Module also offered within study programmes:
General information:
Name:
Computational Techniques
Course of study:
2017/2018
Code:
IES-1-304-s
Faculty of:
Computer Science, Electronics and Telecommunications
Study level:
First-cycle studies
Specialty:
-
Field of study:
Electronics and Telecommunications
Semester:
3
Profile of education:
Academic (A)
Lecture language:
English
Form and type of study:
Full-time studies
Responsible teacher:
dr inż. Korohoda Przemysław (korohoda@agh.edu.pl)
Academic teachers:
dr inż. Korohoda Przemysław (korohoda@agh.edu.pl)
Module summary

Student learns how to design and realize, mainly in Matlab, computational experiment, integrating theoretical knowledge and practical skills from several subjects.

Description of learning outcomes for module
MLO code Student after module completion has the knowledge/ knows how to/is able to Connections with FLO Method of learning outcomes verification (form of completion)
Social competence
M_K001 Student is aware of importance of professional behavior, obeying the rules of professional ethics and mutual respect, he understands nontechnical aspects and consequences of an engineer actions ES1A_K03 Execution of laboratory classes,
Activity during classes
M_K002 Student understands the need and knows methods of constant self-education and improvement of professional competence and he understands the need of working in a team ES1A_K01, ES1A_K04 Execution of laboratory classes,
Activity during classes
Skills
M_U001 Student can verify, with use of the computer based simulations, handbooks theories, in particular formulas and algorithms, while using error criteria and graphical presentation ES1A_U05, ES1A_U01, ES1A_U10 Execution of laboratory classes,
Test
M_U002 Student is able to plan and realize, for example in Matlab, simulation experiment, integrating theoretical knowledge and practical skills from several subjects taught previously or in parallel ES1A_U24, ES1A_U12, ES1A_U02, ES1A_U01 Execution of laboratory classes,
Test
Knowledge
M_W001 Student knows basic mathematical tools enabling creation of software for electronic circuits simulation and solving of the interdisciplinary engineering problems ES1A_W13, ES1A_W01, ES1A_W02 Test results,
Test
M_W002 Student has basic knowledge of the selected numerical methods and about presentation and interpretation of the obtained results ES1A_W14, ES1A_W07 Test results,
Test
FLO matrix in relation to forms of classes
MLO code Student after module completion has the knowledge/ knows how to/is able to Form of classes
Lecture
Audit. classes
Lab. classes
Project classes
Conv. seminar
Seminar classes
Pract. classes
Zaj. terenowe
Zaj. warsztatowe
Others
E-learning
Social competence
M_K001 Student is aware of importance of professional behavior, obeying the rules of professional ethics and mutual respect, he understands nontechnical aspects and consequences of an engineer actions - - + + - - - - - - -
M_K002 Student understands the need and knows methods of constant self-education and improvement of professional competence and he understands the need of working in a team - - + + - - - - - - -
Skills
M_U001 Student can verify, with use of the computer based simulations, handbooks theories, in particular formulas and algorithms, while using error criteria and graphical presentation + - + + - - - - - - -
M_U002 Student is able to plan and realize, for example in Matlab, simulation experiment, integrating theoretical knowledge and practical skills from several subjects taught previously or in parallel + - + + - - - - - - -
Knowledge
M_W001 Student knows basic mathematical tools enabling creation of software for electronic circuits simulation and solving of the interdisciplinary engineering problems + - + + - - - - - - -
M_W002 Student has basic knowledge of the selected numerical methods and about presentation and interpretation of the obtained results + - + + - - - - - - -
Module content
Lectures:

1. Solving sets of equations, applications

Real and imaginary solution of algebraic equations of the 3rd and 4th order, Viete formula for any polynomial order, numerical solving of one-variable equation, extension of the concept to sets of non-linear equations, multidimensional Newton-Raphson method, transmittance as ratio of polynomials, system stability for continuous-time and discrete-time description.

2. Interpolation and extrapolation

Lagrange polynomials, Neville method, interpolation with use of basis function series for various bases, matrix based description, example of spline-based solution. Taylor series with various types of remainder, partial derivatives, two-dimensional Taylor series.

3. Approximation

Mutual relations between skalar product, metric and norm, applications of skalar product, approximation with use of bases, Tchebyshev polynomials, Legendre polynomials, orthonormalization procedure.

4. Regression analysis and discrete transforms

Pseudo-random numbers generators with arbitrarily designed distribution, linear regression for one variable and multivariable, matrix-based solution, nonlinear regression and with nonlinear transition function, discrete orthogonal transform as nonlinear multivariable regression, discrete Karhunen-Loeve transform, LU decomposition, Crout algorithm.

5. Selected applications of mathematical analysis

Numerical computation of finite integral, integration of 1st order linear homogenous and inhomogenous differential equations, Runge-Kutta approach, comparison between analytical and numerical solution, and with use of Laplace transform, generalization towards sets of linear equations, matrix-based solution, application to electric al circuits and physics problems as harmonic oscillations or planetary system model.

Laboratory classes:

1. Comparison of selected methods of solving equations and sets of equations – introduction to exercises, recapitulation of Matlab programming features, methodology of comparative computational experiments, examples in Matlab, presentation of obtained results, creating concluding observations. The selection of detailed exercises is based on tutor suggestions.
2. Interpolation examples and applications of Taylor series – design of experiment illustrating selected techniques, and their realization in Matlab, presentation of the results, concluding observations. The selection of detailed exercises is based on tutor suggestions.
3. Design and realization in Matlab of programming tools for tests of selected approximation methods – general designing rules for testing, selection of initial option and its realization, performing examples of tests, identification of drawbacks and improving the tools, presentation of the results, concluding observations. The selection of detailed exercises is based on tutor suggestions.
4. Design and realization in Matlab of programming tools for tests of selected regression methods – selection of initial option and its realization, performing examples of tests, identification of drawbacks and improving the tools, presentation of the results, concluding observations. The selection of detailed exercises is based on tutor suggestions.
5. Study and further development of demonstrations containing models based on sets of 1st order differential equations – running and detailed study of prepared in advance Matlab demonstration programmes, then suggestion and introduction of additional options extending flexibility of the studied tools, based on newly suggested comparisons and sets of parameters values. Repetition of selected Matlab techniques.
6. Recapitulation and verification of the practical skills and test of the theoretical knowledge.

Project classes:

The students, typically in grups of two, solve some tasks, more advanced than exercised durig laboratory sessions. The tasks may be either relevantly expanded laboratory tasks or may be suggested by the students. The performed job should be properly described in a form of report, and finally the selected details of proposed solution are discussed with the tutor. The mark results from tutor’s assessments of the students performance during realization of the project, the report and final discussion.

Student workload (ECTS credits balance)
Student activity form Student workload
Summary student workload 100 h
Module ECTS credits 4 ECTS
Participation in lectures 14 h
Realization of independently performed tasks 32 h
Participation in laboratory classes 14 h
Participation in project classes 10 h
Realization of independently performed tasks 30 h
Additional information
Method of calculating the final grade:

1. To obtain positive final mark (FM) the student must have positive mark for practical knowledge from laboratory and for theory, verified with test.
2. The weighted average (av) is computed from marks from laboratory (75%) and after the final test (25%).
3. Final mark is obtained according to the following procedure:
if av>=90%, to FM=5.0 else
if av>=80%, to FM=4.5 else
if av>=70%, to FM=4.0 else
if av>=60%, to FM=3.5 else
if av>=50%, to FM=3.0 else FM=2.0
4. When both positive marks from the laboratory session and lectures hase been obtained at basic date, and the student was active during lectures, the final mark will be higher by 0.5.

Prerequisites and additional requirements:

Basics of matrix algebra and analysis (derivatives and differential equations of one variable)
Basics of circuits theory
Basics of programming techniques in high level languages

Recommended literature and teaching resources:

1. S. Osowski, A. Cichocki, K. Siwek: „Matlab w zastosowaniu do obliczeń obwodowych i przetwarzaniu sygnałów”, OWPW, Warszawa 2006.
2.R. Klempka, R. Sikora-Iliew, A. Stankiewicz, B Świątek: „Modelowanie i symulacja układów elektrycznych w Matlabie – przykłady”, AGH – UWN-D, Kraków 2007.
3. R. Klempka, A, Stankiewicz: „ Modelowanie i symulacja układów dynamicznych”, AGH UWN-D, Kraków 2006.
4. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery: “Numerical Recipes in C”, Cambridge University Press 1992.
5. N.S.Kaisere, Computational Techniques for Process Simulations and Analysis Using MATLAB, CRC Press, London, 2018.

Scientific publications of module course instructors related to the topic of the module:

Selected publications, where skills and knowledge related to the subject contributed considerably:

A.Borys, P.Korohoda: Analysis of Critical Sampling Effects Revisited. Proceedings of the Signal Processing –Algorithms, Architectures, Arrangements and Applications (SPA 2017), pp. 131-136, Sept., 2017.

K.Zachwieja, P.Korohoda, J.Kwinta-Rybicka, M.Miklaszewska, A.Moczulska, J.Bugajska, J.Berska, D.Drożdż, J.A.Pietrzyk: Modification of the Schwartz equations for children increases their accuracy at eGFR > 60 mL/min/1.73. Renal Failure, vol. 38 no. 5, pp. 787–798. 2016.

P.Korohoda, R.Rumian: Audio in-band signalling system based on a complementary pair of peak and notch equalizers. Proceedings of the Signal Processing –Algorithms, Architectures, Arrangements and Applications (SPA 2016), pp. 207–212, 2016.

P.Korohoda, R.Rumian: Design of the mutually cancelling narrow passband and stopband filters – a case study. Proceedings of the International Conference on Signals and Electronic Systems, pp. 57-62, Sept. 2016.

P.Korohoda, B.Ziółko, M.Miklaszewska, M.Ziółko: Evaluation of medical images segmentation. Proceedings of the twenty-first national conference on Applications of mathematics in biology and medicine, pp.81-86, Regietów, Sept. 2015.

P.Korohoda, J.Grabska-Chrząstowska: Directional image filtering based on the Fourier transform. Image Processing & Communications an International Journal, vol. 19 no. 2–3, pp. 7–13, 2014.

Additional information:

Classes are conducted using innovative teaching methods developed during 2017-2019 in the POWR.03.04.00-00-D002/16 project, carried out by the Faculty of Computer Science, Electronics and Telecommunications under the Smart Growth Operational Programme 2014-2020.