Module also offered within study programmes:
General information:
Annual:
2017/2018
Code:
MIM-2-104-AM-s
Name:
Computational methods in engineering
Faculty of:
Metals Engineering and Industrial Computer Science
Study level:
Second-cycle studies
Specialty:
Advanced Materials - Processing and Characterization
Field of study:
Materials Science
Semester:
1
Profile of education:
Academic (A)
Lecture language:
English
Form and type of study:
Full-time studies
Course homepage:
 
Responsible teacher:
Szeliga Danuta (szeliga@agh.edu.pl)
Academic teachers:
Szeliga Danuta (szeliga@agh.edu.pl)
Module summary

Lecture content:
- computer representation of numbers
- numerical solution: stability, convergence , complexity,
- numerical methods for various one-dimensional problems,
- linear set of equations

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 A student understands the need and knows methods of constant self-education and improvement of professional competences. She/he understands the need of a team working IM2A_K01, IM2A_K03 Activity during classes,
Participation in a discussion,
Execution of laboratory classes
M_K002 A student is aware of importance of professional behavior, obeying the rules of professional ethics and mutual respect. She/he understands nontechnical aspects and consequences of an engineer actions IM2A_K02 Activity during classes,
Execution of laboratory classes
Skills
M_U001 A student is able to implement numerical methods with high level programming languages and software dedicated numerical computations. IM2A_U01 Activity during classes,
Execution of laboratory classes,
Completion of laboratory classes
Knowledge
M_W001 A student knows numerical methods to solve basic engineering problems IM2A_W04 Test,
Execution of laboratory classes,
Test results,
Completion of laboratory classes
M_W002 A student knows the mathematical tools, software and programming libraries dedicated numerical methods and procedures IM2A_W04 Test,
Execution of laboratory classes,
Test results,
Completion of laboratory classes
M_W003 A student is able to perform the computations for engineering problems, to present and to interpret obtained results IM2A_W04 Activity during classes,
Test,
Execution of laboratory classes,
Completion of laboratory classes
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 A student understands the need and knows methods of constant self-education and improvement of professional competences. She/he understands the need of a team working - - + - - - - - - - -
M_K002 A student is aware of importance of professional behavior, obeying the rules of professional ethics and mutual respect. She/he understands nontechnical aspects and consequences of an engineer actions - - + - - - - - - - -
Skills
M_U001 A student is able to implement numerical methods with high level programming languages and software dedicated numerical computations. - - + - - - - - - - -
Knowledge
M_W001 A student knows numerical methods to solve basic engineering problems + - - - - - - - - - -
M_W002 A student knows the mathematical tools, software and programming libraries dedicated numerical methods and procedures + - - - - - - - - - -
M_W003 A student is able to perform the computations for engineering problems, to present and to interpret obtained results + - - - - - - - - - -
Module content
Lectures:
Computational Methods in Engineering. Lectures

Course Content
1. Basic concepts of computational methods
• Number representation and computer arithmetic
• Well- and ill-conditioned problems
• Numerical stability
• Complexity of a problem

2. Interpolation
• Polynomial interpolation: Lagrange interpolation, Hermit’s interpolation
• Trigonometric interpolation: fast Fourier transformation (FFT), Goertzel and Reinsch algorithms
• Spline interpolation

3. Approximation
• Approximation problem in normed spaces
• Orthogonalization procedure (Gram-Schmidt)
• Series of orthogonal polynomials
• Approximation in unitary space: mean-square approximation by polynomials
• Uniform polynomial approximation

4. Algebraic equations
• Formulation and solution of linear algebraic equations
• Gauss elimination
• LU decomposition
• Iteration methods(Gauss-Seidel), convergence of iteration methods
• Eigenvalues and eigenvectors

5. Quadratures
• Problem of quadrature convergence
• Interpolation quadratures
• Newton-Cotes formula
• Gauss quadrature

6. Differential equations
• Initial and boundary value problems,
• Eigenvalue problems
• Solutions to elliptical and parabolic equations
• Partial differential equations

Laboratory classes:
Computational Methods in Engineering. Lab classes

1. Development and implementation of the selected computational methods presented during the lectures

2. Application of Matlab software to solve selected engineering numerical problems

Student workload (ECTS credits balance)
Student activity form Student workload
Summary student workload 60 h
Module ECTS credits 2 ECTS
Participation in lectures 28 h
Participation in laboratory classes 14 h
Contact hours 10 h
Contact hours 2 h
Preparation for classes 6 h
Additional information
Method of calculating the final grade:

The final mark = the weighted average: 70% of the laboratory marks + 30% of the theory test (lectures knowledge)

Prerequisites and additional requirements:

Zgodnie z Regulaminem Studiów AGH podstawowym terminem uzyskania zaliczenia jest ostatni dzień zajęć w danym semestrze. Termin zaliczenia poprawkowego (tryb i warunki ustala prowadzący moduł na zajęciach początkowych) nie może być późniejszy niż ostatni termin egzaminu w sesji poprawkowej (dla przedmiotów kończących się egzaminem) lub ostatni dzień trwania semestru (dla przedmiotów niekończących się egzaminem).

Recommended literature and teaching resources:

1. Richard W. Hamming, Numerical Methods for Scientists and Engineers, Dover, 1973.
2. Michael Schäfer, Computational engineering : introduction to numerical methods, Springer, Berlin, 2006.
3. Germund Dahlquist, Åke Björck, Numerical methods in scientific computing, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2008.
4. Eugene Isaacson, Herbert Bishop Keller, Analysis of Numerical Methods, Courier Dover Publications, 2012.

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

1) Conventional multiscale modeling of microstructure evolution during laminar cooling of DP steel strips / Maciej PIETRZYK, Jan KUSIAK, Roman Kuziak, Łukasz MADEJ, Danuta SZELIGA, Rafał GOŁĄB // Metallurgical and Materials Transactions. A, Physical Metallurgy and Materials ; ISSN 1073-5623. — 2014 vol. 45 iss. 13, s. 5835–5851. — Bibliogr. s. 5850–5851. — Mini-symposiuym on multi-scale modeling of microstructure deformation in material processing. — tekst: http://vls1.icm.edu.pl/cgi-bin/sciserv.pl?collection=springer&journal=10735623&issue=v45i0013&article=5835_cammomlcodss&form=pdf&file=file.pdf

2) Application of sensitivity analysis to grid-based procedure dedicated to creation of SSRVE / Łukasz RAUCH, Danuta SZELIGA, Daniel BACHNIAK, Krzysztof BZOWSKI, Maciej PIETRZYK // W: eScience on distributed computing infrastructure : achievements of PLGrid Plus domain-specific services and tools / eds. Marian Bubak, Jacek Kitowski, Kazimierz Wiatr. — Switzerland : Springer International Publishing, cop. 2014 + CD. — (Lecture Notes in Computer Science ; ISSN 0302-9743 ; 8500). — ISBN: 978-3-319-10893-3 ; e-ISBN: 978-3-319-10894-0. — S. 364–377. — Bibliogr. s. 376–377, Abstr.

3) Sensitivity analysis as a support for optimization of industrial processes — Analiza wrażliwości jako narzędzie wspomagające optymalizację procesów przemysłowych / Danuta SZELIGA, Jan KUSIAK // Computer Methods in Materials Science : quarterly / Akademia Górniczo-Hutnicza ; ISSN 1641-8581. — Tytuł poprz.: Informatyka w Technologii Materiałów. — 2014 vol. 14 no. 1, s. 94–98. — Bibliogr. s. 98, Abstr., Streszcz.

4) Selection of parameters of the heat treatment thermal cycle for rails with respect to the wear resistance / Danuta SZELIGA, Roman Kuziak, Tadeusz Zygmunt, Jan KUSIAK, Maciej PIETRZYK // Steel Research International ; ISSN 1611-3683. — Tytuł poprz.: Steel Research. — 2014 vol. 85 no. 6 spec. iss.: Multiscale modeling, s. 1070–1082. — Bibliogr. s. 1082

5) Data exploration approach versus sensitivity analysis for optimization of metal forming processes / Krzysztof REGULSKI, Danuta SZELIGA, Jan KUSIAK // Key Engineering Materials ; ISSN 1013-9826. — 2014 vols. 611–612, s. 1390–1395. — Bibliogr. s. 1395, Abstr.. — ESAFORM 2014 : 17th conference of the European Scientific Association on Material Forming : May 7–9 2014, Espoo, Finland. — tekst: http://www.scientific.net/KEM.611-612.1390.pdf

Pozostałe:
http://www.bpp.agh.edu.pl/autor/szeliga-danuta-04360

Additional information:

None