Introduction

In the previous chapter, we learned how to calculate derivatives and integrals. Now, we're going to use those tools to find the lengths of curves and spirals and extend this reasoning to three dimensions to find the area of a complicated surface. We'll also look at a common tool that's used in calculus, the infinite series, which is used to calculate important constants and approximate complicated functions. Finally, we'll look at an important idea in machine learning: finding the minimum point on a curve. When you use a neural network, you create a kind of "error function" and work hard to find the point on the surface that gives the minimum error. We'll create our own kind of gradient descent function to keep traveling downward until we're at the bottom of the surface.