The Geometrical View of y'=f(x,y): Direction Fields, Integral Curves
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Lesson Description:
The Geometrical View of y'=f(x,y): Direction Fields, Integral Curves -- Lecture 1. Understanding the geometrical view of differential equations.
Arthur Mattuck, 18.03 Differential Equations, Spring 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 23, 2008). License: Creative Commons BY-NC-SA.
More info at: http://ocw.mit.edu/terms
Additional Resources:
- Notes - Notes and exercises written by Prof. Mattuck
- Recitation Problems - Recitation Problems and classwork exercises
- Recitation Solutions - Recitation problem solutions
- Separable Differential Equations - A tutorial on separable differential equations.
- Lecture Notes - Lecture Notes
- Supplementary Notes - Chapter 1 Supplementary Notes written by Prof. Miller
Questions answered by this video:
- What are differential equations?
- What are first-order differential equations?
- What are ordinary differential equations?
- What are differential equations?
- What are first-order differential equations?
- What are ordinary differential equations?
- What are ODE's?
- What are separable differential equations?
- What differential equations are not solvable?
- What are direction fields?
- What are integral curves?
- How do you draw a direction field?
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Staff Review
This is a really great video introduction to ordinary differential equations. It explains exactly the geometric interpretation of what is going on. This lesson gives you a very complete, over-arching view of what differential equations look like in a plane. Also, direction fields and integral curves are discussed and drawn for equations.
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