##### 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.