25. Green's Theorem - Contents

1. The Theorem

     1   2
   1. Statement
   2. The Theorem for Regions with Holes

2. Verification

     1
   1. Verification

3. Proof

     1
   1. Proof
      1. Rectangles
      2. Regions of Type \(y\)

4. Alternate Notations

     1   2
   1. 2D Stokes' Theorem
   2. 2D Gauss' Theorem

5. Applications

     1   2   3
   1. Converting Line Integrals to Region Integrals
   2. Converting Region Integrals to Line Integrals
   3. Total Rotation and Circulation

6. Exercises

     1
   1. Exercises