Calculus for Engineers I

We conclude our study of limits - at least for now.  With this unit's material, we expand the uses for limits and our understanding of how they work.

This unit is pretty short in terms of videos to watch, but there is a lot of work to do.  Section 3.4 introduces trigonometric derivatives and the limits required to do them.  Section 3.5 begins the application of calculus to physical problems.  We include example videos showing how CIV 100 questions can be combined with derivatives to create interesting results.  Do make sure to get plenty of practice with the exercises in 3.5.

There is quite a bit of material in this unit, starting with a couple of new applications of the Chain Rule and then beginning to study what derivatives actually tell us about functions. This latter part, the beginning of Chapter 4, will allow us to graph functions, optimize them (that is, find maximum and minimum points), and even set up the concept of integration.

A lot of videos in this unit, but three of the four sections have very little in terms of testable material. Only L'Hopital's Rule requires a lot of practice. We are, however, setting the groundwork for some important mathematics. In these sections, we are introducing the idea of numerical methods, setting the stage for integration, and taking the first step toward Taylor series.

With this unit, we learn about the Fundamental Theorem of Calculus. The great result of the field, it lets us see that integrals and derivatives are (as far as possible) inverse operations. This is a grand result and deserves our careful attention. We also cover the method of substitution, which is the most-used of the ways in which we do integrals (other than, for some people, Wolfram Alpha).