1. SylabUZ
2. Wydział Nauk Inżynieryjno-Technicznych
3. semestr zimowy 2021/2022
4. Elektrotechnika - Program Erasmus pierwszego stopnia
5. Numerical methods

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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 instability.

• Perform data analysis efficiently and accurately using data fitting method based on  interpolation  and  approximation  techniques.

• Derive and analyze numerical methods for ODEs 

• Implement a range of numerical algorithms efficiently in a Matlab  computing/ programming environment

 

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. Secant method. Fixed-point based  methods: Newton -Raphson method.Multidimensional  Newton   method.

Linear Systems: Gaussian elimination process. Gaussian elimination with scaled partial pivoting. Condition Numbers. Tridiagonal and banded systems. LU decomposition. Eigenvalues and eigenvectors. Singular value decomposition.

Interpolation and Numerical Differentiation: Polynomial interpolation schemes- Lagrange  and  Newton   constructions . Runge  effects Cubic splines construction.  Estimating derivatives.

Numerical Integration: Trapezoid, Simpson's and general Newton-Cotes series rules. Gaussian quadratures.

Approximation  schemes: least  squares  problems. Fourier series  and  theirs  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. The problem sets are also individual assessments. These involve numerical implementation of algorithms and guided development of methodologies. 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 dr hab. inż. Paweł Szcześniak, prof. UZ (ostatnia modyfikacja: 08-07-2021 21:49)