##### How to Use
Enter a change of variables from (u,v) coordinates to (x,y) coordinates (in the form x=f (u,v) and y=g(u,v)) into the text input fields marked "x=f(u,v)=" and "y=g(u,v)=".

Example: x=f (u,v)=u-v, y=g(u,v)=u+v

Enter the Jacobian J(u,v)=fu gv - fv gu into the text input field marked "J(u,v)=fugv-fvgu=".

Example: J(u,v)=2

Click the "Graph" button (this button also refreshes the graph).

Move the blue rectangle in the left graph.

Example: (u,v)=(2,3)

This can be done in any of 3 ways:

• Enter the values directly into the text fields marked "u=" and "v=" and click the "Point" button to redraw the blue rectangle in the new left graph position (without recomputing the transformation).
• Click and drag the red spot at the lower left corner of the blue rectangle in the left graph.
• Single-click anywhere in the left graph, which moves the blue rectangle to the grid rectangle in which the mouse was clicked.
(The mouse has no effect in the right graph.)

To erase the graph and all input fields, click the "Clear" button.

##### Examples
Rectilinear:
x=f (u,v)=u-v
y=g(u,v)=u+v

Polar:
f (u,v)=ucos(v)
g(u,v)=usin(v)

Hyperbolic:
f (u,v)=ucosh(v) =u(ev+e-v)/2
g(u,v)=usinh(v) =u(ev-e-v)/2

##### Other Notes
The area of the blue rectangle in the left graph is shown in the field marked "Left Area=".

With the point (u,v), shown in the left graph by the position of the red point, the value of the Jacobian J(u,v) provides a way to approximate the area of the blue region in the right graph, as the product of the left area and J(u,v), shown in the field marked "Area*J(u,v)=". The approximation is more accurate for smaller values of the area in the left graph.