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
Matrix Methods for Inhomogeneous Systems: Theory, Fundamental Matrix, Variation of Parameters
Matrix Methods for Inhomogeneous Systems: Theory, Fundamental Matrix, Variation of Parameters
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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 29, 2008). License: Creative Commons BY-NC-SA.
More info at: http://ocw.mit.edu/terms
More info at: http://ocw.mit.edu/terms
Matrix Methods for Inhomogeneous Systems: Theory, Fundamental Matrix, Variation of Parameters -- Lecture 28. Learn about inhomogeneous systems of ODEs by using matrices.
- Lecture Notes - Lecture Notes
- Linear Systems Notes - Linear Systems Notes
- Supplementary Notes - Chapter 24 Supplementary Notes written by Prof. Miller
- Problem Set 7 - Problem Set 7
- Problem Set 7 Solutions - Problem Set 7 Solutions
- What are Matrix Methods for Inhomogeneous Systems?
- What are Inhomogeneous Systems?
- What is the Fundamental Matrix?
- What is Variation of Parameters?
An interesting discussion of inhomogeneous systems of linear differential equations by using matrices. The lecture is almost entirely theory, but overall, a good explanation of inhomogeneous systems. Wronskians come up again in this lecture as well, and the fundamental matrix is defined with its properties.
