1. SylabUZ
2. Wydział Informatyki, Elektrotechniki i Automatyki
3. semestr zimowy 2018/2019
4. WIEiA - oferta ERASMUS / Informatyka - Program Erasmus drugiego stopnia
5. Numerical methods

Wygeneruj PDF dla tej strony

Numerical methods - opis przedmiotu

Cel przedmiotu

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

Wymagania wstępne

Zapisz zmiany

Foundations  of  Calculus, Foundations of  Linear  Algebra

Zakres tematyczny

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.

Metody kształcenia

-  Series  of  conventional lectures

-   computer laboratory programming/computational  exercises in Matlab  environment

Efekty uczenia się i metody weryfikacji osiągania efektów uczenia się

Opis efektu	Symbole efektów	Metody weryfikacji	Forma zajęć

Warunki zaliczenia

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. 

Literatura podstawowa

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

 

Literatura uzupełniająca

1. Laboratory  Notes

2. Matlab  documentation

Uwagi

Zmodyfikowane przez prof. dr hab. Roman Gielerak (ostatnia modyfikacja: 22-04-2018 11:13)