Vector Fields: Homework 16.1, #5, 20, 26, 36
MAT329, Fall, 2015
Andy Long

#5, p. 1085

Clear[f,v,s,fx,fy,x,y]

v=VectorDensityPlot[{y/Sqrt[x^2+y^2],x/Sqrt[x^2+y^2]},{x,-3,3},{y,-3,3}];
s=StreamPlot[{y/Sqrt[x^2+y^2],x/Sqrt[x^2+y^2]},{x,-3,3},{y,-3,3}];
{v,s}
Show[v,s]

#20, p. 1086

r[x_,y_]:=Sqrt[x^2+y^2]
v=VectorDensityPlot[{(r[x,y]-2)r[x,y]x,(r[x,y]-2)r[x,y]y},{x,-3,3},{y,-3,3}];
s=StreamPlot[{(r[x,y]-2)r[x,y]x,(r[x,y]-2)r[x,y]y},{x,-3,3},{y,-3,3}];
{v,s}
Show[v,s]

#26, p. 1086

f[x_,y_]:=Sqrt[x^2+y^2]
fx[x_,y_]=D[f[x,y],x]
fy[x_,y_]=D[f[x,y],y]
v=VectorDensityPlot[{fx[x,y],fy[x,y]},{x,-3,3},{y,-3,3}];
s=StreamPlot[{fx[x,y],fy[x,y]},{x,-3,3},{y,-3,3}];
{v,s}
Show[v,s]

#36, p. 1086

v=VectorDensityPlot[{1,x},{x,-3,3},{y,-3,3}];
s=StreamPlot[{1,x},{x,-3,3},{y,-3,3}];
{v,s}
Show[v,s]