Curl and Rotation

Math 3335

Helmut  Knaust - Department of Mathematical Sciences, University of Texas at El Paso, hknaust@utep.edu
10/27/16

1

f[x_,y_]={-y,x}
VectorPlot[f[x,y],{x,-1,1},{y,-1,1}]

Curl[f[x,y],{x,y}]

2

f[x_,y_]={y,-x}
VectorPlot[f[x,y],{x,-1,1},{y,-1,1}]

Curl[f[x,y],{x,y}]

3

f[x_,y_]={y,-x}/(x^2+y^2)
VectorPlot[f[x,y],{x,-1,1},{y,-1,1}];

Curl[f[x,y],{x,y}]

Simplify[%,Assumptions->Not[{x,y}=={0,0}]]