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
Introduction to First-order Systems of ODEs; Solution by Elimination, Geometric Interpretation of a System
Introduction to First-order Systems of ODEs; Solution by Elimination, Geometric Interpretation of a System
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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 27, 2008). License: Creative Commons BY-NC-SA.
More info at: http://ocw.mit.edu/terms
More info at: http://ocw.mit.edu/terms
Introduction to First-order Systems of ODEs; Solution by Elimination, Geometric Interpretation of a System -- Lecture 24. A very complete lecture on systems of differential equations.
- Lecture Notes - Lecture Notes
- Muddy Card Responses - Muddy Card Responses are explanations of topics that were confusing to students
- Recitation Problems - Recitation Problems and classwork exercises
- Recitation Solutions - Recitation problem solutions
- What are first-order systems of ODEs?
- How do you solve First-order systems of ODEs?
- How do you solve systems of ODEs by elimination?
- What is the geometric interpretation of a system?
- What is an application of systems of differential equations?
- What is an autonomous system?
- What is a velocity field?
The beginning of first-order systems of differential equations. From this lecture on, this will be the topic of discussion of the course. These are interesting because they must be solved simultaneously. This is a very involved lesson that includes real-world applications of several circuits connected together.
