7 videos in "Systems of ODEs"
-
Introduction to First-order 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
-
Non-linear Autonomous Systems: Finding the Critical Points and Sketching Trajectories; the Non-linear Pendulum
-
Relation Between Non-linear Systems and First-order ODEs; Structural Stability of a System, Borderline Sketching Cases; Illustrations Using Volterra's Equation and Principle
Relation Between Non-linear Systems and First-order ODEs; Structural Stability of a System, Borderline Sketching Cases; Illustrations Using Volterra's Equation and Principle
Relation Between Non-linear Systems and First-order ODEs; Structural Stability of a System, Borderline Sketching Cases; Illustrations Using Volterra's Equation and Principle
1205 views - 00:50:08
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 BY-NC-SA.
More info at: http://ocw.mit.edu/terms
More info at: http://ocw.mit.edu/terms
Relation Between Non-linear Systems and First-order ODEs; Structural Stability of a System, Borderline Sketching Cases; Illustrations Using Volterra's Equation and Principle -- Lecture 33. A bunch of topics all shoved into one huge lecture.
- Practice Final Exam - Practice Final Exam
- Final Exam - Final Exam
- Lecture Notes 1 - Lecture Notes 1
- Lecture Notes 2 - Lecture Notes 2
- Lecture Notes 3 - Lecture Notes 3
- Lecture Notes 4 - Lecture Notes 4
- Muddy Card Responses - Muddy Card Responses are explanations of topics that were confusing to students
- Graphing Systems Notes - Graphing Systems Notes
- Problem Set 8 - Problem Set 8
- Problem Set 9 - Problem Set 9
- Problem Set 8 Solutions - Problem Set 8 Solutions
- Problem Set 9 Solutions - Problem Set 9 Solutions
- What is the relation between non-linear systems and first-order ODEs?
- What is the structural stability of a system?
- What are borderline sketching cases?
- What is Volterra's Equation?
- What is Volterra's Principle?
This lecture is packed full of a lot of good topics. The relation between non-linear systems and first-order ODEs is explained. The structural stability of a system is explained, and examples of borderline sketching is done for several cases. Finally, there are several illustrations using Volterra’s Equation and Volterra’s Principle. A lot of big ideas are presented here.
