SylabUZ
| Course name | Numerical methods |
| Course ID | 11.9-WE-INFD-NumMet-Er |
| Faculty | Faculty of Computer Science, Electrical Engineering and Automatics |
| Field of study | Computer Science |
| Education profile | academic |
| Level of studies | Second-cycle Erasmus programme |
| Beginning semester | winter term 2021/2022 |
| Semester | 1 |
| ECTS credits to win | 4 |
| 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 | 30 | 2 | - | - | Credit with grade |
-to familarize students with basic numerical algorithms for solving most frequently appearing in the professional activity computational problems
-to introduce students to work within Matlab environement and similar on - engineers oriented packages
Foundations of calculus and linear algebra ,programming foundations
Float-point arithmetics :arithmetic-conversions, float-point representations,standards od single- and double- precisions formats, classification of numerical errors, numerical instabilities and badly numerically conditioned problems
Linear Algebra problems :linear systems of equations,Gauss elimination methods , iterative methods of Jacobi and Gauss -Seidel.Unstable linear systems , numerical conditiong of systems.
Nonlinear equations case :scalar equations , bisection algoritms and its acceleration by Newton , Newton algorithm, fixed-point algorithms .Newton algorithm for systems of equations.Applications to nonlinear optimalisation problems.
Interpolation:polynomial interpolation methods : Lagrange formula and Newton method , cubic splines techniques.Applications to numerical integration- Newton - Cotes formulas.
Approximation based methods :discrete and continous least -squares approximation problems . Fourier series . Orthogonal polynomials .
Ordinary differential equations algorithms : Euler algorithm. Runge_Kuta algorithms. Application to real problems .
Series of lectures
Laboratory exercises in Matlab enviroments
| Outcome description | Outcome symbols | Methods of verification | The class form |
Lecture –the necessary passing condition is to obtain a positive grade from final exam.
Laboratory – the main condition to get a pass are sufficient marks for all exercises and tests
conducted during the semester.
Calculation of the final grade: lecture 50% + laboratory 50%
1. Lloyd N. Trefethen and David Bau, III: Numerical Linear Algebra, SIAM, 1997
2. H.M. Antia: Numerical Methods for Scientists and Engineers, Birkhauser, 2000
3. Richard L. Burden, J. Douglas Faires, Numerical analysis, Brooks /Cole Publishing Company, ITP An International Thomson Publishing Company, sixth edition, 1997
4. Kendall Atkinson, Elementary numerical anlysis, John Wiley & Sons, Inc., second edition, 1993
1. Tutorials of Matlab
2. List of problems to be solved in Laboratory
Modified by prof. dr hab. Roman Gielerak (last modification: 14-07-2021 13:00)
