Assistant Professor

Mathematics for Engineers

Master Program, Arts & Métiers, 2019

This course is part of the international master program Factory of the future proposed by Arts et Métiers Institute of Technology. Students enrolling in this program may come from very different backgrounds. As such, the aim of this course is to teach them the basic tools from linear algebra (linear systems of equations, vector spaces, eigenvalues and eigenvectors) and discrete-time MIMO linear systems they may need for other courses in this program. One or two small numerical projects in python or octave are also proposed.

Prerequisite

  • Basic mathematics (e.g. derivative and integrals, complex numbers, etc).
  • Prior knowledge of python, octave or matlab would be beneficial.

Lesson plan

The course is divided in ten different sessions. The tentative lesson plan below may be subject to modifications as the course evolves pretty much every year when interacting with students. I will try to keep this README up to date every time the course is modified.

  • Lecture 1: Basics of linear algebra.
  • Lecture 2: General solution to a linear system of equations.
  • Lecture 3: Underdetermined systems of equations and p-norm minimization.
  • Lecture 4: Overdetermined systems of equations, ordinary least-squares and variations.
  • Lecture 5: Introduction to linear time invariant dynamical systems.
  • Lecture 6: Stability, Observability and Controlability of linear systems.
  • Lecture 7: Hankel and Toeplitz matrices for state space model and convolution model identification.
  • Lecture 8: Singular value decomposition and the EigenRealization Algorithm.
  • Lecture 9: Introduction to control theory.
  • Lecture 10: Introduction to Kalman filters.