SylabUZ
Nazwa przedmiotu | Numerical methods |
Kod przedmiotu | 11.9-WE-INFD-NumMet-Er |
Wydział | Wydział Informatyki, Elektrotechniki i Automatyki |
Kierunek | WIEiA - oferta ERASMUS / Informatyka |
Profil | - |
Rodzaj studiów | Program Erasmus drugiego stopnia |
Semestr rozpoczęcia | semestr zimowy 2018/2019 |
Semestr | 1 |
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 | - | - | Egzamin |
Laboratorium | 30 | 2 | - | - | Zaliczenie na ocenę |
After this course, students should be able to:
• Apply standard techniques to analyze key properties of numerical algorithms performed within floating-point arithmetic regime, such as stability and convergence.
• Understand and analyze common pitfalls in numerical computing such as ill-conditioning and numerical instabilities.
• Perform data analysis efficiently and accurately using data fitting method based on interpolation and approximation techniques.
• Apply and analyze numerical methods for ODEs
• Implement basic numerical algorithms efficiently in a Matlab computing/ programming environement
Foundations of Calculus, Foundations of Linear Algebra
Basics of computer arithmetic. Floating-point representations. Roundoff error. Loss of significance.
Nonlinear Equations: Bisection method and their generalisations. . Fixed-point based methods: Newton -Raphson method. Multidimensional Newton method.
Linear Systems: Gaussian elimination process. Gaussian elimination with scaled partial pivoting. Tridiagonal and banded systems. LU decomposition. Eigenvalues and eigenvectors. Singular value decomposition.
Polynomial interpolation schemes- Lagrange and Newton constructions . Runge effects Cubic splines construction. Estimating derivatives.
Numerical Integration and Differentation: Trapezoid, Simpson's and general Newton-Cotes series rules. Gaussian quadratures.Estimating derivatives
Approximation schemes: least squares problems. Fourier series and their summations.
Ordinary differential equations .Initial Values Problems: Taylor series methods. Euler's method. Runge-Kutta methods.
- Series of conventional lectures
- computer laboratory programming/computational exercises in Matlab environment
Opis efektu | Symbole efektów | Metody weryfikacji | Forma zajęć |
Assignments The laboratory tests and the final test are both written individual papers with emphasis on the interpretation of the results amd the ability of use Matlab. The problem sets are also individual assessments and their presented solutions evaluated. These involve numerical implementation of algorithms and practical computations within Matlab enviroment.. As such, some problems require simple programming in Matlab.
Final grade will be formed on the basis on the laboratory activity and achievements there together with the result of final test.
1. Robert J Schilling, Sandra l Harries , ” Applied Numerical Methods for Engineers using MATLAB and C.”, 3rd edition
2. Richard L. Burden, J.Douglas Faires, “Numerical Analysis 7th edition”, Thomson /
3. John. H. Mathews, Kurtis Fink ,” Numerical Methods Using MATLAB 3rd edition ” ,Prentice Hall publication
1. Laboratory Notes
2. Matlab documentation
Zmodyfikowane przez prof. dr hab. Roman Gielerak (ostatnia modyfikacja: 22-04-2018 11:13)