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 Python software.

Course material

Course text (Required) : Basistechnieken voor Computersimulaties, Lacor - Bellemans, VUB, 2220170009537, 2022
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) : Linear Algebra and its applications, Strang, 4de, Brooks Cole, 9780030105678, 2006
Handbook (Recommended) : Python programming and numerical methods, a guide for engineers and scientists, Kong, Siauw and Bayen, Academic Press (Elsevier), 9780128195499, 2021

Additional info

Basic reference 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 in Matlab: Applied Numerical Methods with Matlab for Engineers and Scientists, S.C. Chapra, 4th edition, McGraw-Hill Higher Education, 2017.

A book covering methods and applications in Python: Python Programming and Numerical methods, A guide for engineers and scientists, Q. Kong, T. Siauw, A. M. Bayen, Elsevier, 2021.
A book on linear algebra: Strang, Linear Algebra and its applications, Academic Press Inc., 2nd Ed.,1980.

Extra information:

The course is organised using a study guide on the Canvas platform. Every module contains small movies with extra information on certain numerical methods. At the end of each module, the students can test their knowledge and skills with a self-quiz.

The homeworks are published after each WPO session on Canvas.

During the course sessions with the teacher, we will treat the course material interactively (using Wooclap).

Guidance and questions: after the course, after an appointment or via email.

Learning Outcomes

General competencies

Aim
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 Python 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.
The student must also have sufficient basic knowledge to be able to, independently, understand alternative methods or more advanced methods from the literature.
The student 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:
Written Exam determines 80% of the final mark.
PRAC Practical Assignment determines 20% of the final mark.

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

schriftelijk examen op de pc with a relative weight of 1 which comprises 80% of the final mark.

Note: 20%

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

python opdrachten with a relative weight of 1 which comprises 20% of the final mark.

Note: 80%

Additional info regarding evaluation

First session:

WPO homeworks (20% of the total grade)
1. every WPO sessions contains a homework. The student has 2 weeks to complete these tasks in Python. The homework needs to be submitted via Canvas.
Written exam on the computer (80% of the total grade)
1. multiple-choice questions on the theory
2. Programming exam where the students need to solve practical engineering problems by using the algorithms they learned in class in Python.

Second session: the written examn on the computer counts for 100% of the grade.

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