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 Exponentials; Application to Solving Systems
Matrix Exponentials; Application to Solving Systems
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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 Exponentials; Application to Solving Systems -- Lecture 29. Solving systems of ODEs again; this time with some applications.
- Lecture Notes - Lecture Notes
- Linear Systems Notes 2 - Linear Systems Notes 2
- What is a fundamental matrix?
- What are matrix exponentials?
- What is e^At?
- How do you compute A^2?
- How do you compute e^At?
In this video, applications to systems of differential equations are discussed. Matrix exponentials (powers of matrices such as e^At and A^2 are included) and fundamental matrices are used to solve the systems.
