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=".
Click the "Graph" button (this button also refreshes the graph).
Move the blue rectangle in the left graph.
This can be done in any of 3 ways:
To erase the graph and all input fields, click the "Clear" button.
f (u,v)=ucosh(v) =u(ev+e-v)/2
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.