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Teaching coordinator :

Isabelle Rivals
  

Teaching staff :
Yacine Oussar
Maxime Ardré
Brigitte Quenet

Research center

Level : 2nd year

Course Language : French

Term : core curriculum

Number of hours : 23

ECTS Credits : 1
ANUM Numerical analysis with Matlab
Teaching site :
Laboratory sessions: 23 h

Objectives

The goals of this course are:
  • To be able to program with Matlab, not as a black box, but using its specific features (exploiting vectorisation), and successfully analysing the results and assessing the confidence that can be placed in them (importance of the numerical conditioning of linear systems).
  • The theoretical and practical acquisition of mathematical tools (methods for numerical integration, for solving partial derivative equations, discrete Fourier transform for numerical signal processing).
  • Encourage the reflex to use Matlab for the solution of problems encountered in other courses via various real-life applications (image processing, vehicle modeling, chromatographic data analysis, etc.).


Syllabus

This course is taught in the form of lab sessions-lectures during which the concepts and associated tools are introduced briefly, immediately followed by practical exercises.

  1. Introduction to MATLAB

    • Development environment
    • Data handling
    • Graph handling
    • Programming
    • Reading and writing data

  2. Linear algebra and modeling

    • Linear systems and least-squares resolution
    • Eigen values and vectors
    • Singular values and vectors (SVD factorisation)

  3. Numerical integration methods

    • Rectangles and trapezes, Simpson
    • Monte-Carlo
    • Gaussian quadrature

  4. Signal processing elements

    • Steady state signals
    • Discrete time signals
    • Linear filtering elements

  5. Partial differential equations

    • 2D-Poisson equation
    • 1D-wave equation
    • 1D-diffusion equation

Links with other course modules



Requirements : The first year introduction to Matlab. Basic programming skills are necessary, and normally acquired during the first year Programming course in the C/C++ language of the ESPCI, or when learning another programming language, such as Python for example.

Evaluation mechanism : report + Matlab program illustrating one of the themes mentionned above.

Last Modification : Monday 10 September 2018

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