Numerical Algorithms

5 ECTS credits
125 h study time

Offer 1 with catalog number 1007574BNR for all students in the 2nd semester at a (B) Bachelor - advanced level.

Semester

2nd semester

Enrollment based on exam contract

Impossible

Grading method

Grading (scale from 0 to 20)

Can retake in second session

Yes

Enrollment Requirements

Om een inschrijving te kunnen nemen voor Basistechnieken voor computersimulaties moet men geslaagd zijn voor Analyse: afleiden, integreren, wiskundige software en ingeschreven of geslaagd zijn voor Lineaire algebra: stelsels, matrices en afbeeldingen.

Taught in

Dutch

Faculty

Faculteit Ingenieurswetenschappen

Department

Applied Mechanics

Educational team

Aurélie Bellemans (course titular)

Activities and contact hours

24 contact hours Lecture
36 contact hours Seminar, Exercises or Practicals

Course Content

The following problems are discussed: error theory, solving non-linear equations, solving systems of linear equations, computing eigenvalues and eigenvectors, singular value decomposition of a matrix, interpolation and approximation of functions, fast Fourier transform, numerical differentiation and integration, numerical solution of differential and partial differential equations.
During the exercises, we illustrate the algorithms, discussed during the course, on practical examples, hereby using the MATLAB software.

Course material

Course text (Required) : Basistechnieken voor Computersimulaties, C. Lacor, VUB, 2220170007588, 2020
Handbook (Recommended) : Numerical Analysis, Jacques and Judd, Chapman and Hall, 9789401079198, 1987
Handbook (Recommended) : Numerical Analysis, Burden and Faires, 10de, Brooks/Coles Cengage Learning, 9781305253667, 2016
Handbook (Recommended) : A first course in numerical analysis, Ralston and Rabinowitz, 2de, Dover Publications, 9780486414546, 2001
Handbook (Recommended) : Numerical Recipes in Fortran 77, Teukolsky, Vetterling and Flannery, 2de, Cambridge Univ. Press, 9780521430647, 1992
Handbook (Recommended) : Linear Algebra and its applications, Strang, 4de, Brooks Cole, 9780030105678, 2006

Additional info

basic work : Jacques and Judd, Numerical Analysis, Chapman and Hill, 1987
More elaborated works: Burden and Faires, Numerical Analysis, PWS-Kent Publ. Co.,4th Ed.,1989 or Ralston, A first course in numerical analysis, McGraw-Hill,NY,1965
A book covering many numerical algorithms for practical use: Press, Teukolsky, Vetterling and Flannery, Numerical Recipes in Fortran, Cambridge Univ. Press,2nd Ed.,1992
A book on linear algebra: Strang, Linear Algebra and its applications, Academic Press Inc., 2nd Ed.,1980

Learning Outcomes

General competencies

Aims
This course gives an introduction to the most important numerical techniques and methods. After successfully ending this course, the student should be able to tackle more specialised courses where numerical techniques are being used (such as e.g. CFD, image processing etc.).
The course aims also at emphasing the need of numerical methods for solving physical problems. This aspect is treated both during the lectures (in an introductory lecture) and during the exercises (where the assignments in most cases have a physical background)

Final competences
The student gets an overview of the most important numerical techniques (cf. content).
The aim is that the student not only can apply the techniques to practical problems (in the assignments the students will program using the MATLAB software) but that he also understands the theory behind the methods.
The student must be able to solve independently simple numerical problems e.g. finding roots of (systems of) non-linear equations, solving linear systems, determining eigenvalues of matrices, solving simple ordinary and partial differential equations.
He must also have sufficient basic knowledge to be able to, independently, understand alternative methods or more advanced methods from the literature.
He must be able to mathematically describe simple physical problems and subsequently solve these using the methods taught in the course.

Grading

The final grade is composed based on the following categories:
Oral Exam determines 60% of the final mark.
PRAC Practical Assignment determines 40% of the final mark.

Within the Oral Exam category, the following assignments need to be completed:

Oral exam with a relative weight of 1 which comprises 60% of the final mark.

Note: Mondeling examen over het theoretisch gedeelte (60%). De student mag de gestelde vragen gedurende een 10-tal minuten (voor alle vragen samen) met open boek voorbereiden. Bedoeling is ev. details terug op te halen. Ev. gemaakte nota's tijdens deze voorbereiding worden vervolgens verwijderd. De student werkt daarna (met gesloten boek) de antwoorden uit op papier waarna hij mondeling ondervraagd wordt.

Within the PRAC Practical Assignment category, the following assignments need to be completed:

MATLAB with a relative weight of 1 which comprises 40% of the final mark.

Note: Oefening examen : problemen, zoals behandeld tijdens de oefeningen sessies, moeten opgelost worden dmv de algoritmen uit de cursus en met gebruik van MATLAB (40%)

Additional info regarding evaluation

First session:
Oral exam about the theoretical part (60%). The student may prepare the questions during about 10 minutes (for all questions) with open book. Aim is to possibly refresh some details. Notes taken during these 10 minutes, are subsequently removed. Next, the student works out the answers to the questions on blank paper, after which the oral examination starts.
Exam exercises : problems, similar as those solved during the course exercises, will have to be solved, using the algorithms discussed in the course and MATLAB (40%)
Second session: idem

Allowed unsatisfactory mark

The supplementary Teaching and Examination Regulations of your faculty stipulate whether an allowed unsatisfactory mark for this programme unit is permitted.

Academic context