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.
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.
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.
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.
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:
Within the PRAC Practical Assignment category, the following assignments need to be completed:
First session:
Second session: the written examn on the computer counts for 100% of the grade.
This offer is part of the following study plans:
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