How to Use
Enter the functions
f (x,y) and
g (x,y) in the text input fields marked
"f(x,y)=" and
"g(x,y)=".
Example:
f (x,y)=-y,
g (x,y)=x
Compute and enter the divergence and
curl into the corresponding text input fields:
field marked "div F=" for divergence,
field marked "curl F=" for curl.
Example: for
F (x,y)=<-y,x>,
div F=0 and curl F=2
Click the "Graph" button
(this button also refreshes the graph).
Choose the initial point
(x,y).
Example:
(x,y)=(1,0)
This can be done either of two ways:
- Enter the values directly into the text fields marked
"x=" and
"y="
and click the
"Graph" button to refresh.
The text input fields can accept any decimal number input.
- Click and drag the
red point on the graph using the mouse.
To erase the graph and all input fields, click the
"Clear" button.
Examples
Positive divergence:
F (x,y)=<x,y>
Positive curl:
F (x,y)=<-y,x>
Other Notes
The starting square and the resulting quadrilateral (both drawn in
blue) give the basis for the geometric
interpretations of divergence and curl:
- If divergence is positive, then the verteces move apart,
resulting in a quadrilateral with area larger than the original square;
if divergence is negative, the verteces move together.
- If curl is positive, then the verteces rotate counterclockwise;
if curl is negative, the rotation is clockwise.
The flow curve segments are graphed by determining
numerical approximations using the classical (order four)
Runge-Kutta Method.