18.385j/2.036j Rodolfo R. Rosales	MIT, Fall 2020 Back to 18.385 home page
Lectures
This page contains information relevant to the lectures: Lecture notes and summaries, etc. Note that: The lectures will be "live" (on-line) and recorded, with the videos later accesible through the canvas website for this course.
Lecture 01.   2020/09/01; 11-12:30 (Tue). Lecture 02.   2020/09/03; 11-12:30 (Thu).   Whiteboard (zip). Lecture 03.   2020/09/08; 11-12:30 (Tue).   Whiteboard (pdf). Lecture 04.   2020/09/10; 11-12:30 (Thu).   Whiteboard (pdf). Lecture 05.   2020/09/15; 11-12:30 (Tue).   Whiteboard (pdf).                       Structural stability hand written notes. Lecture 06.   2020/09/17; 11-12:30 (Thu).   Whiteboard (pdf).                       Structural stability pictures (use MatLab toolkit). Lecture 07.   2020/09/22; 11-12:30 (Tue).   Whiteboard (pdf).                       Bifurcation calculation. Lecture 08.   2020/09/24; 11-12:30 (Thu).   Whiteboard (pdf). Lecture 09.   2020/09/29; 11-12:30 (Tue).   Whiteboard (pdf). Lecture 10.   2020/10/01; 11-12:30 (Thu).   Whiteboard (pdf). Lecture 11.   2020/10/06; 11-12:30 (Tue).   Whiteboard (pdf). Lecture 12.   2020/10/08; 11-12:30 (Thu).   Whiteboard (pdf). Lecture 13.   2020/10/15; 11-12:30 (Thu).   Whiteboard (pdf). Lecture 14.   2020/10/20; 11-12:30 (Tue).   Whiteboard (pdf).                       van der Pol trapping and relaxation osc. period.                       Relaxation oscillations from friction. Lecture 15.   2020/10/22; 11-12:30 (Thu).   Whiteboard (pdf).                       Reduction to 1-D systems.                       The slow time is NEEDED. On Fourier Series.   See the Fourier Series link in this page. Asymptotics, two timing.   See Method of multiple scales             in the Lecture Notes in Asymptotics in this page. Lecture 16.   2020/10/27; 11-12:30 (Tue).   Whiteboard (pdf).                       Asymptotic versus convergent. Lecture 17.   2020/10/29; 11-12:30 (Thu).   Whiteboard (pdf). Lecture 18.   2020/11/03; 11-12:30 (Tue).   Whiteboard (pdf).                       Hopf Bifurcation Using Complex Notation. Lecture 19.   2020/11/05; 11-12:30 (Tue).   Whiteboard (pdf).                       Homoclinic Bifurcation of a Limit Cycle. Lecture 20.   2020/11/10; 11-12:30 (Tue).   Whiteboard (pdf). Lecture 21.   2020/11/12; 11-12:30 (Tue).                         Iterations of the shear map (zip archive).                       URL's for the videos shown at the lecture. Lecture 22.   2020/11/17; 11-12:30 (Tue).   Whiteboard (pdf). Lecture 23.   2020/11/19; 11-12:30 (Thu).   Whiteboard (pdf). Lecture 24.   2020/01/01; 11-12:30 (Tue).   Whiteboard (pdf).                       The manta ray attractor.       TheVideos.zip.                       TheVideos README. Lecture 25.   2020/01/03; 11-12:30 (Thu).   Whiteboard (pdf). Lecture 26.   2020/01/08; 11-12:30 (Tue).   Whiteboard (pdf).                       Iterates of the logistic map (zip archive).