ยง16.2 Vector Fields and Line Integrals
Lecture notesMath3d is good for experimenting with vector fields (click on "Add Object" then "Vector Field")
Vector fields
Line integrals; Work and Circulation
Flux
Examples
- Find the work done by \[ \F = -y\i + x\j - z\k \] along
- the straight line segments connecting $(0,0,0)\to(1,1,0)\to(1,1,1);$
- the curve $\r(t)=(t,t^2,t^3),\quad 0\le t\le 1.$
- Find the circulation of
- $\F = -y\i + x\j + \k$
- $\F = x\i + y\j + z\k$
-
Find the flux of \[ \F = (x-y)\i + (x+y)\j \] across the circle $x^2+y^2=1.$