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
Sketching Solutions of 2x2 Homogeneous Linear System with Constant Coefficients
Sketching Solutions of 2x2 Homogeneous Linear System with Constant Coefficients
671 views - 00:50:25
Part of video series Differential Equations Course acquired through MIT OpenCourseWare
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Arthur Mattuck, 18.03 Differential Equations, Spring 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 28, 2008). License: Creative Commons BY-NC-SA.
More info at: http://ocw.mit.edu/terms
More info at: http://ocw.mit.edu/terms
Sketching Solutions of 2x2 Homogeneous Linear System with Constant Coefficients -- Lecture 27. Learn what graphs of systems of differential equations look like.
- Lecture Notes - Lecture Notes
- Supplementary Notes - Chapter 22 Supplementary Notes written by Prof. Miller
- What is a 2x2 Homogeneous Linear System?
- How do you solve a 2x2 Homogeneous Linear System?
- How do you sketch the solutions of a linear system of differential equations?
A really interesting lecture with the always anecdotal professor Mattuck. You will learn how to truly understand the solutions to homogeneous linear systems with constant coefficients. You will actually see what is happening to a graph as t increases depending on what values of constants are.
