6 ECTS credits
150 h study time

Offer 1 with catalog number 1015193ANR for all students in the 2nd semester at a (A) Bachelor - preliminary 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
Enrolling in 'Scientific Computation’ means that students bachelor mathematics and data science simultaneously follow 'Analysis I', 'Analysis II' and 'Linear Algebra' or have successfully passed 'Analysis I', 'Analysis II' and 'Linear Algebra'. 'Enrolling in 'Scientific Computation’ means that students bachelor geography simultaneously follow ‘Mathematics: Calculus and Linear Algebra' volgen or have successfully passed 'Mathematics: Calculus and Linear Algebra'.
Taught in
Dutch
Faculty
Faculty of Sciences and Bioengineering Sciences
Department
Mathematics
Educational team
Tomas Everaert
Jan De Beule (course titular)
Activities and contact hours
26 contact hours Lecture
26 contact hours Seminar, Exercises or Practicals
Course Content

Error analysis

            Computer arithmetics

            Machine precision

            Numerical stability and conditioning

Linear system of equations

            Direct method

            LU decomposition

            Iterative methods for large systems (WPO)

            Cholesky decomposition (WPO)

            Matrix inverse (WPO)

QR-decomposition

            Gram-Schmidt orthogonalisation

            QR decomposition

            Eigenvalues en eigenvectors

            Least squares (WPO)

            Geconjugated gradients (WPO)

Root solving of nonlinear equations

            Binary search

            Banach fixpoint iterations

            Steffenson fixpoint iterations

            Newton methodes

            Damping

            Optimalisation – Newton-Raphson (WPO)

Numerical integration

            Trapezoidal rule

            Simpson rule

            Newton-Cotes formulas

            Romberg extrapolation

            Differential equations (WPO)

Course material
Digital course material (Required) : Slides in PDF formaat
Handbook (Recommended) : Inleiding tot de numerieke wiskunde, Adhemar Butheeel, BIB, 9789033462535, 2006
Handbook (Recommended) : A friendly Introduction to Numerical Analysis, Bradie, B., Pearson, 9780130130549, 2006
Handbook (Recommended) : Numerical Analysis, A mathematical introduction, Michelle Schatzman, Oxford University Press, 9780198508526, 2002
Additional info

none

Learning Outcomes

General competencies

The student obtains a foundation in numerical techniques. The student revisits classical results from linear algebra and analysis with the aim to establishing these results from a constructive viewpoint. The student sees that various implementations ways do not reveal equivalent results although these are analytically equivalent. The student learns to analyze computational complexity, numerical stability and discriminate between various sources of error.

The student programs the solutions from the course in Matlab. In particular, the student learns how to translate abstract mathematical theorems to a practical Matlab solution.

Grading

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

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

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

Additional info regarding evaluation

Oral exam determines 60% of the final mark. 30% of the mark is based on the Matlab exercises while the remaining 30% covers the theory. The practical exam is prepared on PC for the exercises and defended with the assistant, for the theory on paper and defended with the professor.

Project in group determines 40% of the final mark in which a numerical problem is solved through methods described in the course. The group proposes the solution of the numerical problem by a report of max. 10 pages. The project is defended in group during one of the sessions.

 

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

This offer is part of the following study plans:
Bachelor of Business Economics: Minor Minor Education (only offered in Dutch)
Bachelor of Geography: Default track (only offered in Dutch)
Bachelor of Political Science and Sociology: - afstudeerrichting sociologie, minor onderwijs (only offered in Dutch)
Bachelor of Mathematics and Data Science: Standaard traject (only offered in Dutch)
Master of Teaching in Social Sciences: politieke wetenschappen en sociologie (90 ECTS, Etterbeek) (only offered in Dutch)
Master of Teaching in Science and Technology: biologie (120 ECTS, Etterbeek) (only offered in Dutch)
Master of Teaching in Science and Technology: geografie (120 ECTS, Etterbeek) (only offered in Dutch)
Master of Teaching in Science and Technology: chemie (120 ECTS, Etterbeek) (only offered in Dutch)
Master of Teaching in Science and Technology: fysica (120 ECTS, Etterbeek) (only offered in Dutch)
Master of Teaching in Science and Technology: computerwetenschappen (120 ECTS, Etterbeek) (only offered in Dutch)
Master of Teaching in Science and Technology: ingenieurswetenschappen (120 ECTS, Etterbeek) (only offered in Dutch)