This course aims to teach students how to efficiently and rationally use computers in a scientific context. The main topic deals with numerical problem resolution with up-to-date scientific conceptual and practical tools, with emphasize on numerical computation possibilities and limitations. Some complements in computer programming are also taught to help students to practically implement numerical algorithms.
Teaching is done by alternating sequences of short lectures and hands-on practical tutorials in a computer room with the Matlab^® software, largely used in the academic and industrial world.

 Syllabus for 2019-2020.  
The course syllabus is as follow :

Use of Matlab software [~8h] :

• reminder on fundamental Matlab objects: scalars, vectors, matrices. Array (element-wise) operations.
  
• 2D (reminder) and 3D graphics. Image display.
  
• Programming basics (revisions and complements)
  
  Numerical computing fundamentals [~24h] :
  
• Rounding error. Method error. Numerical stability of algorithms.
  
• Square linear system solving. Notion on matrix condition number.
  
• Least-square sense linear system solving.
  
• Singular Value Decomposition [SVD], pseudo-inverse and condition number.
  
• Discrete Fourier Transform and Fast Fourier Transform, 1D (revisions) and 2D.
  
• Non-linear problem solving (zero finding, numerical quadrature tool use, local and global optimization tool use, ...)
  
• Ordinary Differential Equation [ODE] solving
  
• Introduction to Partial Differential Equation [PDE] solving with COMSOL software
  

Requirements : General undergraduate knowledge of mathematics: real and complex calculus, linear algebra, Fourier transform and discrete Fourier transform, ordinary differential equations, ... Some basic knowledge of the Matlab software and of numerical computing could be useful but is not mandatory...

Evaluation mechanism : Individual final exam

Last Modification : Sunday 29 August 2021