Chapter 3. Differential Laws
The differential is the central idea in Calculus. This text is devoted to exploring interpretations and consequences of differential laws. We'll see in due time that the differential allows us to make sense of many geometric ideas including slope, bend, warp, gradient, length, and area. Before we get to all of that, however, it's helpful to get some practice calculating.
As you work through this chapter, you'll be seeing many laws and many examples of calculations. Don't skip the examples! It's your job to become familiar with these differential laws, and this takes some time and energy. You should be able to justify each step in a calculation with one or more laws. That said, we'll be covering too many laws for you to try to memorize every last one. I would recommend making a hand-written list of the differential laws as you encounter them. This will help you learn the easy laws, and will serve as a reference for the laws that are too unpleasant to commit to memory.