MA 242.003 • Day 55 – April 5, 2013 • Section 13.3: The fundamental theorem for line integrals – An interesting example • Section 13.5: Curl of a vector field
Dec 31, 2015
MA 242.003
• Day 55 – April 5, 2013• Section 13.3: The fundamental theorem for line
integrals– An interesting example
• Section 13.5: Curl of a vector field
D simply-connected means that each closed curve in D contains only points in D.
Simply connected regions “contain no holes”.
D simply-connected means that each closed curve in D contains only points in D.
Simply connected regions “contain no holes”.
All of these velocity vector fields are ROTATING.
What we find is the following:
Example: F = <x,y,z> is diverging but not rotating
curl F = 0
All of these velocity vector fields are ROTATING.
What we find is the following:
Example: F = <x,y,z> is diverging but not rotating
curl F = 0
F is irrotational at P.
All of these velocity vector fields are ROTATING.
What we find is the following:
Example: F = <-y,x,0> has non-zero curl everywhere!
curl F = <0,0,2>
Differential Identity involving curl
Recall from the section on partial derivatives:
We will need this result in computing the “curl of the gradient of f”