Dynamical systems

- Simple notions of real analysis.
- Introduction to computer programming.

- Useful notions of analysis (4 slides per page).

- Introduction to computer software: octave (a GPL -free- MatLab equivalent) and maxima (a GPL -free- Maple equivalent).

- One dimensional iteration (4 slides per page).
- Supplementary material: analysis of the logistic equation.
- Iterates of the logistic map.
- Cobwebbing for the logistic map.
- Cascade of bifurcation for the logistic map.

- General theory of differential equations (4 slides per page).

- Theory of linear equations (4 slides per page).

- Analysis near fixed points.
- Bifurcations (4 slides per page).

- Summary (after a first trim down), and 4 slidesper page version. Same version but without sectionning info (less than 100 pages) summary and 4 slides per page version.

- Old final examinations.
- Mock midterm.
- Midterm and solutions.