1. SylabUZ
2. Faculty of Computer Science, Electrical Engineering and Automatics
3. winter term 2022/2023
4. Electrical Engineering - Second-cycle Erasmus programme
5. Numerical methods in engineering

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Numerical methods in engineering - course description

Aim of the course

- to introduce to the basics of the very nature of floating-point arithmetic and threats resulting from its use
- to familiarize students with the basic numerical algorithms used in modeling and engineering calculations performed with the use of computer techniques
- to introduce basic numerical algorithms for solving typical computational tasks emerging in the process of modeling technical  systems and processes encountered in the analytical work of an engineer with specialties related to electrical engineering

Prerequisites

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Mathematical analysis, Selected issues of circuit theory I, Numerical method

Scope

Mathematical foundations: standards and assumptions of variable-point arithmetic with finite precision. Basic definitions and types of errors. Numerical tasks and their numerical conditioning, numerical stability, ways of avoiding errors
Basic issues of linear algebra: matrix calculus, systems of linear equations and numerical algorithms for solving them: Gaussian elimination algorithm and the problem of optimal element selection. Iterative methods: Gauss-Seidel algorithm and Jacobi algorithm. Fixed point methods. Applications for numerical calculations on matrices.
Fixed point methods: solving equations and systems of nonlinear equations using Newton's algorithm.
Interpolation techniques  and their applications: polynomial interpolations, van der Monde linear systems and their numerical instability, Lagrange and Newton methods, the method of splines , in particular the technique of cubic  splines .Applications of interpolation techniques to numerical integration :Newton-Cotte  series . Gaussian  quadratures.

Approximation techniques: minimal  sum  of  squares error polynomial approximations, numerical instabilities in the tasks of discrete approximation, orthogonal polynomials and their applications. Approximation with trigonometric polynomials, Fourier series and their applications. Min-max  error  minimization  error  problems.
Initial and boundary problems for ordinary differential equations. Mathematical introduction and review of applications of ordinary equations in electrical engineering. Numerical algorithms for initial problems: Euler's algorithm, Runge-Kuty algorithms. Numerical algorithms for boundary problems.

Teaching methods

Lecture, laboratory exercises

Learning outcomes and methods of theirs verification

Outcome description	Outcome symbols	Methods of verification	The class form

Assignment conditions

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%

Recommended reading

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.

5. Abhishek K Gupta, Numerical Methods using MATLAB, Springer, 2014.

6. C. Woodford, C. Phillips, Numerical Methods with Worked Examples: Matlab Edition, Springer, 2012.

Further reading

1. S.R. Otto, J.P. Denier, An Introduction to Programming and Numerical Methods in MATLAB, Springer, 2005.

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Notes

Modified by dr hab. inż. Krzysztof Sozański, prof. UZ (last modification: 21-04-2022 23:08)