• 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)=f_u g_v - f_v g_u into the text input field marked "J(u,v)= f_ug_v-f_vg_u="
  (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)
  • Use the mouse to click and drag the red spot at the lower left corner of the blue rectangle in the left graph
  • Use the mouse to single-click anywhere in the left graph, moving 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

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.