Summary

The tools of calculus allowed mathematicians and scientists to deal with constantly changing values, and those tools changed the way science is done. All of a sudden, we could use infinitely small steps to approximate the slope of a curve at a point, or infinitely small rectangles to approximate the area under a curve. These tools were developed hundreds of years before our modern world of computers and free programming software, but there's no reason to limit ourselves to the tools available to Newton, Leibniz, and the Bernoullis.

In this chapter, we learned to take derivatives of functions by simply dividing the rise of the function from one point to another by the infinitesimal run between those points. We simply told Python to divide 1 by a million to give us that small number. Without a computer, plugging those decimals into a function would be a daunting task, but Python plugs a decimal into a function as easily as a whole number.

We used the derivative idea...