SylabUZ
Nazwa przedmiotu | Numerical Methods |
Kod przedmiotu | 06.9-WM-ER-IB-39_18 |
Wydział | Wydział Nauk Inżynieryjno-Technicznych |
Kierunek | WM - oferta ERASMUS |
Profil | - |
Rodzaj studiów | Program Erasmus |
Semestr rozpoczęcia | semestr zimowy 2023/2024 |
Semestr | 2 |
Liczba punktów ECTS do zdobycia | 4 |
Typ przedmiotu | obowiązkowy |
Język nauczania | angielski |
Sylabus opracował |
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Forma zajęć | Liczba godzin w semestrze (stacjonarne) | Liczba godzin w tygodniu (stacjonarne) | Liczba godzin w semestrze (niestacjonarne) | Liczba godzin w tygodniu (niestacjonarne) | Forma zaliczenia |
Wykład | 15 | 1 | - | - | Zaliczenie na ocenę |
Laboratorium | 30 | 2 | - | - | Zaliczenie na ocenę |
• 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.
Mastery of knowledge and skills in the subject Elements of Algebra and Mathematical Analysis
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.
Lecture: Lecture conventional
Laboratory: The laboratory exercises on which a students solve tasks from list.
Opis efektu | Symbole efektów | Metody weryfikacji | Forma zajęć |
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.
Zmodyfikowane przez dr hab. inż. Tomasz Klekiel, prof. UZ (ostatnia modyfikacja: 10-05-2024 13:51)