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
Introduction to Firstorder Systems of ODEs; Solution by Elimination, Geometric Interpretation of a System
Introduction to Firstorder Systems of ODEs; Solution by Elimination, Geometric Interpretation of a System
2993 views, 2 ratings  00:47:02
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 27, 2008). License: Creative Commons BYNCSA.
More info at: http://ocw.mit.edu/terms
More info at: http://ocw.mit.edu/terms
(
download video
)
Introduction to Firstorder Systems of ODEs; Solution by Elimination, Geometric Interpretation of a System  Lecture 24. A very complete lecture on systems of differential equations.
 Lecture Notes  Lecture Notes
 Muddy Card Responses  Muddy Card Responses are explanations of topics that were confusing to students
 Recitation Problems  Recitation Problems and classwork exercises
 Recitation Solutions  Recitation problem solutions
 What are firstorder systems of ODEs?
 How do you solve Firstorder systems of ODEs?
 How do you solve systems of ODEs by elimination?
 What is the geometric interpretation of a system?
 What is an application of systems of differential equations?
 What is an autonomous system?
 What is a velocity field?
The beginning of firstorder systems of differential equations. From this lecture on, this will be the topic of discussion of the course. These are interesting because they must be solved simultaneously. This is a very involved lesson that includes realworld applications of several circuits connected together.