![differential geometry - Motivation for constructing $F$ s.t. $\ker(\text{curl}) \subset \text{Im}(\text{grad})$, $\ker(\text{div}) \subset \text{Im}(\text{curl})$ - Mathematics Stack Exchange differential geometry - Motivation for constructing $F$ s.t. $\ker(\text{curl}) \subset \text{Im}(\text{grad})$, $\ker(\text{div}) \subset \text{Im}(\text{curl})$ - Mathematics Stack Exchange](https://i.stack.imgur.com/8Js6T.png)
differential geometry - Motivation for constructing $F$ s.t. $\ker(\text{curl}) \subset \text{Im}(\text{grad})$, $\ker(\text{div}) \subset \text{Im}(\text{curl})$ - Mathematics Stack Exchange
![9.7 Divergence and Curl Vector Fields: F(x,y)= P(x,y) i + Q(x,y) j F(x,y,z) = P(x,y,z) i + Q(x,y,z) j + R(x,y,z) k Example 1 : Graph the 2-dim vector field. - ppt 9.7 Divergence and Curl Vector Fields: F(x,y)= P(x,y) i + Q(x,y) j F(x,y,z) = P(x,y,z) i + Q(x,y,z) j + R(x,y,z) k Example 1 : Graph the 2-dim vector field. - ppt](https://images.slideplayer.com/16/5192535/slides/slide_3.jpg)
9.7 Divergence and Curl Vector Fields: F(x,y)= P(x,y) i + Q(x,y) j F(x,y,z) = P(x,y,z) i + Q(x,y,z) j + R(x,y,z) k Example 1 : Graph the 2-dim vector field. - ppt
![SOLVED:Plot the vector field and guess where div F > 0 and where div F < 0 . Then calculate div F to check your guess. F = ⟨x^2, y^2 ⟩ SOLVED:Plot the vector field and guess where div F > 0 and where div F < 0 . Then calculate div F to check your guess. F = ⟨x^2, y^2 ⟩](https://cdn.numerade.com/previews/8e53296b-7b9b-4ecf-ac68-b2b1f8d6da65_large.jpg)
SOLVED:Plot the vector field and guess where div F > 0 and where div F < 0 . Then calculate div F to check your guess. F = ⟨x^2, y^2 ⟩
![SOLVED: 4-19. If F is vector field on R%, define the forms wp = Fl dr + F2 dy + F8 d2, w = Fl dy ^ d2 + F? d2 ^ SOLVED: 4-19. If F is vector field on R%, define the forms wp = Fl dr + F2 dy + F8 d2, w = Fl dy ^ d2 + F? d2 ^](https://cdn.numerade.com/ask_images/9e27355931994eedaf1fd1c90d1b3bf4.jpg)
SOLVED: 4-19. If F is vector field on R%, define the forms wp = Fl dr + F2 dy + F8 d2, w = Fl dy ^ d2 + F? d2 ^
e) div( div F), (f) curl( curl F), (g) div(curl(grad f) ) . the part of the plane2x + 3y+ z =6 that lies in the first octant.
![Calculus 3: Divergence and Curl (31 of 50) Identity 7: CURL[CURL(F)]=Grad[ DIV(f)] – (Grad)^2(F) - YouTube Calculus 3: Divergence and Curl (31 of 50) Identity 7: CURL[CURL(F)]=Grad[ DIV(f)] – (Grad)^2(F) - YouTube](https://i.ytimg.com/vi/w1LxPgSRz94/hqdefault.jpg)