1. Gauss Divergence theorem

2. Gauss Divergence Theorem
Example Problem
Problem from:

3. Stokes Theorem

4. Finer points Awesome T-shirt!
Stokes requires that we walk around circuit (‘loop’) C in CCW dirction
Stokes applies to any open surface (“membrane”) S that is bounded by C
Awesome T-shirt!

5. Stokes Theorem
Either walk around the square loop and do the line integral (easy) or work hard to compute flux through a curved parabolic surface whose normal changes with x and y (harder)
Image credit: Maria Belk, Bard College

6. Line Integrals
By Lucas V. Barbosa - Own work, Public Domain,

7. Gradient Theorem