7 videos in "Systems of ODEs"
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Introduction to First-order Systems of ODEs; Solution by Elimination, Geometric Interpretation of a System
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Sketching Solutions of 2x2 Homogeneous Linear System with Constant Coefficients
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Matrix Methods for Inhomogeneous Systems: Theory, Fundamental Matrix, Variation of Parameters
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Matrix Exponentials; Application to Solving Systems
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Decoupling Linear Systems with Constant Coefficients
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Non-linear Autonomous Systems: Finding the Critical Points and Sketching Trajectories; the Non-linear Pendulum
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Relation Between Non-linear Systems and First-order ODEs; Structural Stability of a System, Borderline Sketching Cases; Illustrations Using Volterra's Equation and Principle
Non-linear Autonomous Systems: Finding the Critical Points and Sketching Trajectories; the Non-linear Pendulum
Non-linear Autonomous Systems: Finding the Critical Points and Sketching Trajectories; the Non-linear Pendulum
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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
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Non-linear Autonomous Systems: Finding the Critical Points and Sketching Trajectories; the Non-linear Pendulum -- Lecture 31. Some very deep non-linear ODE discussion.
- Lecture Notes - Lecture Notes
- Supplementary Notes - Chapter 25 Supplementary Notes written by Prof. Miller
- 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?
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.
