Math 392 Lecture 7 - Green's Theorem - Section 13.4 in Essential Calculus, 1st Edition.

Welcome to lecture 7 of Vector Calculus and Linear Algebra!

In this lecture, I start out by answering some random conceptual questions from the class, and then move on to section 13.4 in Stewart's Essential Calculus, ed 1. -- Green's Theorem! One of the four major theorems of the semester (The fundamental theorem for line integrals, Green's theorem, Stokes' theorem, Divergence theorem). Before stating Green's theorem, we refresh our mind about the orientation of closed curves (Green's theorem is orientation dependent). We then state the theorem and jump into examples. We also recall the handy formula that allows us to compute a constant double integral in terms of area. We also show how Green's theorem can be used to prove that the line integral over a conservative vector field is 0 for closed curves, and how we can use Green's theorem to compute the area of regions (which will not be our focus at any point :p just something to know).

[ranashahrose]

Thank ypu for the videos, however, i didnt understand how u got limits at 33:00 and 35:35.. i always mess up in putting limits. I'll b glad if u can explain!!!

[sams]

At 12:50, What if 'C' is a single smooth closed curve as opposed to multiple piecewise curves; Can Green's theorem still be applied?

[brianzar]

Thank you for posting these videos, they're really helpful. However, I have a question: in 26:58 the long way was -2(r) dr dθ, shouldn't be just -2 dr dθ? Thank you!