5 videos in "First-Order Linear ODEs"
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Solving First-order Linear ODE's; Steady-state and Transient Solutions
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First-order Substitution Methods: Bernouilli and Homogeneous ODE's
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First-order Autonomous ODE's: Qualitative Methods, Applications
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First-order Linear with Constant Coefficients: Behavior of Solutions, Use of Complex Methods
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Continuation; Applications to Temperature, Mixing, RC-circuit, Decay, and Growth Models
First-order Substitution Methods: Bernouilli and Homogeneous ODE's
First-order Substitution Methods: Bernouilli and Homogeneous ODE's
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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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First-order Substitution Methods: Bernouilli and Homogeneous ODE's -- Lecture 4. Learn how to change variables in differential equations.
- Lecture Notes - Lecture Notes
- Supplementary Notes - Chapter 3 Supplementary Notes written by Prof. Miller
- Problem Set 1 - Problem Set 1
- Problem Set 1 Solutions - Problem Set 1 Solutions
- Recitation Problems - Recitation Problems and classwork exercises
- Recitation Solutions - Recitation problem solutions
- What are the First-order Substitution Methods?
- What are Bernouilli ODEs?
- What are Homogeneous ODEs?
- What is scaling?
- What is direct substitution?
- What is inverse substitution?
- What is an integrating factor?
This video talks about the change of variables and substitution to make an equation solvable. Also, scaling is discussed in various differential equations to change units, make unit dimensionless, or to reduce the number of or simplify constants in a function. Some examples are shown, and this video covers a lot of very important and intense differential equations topics.
