Lecture 22: Green's theorem
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Lesson Description:
Learn about Green's Theorem and how it is used.
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.
Additional Resources:
- Transcript of Lesson - Written transcript from this lesson.
- Lecture Notes - Lecture Notes from this lesson.
- Problem Set - A problem set with some problems from this lecture.
Questions answered by this video:
- What is Green's Theorem?
- What is a way to avoid calculating line integrals?
- How do you compute the line integral along a closed curve of M dx + N dy?
- What is the line integral of ye^-x dx + 1/2x^2 - e^-x dy?
- What happens to Green's Theorem if curl F equals 0?
- How do you prove Green's Theorem?
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Staff Review
This video explains Greenâs Theorem and how it helps make line integral computations easier. This method is a very interesting and helpful way of making calculations. Of course, this only works if you have a closed curve. Some good examples are shown of how Greenâs Theorem actually works in practice. The geometry of these theorems is examined in much of this lecture to help understand what is really going on. This video also serves to justify and prove parts of Greenâs Theorem.
