4 videos in "Second-Order Linear ODEs"
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Solving Second-order Linear ODE's with Constant Coefficients: The Three Cases
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Theory of General Second-order Linear Homogeneous ODE's: Superposition, Uniqueness, Wronskians
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Continuation: General Theory for Inhomogeneous ODEs. Stability Criteria for the Constant-coefficient ODEs
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Finding Particular Solutions to Inhomogeneous ODEs: Operator and Solution Formulas Involving Exponentials
Continuation: General Theory for Inhomogeneous ODEs. Stability Criteria for the Constant-coefficient ODEs
Continuation: General Theory for Inhomogeneous ODEs. Stability Criteria for the Constant-coefficient ODEs
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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 26, 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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Continuation: General Theory for Inhomogeneous ODEs. Stability Criteria for the Constant-coefficient ODEs -- Lecture 12. More examples of second-order ODEs.
- Lecture Notes - Lecture Notes
- Notes - Notes and exercises written by Prof. Mattuck
- Supplementary Notes - Chapter 7 Supplementary Notes written by Prof. Miller
- What is an inhomogeneous second-order differential equation?
- What is the reduced equation?
- What is a passive system?
- What is a forced system?
This lesson has many more examples of real-world functions and both inhomogeneous and homogeneous second-order ODEs and their solution equations and theorems. The spring equation is used for a second-order ODE example. Solutions and stability conditions for different ODEs are also discussed. A good video for more second-order ODE work.
