Z., Macukow B., Wąsowski J., Metody numeryczne. Warszawa: Wydawnictwa Naukowo-Techniczne, 1995.

4. Demidowicz B. P., Maron I. A., Metody numeryczne. Tom 1. Analiza, algebra, metody Monte Carlo. Warszawa: Państwowe Wydawnictwo Naukowe, 1965.

5. Demidowicz B. P., Maron I. A., Szkwałowa E. Z., Metody numeryczne. Tom 2. Przybliżanie funkcji: równania różniczkowe i całkowe. Warszawa:PWN, 1965.

Literatura uzupełniająca

Uwagi

Zmodyfikowane przez dr hab. inż. Tomasz Klekiel, prof. UZ (ostatnia modyfikacja: 09-05-2019 11:11)