Green's Theorem for Simply Connected Regions
In this video, I discuss Green's Theorem that equates line integrals to double integrals. I discuss how the use of Green's Theorem can simplify integration both for the finding of line integrals and also for finding areas. I finish with the flux formulation of Green's Theorem.
00:00 - Introduction to Green's Theorem
01:26 - Discussion of the concept of Green's
06:40 - Statement of Green's Theorem
08:14 - Green's Theorem on Conservative Fields
10:48 - Ex1: Line Integral to Area
13:16 - Ex2: Line Integral to Area- Circle
16:47 - Ex3: Line Integral to Area- Triangle
19:22 - Ex4: Area to Line Integral
25:53 - Area using line integrals equati
26:06 - Flux Form of Green's
28:38 - Flux Form Example 1- Circle
30:11 - Flux Form Example 2- Rectangle
32:38 - Summary of section