Multivariable calculus, class #31: Green's Theorem

Mathematician spotlight: Pamela Harris

We briefly discuss the blocking problem for integer points from the origin. We do an example of a vector line integral with new notation. We do an example of a vector line integral on a triangle, which takes a lot of work. We give Green's Theorem, along with an explanation of why it works. We then apply the Theorem to our second example, and see that it is much easier to compute this way. We discuss how Green's Theorem, and the other two big theorems of the semester (Stokes' Theorem and Divergence Theorem) are generalizations of the Fundamental Theorem of Calculus. We do an example of a clockwise vector line integral, computing it with Green's Theorem.