Math for Programmers

8 Understanding rates of change

This chapter covers

• Calculating the average rate of change in a mathematical function
• Approximating the instantaneous rate of change at a point
• Picturing how the rate of change is itself changing
• Reconstructing a function from its rate of change

In this chapter, I introduce you to two of the most important concepts from calculus: the derivative and the integral. Both of these are operations that work with functions. The derivative takes a function and gives you another function measuring its rate of change. The integral does the opposite; it takes a function representing a rate of change and gives you back a function measuring the original, cumulative value.

I focus on a simple example from my own work in data ...