Lecture 22: Green's theorem

Lecture 22: Green's theorem
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Taught by OCW
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.
Learn about Green's Theorem and how it is used.
  • 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?
This video explains Green’s 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 Green’s 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 Green’s Theorem.
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Reviewed by MathVids Staff on March 22, 2009.
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