20h Th, 20h Pr
Number of credits
Language(s) of instruction
Organisation and examination
Teaching in the first semester, review in January
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 8 tutorials.
Mode of delivery (face-to-face ; distance-learning)
Recommended or required readings
The syllabus is available at the CdC.
Assessment methods and criteria
A written exam. One theoretical question accounts for 25% of the final grade, the rest being exercises.
The theoretical lectures are taught in English.