SylabUZ
| Course name | Numerical methods |
| Course ID | 11.9-WE-ELEKTP-NM-Er |
| Faculty | Faculty of Computer Science, Electrical Engineering and Automatics |
| Field of study | Electrical Engineering |
| Education profile | academic |
| Level of studies | First-cycle Erasmus programme |
| Beginning semester | winter term 2019/2020 |
| Semester | 2 |
| ECTS credits to win | 3 |
| Course type | obligatory |
| Teaching language | english |
| Author of syllabus |
|
| The class form | Hours per semester (full-time) | Hours per week (full-time) | Hours per semester (part-time) | Hours per week (part-time) | Form of assignment |
| Lecture | 15 | 1 | - | - | Credit with grade |
| Laboratory | 15 | 1 | - | - | Credit with grade |
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
Foundations of Calculus, Foundations of Linear Algebra
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.
- Series of conventional lectures
- computer laboratory programming/computational exercises in Matlab environment
| Outcome description | Outcome symbols | Methods of verification | The class form |
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.
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
Modified by dr hab. inż. Radosław Kłosiński, prof. UZ (last modification: 27-10-2019 18:37)
