WTW258: LU 3.5: ROTATION AND DIVERGENCE Lecture notes

3. 5. Rotation and
divergence
Of = < f)I , fy ,
fz >


F- =
< P, Q ,
R >


Then

g. f-
= < Han , May 2/22-7 ,
°
L P
,
Q , R>
✓
Rt → div É
put
Qyi
=


Dot
Product of E
Divergence
- - - -
-
-
- - -
- - -
-
-
-




g.✗ F- i
j K curl F-
=
=



W
Max May %ᵗ
cross
Rotation of F-
B Q R
product


for E in < P, Q > a vector field in /R2 :



F- familiar !
Qy
)
div =
Pay seems
curl E ( pygpi
=
q ,, _




◦
vector field E conservative → it and ONLY if
Curt E 0

Qx=Pih)
=


↓
can apply
Fundamental
Theorem