Relation Between Non-linear Systems and First-order ODEs; Structural Stability of a System, Borderline Sketching Cases; Illustrations Using Volterra's Equation and Principle
In this lecture, the relationship between nonlinear systems and first-order ODEs is explored, as well as the structural stability of a system and borderline sketching cases. The lecturer uses Volterra's equation and principle to illustrate these concepts. The conversion of a nonlinear system to a first-order equation is discussed, and the benefits and drawbacks of losing information, such as eliminating time from the solution, are examined. A simple example of a predator-prey equation is used to demonstrate these concepts and highlight the three points needed to analyze nonlinear systems effectively.
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.
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
- 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?
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Staff Review
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 Volterraâs Equation and Volterraâs Principle. A lot of big ideas are presented here.
