Duration
20h Th, 20h Pr
Number of credits
Lecturer
Language(s) of instruction
English language
Organisation and examination
Teaching in the first semester, review in January
Schedule
Units courses prerequisite and corequisite
Prerequisite or corequisite units are presented within each program
Learning unit contents
Numerical analysis is at the boundary between Mathematics and Computer Science. It consists in studying how to practically obtain in a computer different mathematical concepts studied in other courses.
There are two main types of problems studied by numerical analysis:
- how to actually compute results for which an analytical expression exists but that can be obtained more or less accurately depending on the selected method
- how to compute solutions of real problems for which no analytical solution is known but that can be approximated using a computer.
The course is structured in four main chapters.
Ch 1: Polynomial interpolation and regression
Ch 2: Numerical linear algebra and basic linear programming
Ch 3: Non linear systems and some basics about non linear optimization
Ch 4: Numerical derivation and integration
Learning outcomes of the learning unit
At the end of the course, the student will have to
- master the main numerical methods to approximate derivatives, definite integrals, linear and nonlinear systems, eigenvalues, regressions,
- understand the bases of linear optimization and the simplex algorithm,
- be able to analyze the behaviour of these numerical methods and in particular to be able to discuss their stability, their order of convergence and their conditions of application,
- be able to apply these methods to academic and simple practical instances.
Prerequisite knowledge and skills
An introductory course on linear algebra and calculus.
Planned learning activities and teaching methods
The course is organized as follows: 10 lectures and 7 tutorials.
Mode of delivery (face to face, distance learning, hybrid learning)
The course is given in face-to-face.
The rooms are such that we can fit all students with one free seat in between them.
Organisational adjustments related to the current health context
If face-to-face is allowed:
Written exam mixing theory (true/false) and exercises similar to the problem sessions.
If remote evaluation as imposed by the health conditions:
Written exam to be done at home in exam conditions, mixing theory (true/false) and exercises similar to the problem sessions.
The pdf with the exam questions is available on the dox repository at the time of the exam. The scan of the student's answers is to be uploaded on the submission platform https://submit.montefiore.ulg.ac.be
Recommended or required readings
The syllabus is available at the CdC.
Assessment methods and criteria
Below you will find information on the evaluation methods planned for in-person and remote exams as well as those planned for hybrid sessions. Depending on how the health crisis evolves, the chosen method will be communicated to you no later than one month before the start of the exam session.
A written exam. One theoretical question accounts for 25% of the final grade, the rest being exercises.
Work placement(s)
Organizational remarks
The theoretical lectures are taught in English. The problem sessions are taught in French.
All documents of the course are available on the dox repository:
https://dox.uliege.be/index.php/s/mdrMsQ33r8uSU5E
This includes the slides, the annotated slides, he organizational details.
Contacts
q.louveaux@uliege.be
dlamy@uliege.be