Riemann Sums for Functions of Two Variables

This Demonstration is meant for students of multivariable calculus. It illustrates the concept of a Riemann sum for a real–valued function of two real variables. Choose one of four functions. Then you can freely select a uniform partition of either the x or y axis into 5, 10, 20, or 40 parts. You may also select the point on each subrectangle at which the function is evaluated (to determine the height of the rectangular solid to be constructed over that subrectangle). Initially, the function is evaluated at the center. This feature is included to show that as the partition becomes finer, the choice of this point becomes less consequential, suggesting that in the limit it simply does not matter.