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{ VECTOR_FUNCTIONS.PDE  

 

 This example illustrates the vector functions

 

 VECTOR

 MAGNITUDE

 DOT

 CROSS

 NORMAL

 TANGENTIAL

 

}  

 

title  

"vector functions"  

 

select  

 elevationgrid=500  

 

{no variables}  

 

definitions  

 

 u= exp(-x^2+ y)               { A scalar potential, perhaps }  

 f= grad(u)                   { F = grad(u)  is a vector }  

 df= div(f)                   { Divergence of F is a scalar}  

 cf= curl(f)                   { Curl of F is a new vector }  

 vx= -sin(y)   vy= 2*sin(x)   { vector components }  

 v= vector(vx,vy)             { Another vector }  

 mv= magnitude(v)             { Magnitude of v }  

 cv= curl(v)  

 ccv= curl(curl(v))  

 tvv = v*v { v*v is a tensor }

 divtx = 2*vx*dx(vx)+vx*dy(vy)+vy*dy(vx)   {x-component of div(t) }

 divty = vx*dx(vy)+vy*dx(vx)+2*vy*dy(vy)   {y-component of div(t) }

 divt = vector(divtx,divty)

 

{no equations}  

 

{plot domain -- required}  

boundaries  

region 1  

  start "Outer" (-1,0)  

  line to (1,0) to (1,1) to (-1,1) to close  

 

feature  

  start "inner" (-1/2,1/2) line to (1/2,1/2)  

 

plots  

vector(f) as "f = grad(-x^2+y)"  

elevation(normal(f)) on "Outer"  

elevation(tangential(f)) on "inner"  

contour(df)   as "Div F"  

vector(v) as "V = (-sin(y), 2*sin(x))"

contour(mv)   as "Magnitude V"  

contour(dot(v,vector(x,0)))  

contour(zcomp(cross(f,v)))  

contour(zcomp(cv))   as "Zcomp(Curl V)"  

vector(ccv)   as "Curl Curl V"  

vector(div(v*v)) as "Div(V*V) inline"

vector(divt) as "Div(V*V) expanded"

vector(div(tvv)) as "Div(V*V) tensor parameter"  

end