Calculus for Reservoir Overflow Prediction

The Net Change Theorem links a function’s rate of change to its total accumulated change over an interval. In calculus, this means the definite integral of a derivative on [a,b] gives the net change in the original function. The theorem is useful in physics, economics, and engineering because it turns a rate into a total amo...

The Net Change Theorem is an interpretation of the Fundamental Theorem of Calculus. It states that when a rate function is integrated over an interval, it gives the net change in the original quantity.

This applies to real systems like reservoir management. Here, the net rate of volume change includes inflow from a river and outflow throug...