Non-linear Autonomous Systems: Finding the Critical Points and Sketching Trajectories; the Non-linear Pendulum

Sick of ads?‚Äč Sign up for MathVids Premium
Taught by OCW
  • Currently 4.0/5 Stars.
6545 views | 1 rating
Lesson Description:

Non-linear Autonomous Systems: Finding the Critical Points and Sketching Trajectories; the Non-linear Pendulum -- Lecture 31. Some very deep non-linear ODE discussion.

Arthur Mattuck, 18.03 Differential Equations, Spring 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 29, 2008). License: Creative Commons BY-NC-SA.
More info at: http://ocw.mit.edu/terms

Additional Resources:
Questions answered by this video:
  • What is a non-linear system of differential equations?
  • How do you solve non-linear ODEs?
  • How do you find critical points?
  • How do you sketch trajectories?
  • What is the non-linear pendulum?
  • What is a spiral in ODEs?
  • What is a sink in ODEs?
  • What is a Jacobian matrix?
  • How do you use a Jacobian matrix?
  • What are some examples of using a Jacobian matrix?
  • Staff Review

    • Currently 4.0/5 Stars.
    This video is a very new idea to this course. This lecture deals with non-linear autonomous systems of ODEs. To solve them, you must find critical points and sketch trajectories for the systems. A lot of sketching graphs and writing systems of differential equations from the pictures is done. Some actual concrete problems are also discussed. Jacobian matrices and actual problems using them are shown as well.