7 videos in "Systems of ODEs"

Introduction to Firstorder Systems of ODEs; Solution by Elimination, Geometric Interpretation of a System

Sketching Solutions of 2x2 Homogeneous Linear System with Constant Coefficients

Matrix Methods for Inhomogeneous Systems: Theory, Fundamental Matrix, Variation of Parameters

Matrix Exponentials; Application to Solving Systems

Decoupling Linear Systems with Constant Coefficients

Nonlinear Autonomous Systems: Finding the Critical Points and Sketching Trajectories; the Nonlinear Pendulum

Relation Between Nonlinear Systems and Firstorder ODEs; Structural Stability of a System, Borderline Sketching Cases; Illustrations Using Volterra's Equation and Principle
Nonlinear Autonomous Systems: Finding the Critical Points and Sketching Trajectories; the Nonlinear Pendulum
Nonlinear Autonomous Systems: Finding the Critical Points and Sketching Trajectories; the Nonlinear Pendulum
5025 views, 1 rating  00:47:09
Part of video series Differential Equations Course acquired through MIT OpenCourseWare
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 BYNCSA.
More info at: http://ocw.mit.edu/terms
More info at: http://ocw.mit.edu/terms
(
download video
)
Nonlinear Autonomous Systems: Finding the Critical Points and Sketching Trajectories; the Nonlinear Pendulum  Lecture 31. Some very deep nonlinear ODE discussion.
 Lecture Notes  Lecture Notes
 Supplementary Notes  Chapter 25 Supplementary Notes written by Prof. Miller
 What is a nonlinear system of differential equations?
 How do you solve nonlinear ODEs?
 How do you find critical points?
 How do you sketch trajectories?
 What is the nonlinear 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?
This video is a very new idea to this course. This lecture deals with nonlinear 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.