How to Use
Enter the functions
f (x,y) and
g (x,y) in the text input fields marked
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.
div F=0 and curl F=2
Click the "Graph" button
(this button also refreshes the graph).
Choose the initial point
This can be done either of two ways:
To erase the graph and all input fields, click the
- Enter the values directly into the text fields marked
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.
The starting square and the resulting quadrilateral (both drawn in
blue) give the basis for the geometric
interpretations of divergence and curl:
The flow curve segments are graphed by determining
numerical approximations using the classical (order four)
- 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.