Lecture 23: Flux and the normal form of Green's theorem
In this lesson, the concept of flux of a vector field across a curve is explored, with a focus on the interpretation of flux as a measure of how much fluid passes through the curve per unit time, counting positively what goes to the right and negatively what goes to the left. The computation of flux in coordinates is also introduced, providing a more practical way to calculate it when a geometric interpretation is not available. Examples are provided, including the flux of a vector field across a circle and how to handle a vector field that is tangent to the curve.
A lesson about flux and more on Green's Theorem.
Denis Auroux. 18.02 Multivariable Calculus, Fall 2007. (Massachusetts Institute of Technology: MIT OpenCourseWare). http://ocw.mit.edu (Accessed March 21, 2009). License: Creative Commons Attribution-Noncommercial-Share Alike.
- Flux Across a Circle Applet - Java applet about finding the flux across a circle
- Problem Set - A problem set with some problems from this lecture.
- Lecture Notes - Lecture Notes from this lesson.
- Transcript of Lesson - Written transcript from this lesson.
- What is div F?
- What is the flux of a vector field for a curve?
- What is the definition of flux?
- What is Green's Theorem for flux?
- What is the divergence of a field?
- What is the tangential form of Green's Theorem?
- What is the geometrical interpretation of divergence?
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Staff Review
Flux, another type of line integral in the plane, is discussed in this lecture. Flux is described as measuring how much fluid passes through a curve C per unit time in a velocity field. Greenâs Theorem also has something to say about flux, and this is explained in this lecture as well. Divergence, what it means, what it measures, and its geometrical interpretation are also explained.
