L3 ENS Paris

Caroline MULLER


# I. Fundamentals:
    - linear spaces, dimension, basis
    - linear mappings
    - rank–nullity theorem
    - implications of the theorem (linear systems of equations)

# II. Matrices:
    - matrices and linear mappings
    - change of basis
    - square matrices, rank, inverse
    - determinant, eigenvalues and eigenvectors

# III. Applications:
    - waves, dispersion relations
    - linear stability analysis, chaos

Linear Algebra and Its Applications, by Peter Lax

Linear Algebra Done Right, by Sheldon Axler
Elementary Differential Equations and Boundary Value Problems, by William Boyce and co-authors

- Nice movie of surface waves in the lab

- DM and Solution

-TP Dynamical systems : TP, Code and Solution

- How to cut a Parallelepiped into 6 Tetrahedrons : link