Summary

In the previous chapter, we learned the power of derivatives and integrals, so in this chapter, we built on those tools to solve some pretty difficult problems, such as the length of a spiral and the area of a 3D surface. We even extended derivatives and integrals to three dimensions by introducing partial derivatives. In a calculus class, we would be using lots of algebra in order to use these tools, but by using Python, we modeled the situation and tested our functions. We created variables that will contain our changing values and looped through the calculations millions of times, if necessary. To the mathematicians of previous centuries, this would have seemed like some kind of magic lamp.

In the next chapter, we'll deal with more changing rates and amounts and avoid a lot of algebra by using Python. We'll find out how much salt is in an ever-changing mixture, when and where a predator will catch its prey, and how long we'll have to invest our money to...