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There is some vital stuff in this unit.  Section 4.3, on graphing functions, ties together every single topic we have looked at so far, other than word problems.  A good graphing question involves arithmetic, limits, first and second derivatives, and combinations of these, together with the actual graphing.  Section 4.4 deals with optimization and gives us the word problems that are not there in the previous section. 

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.

This is a highly focused unit - nothing but the Chain Rule and some of its applications.  We delve much more deeply into applications of our material to other courses in the examples (with even more examples to come in the following units).  If you are comfortable with the Chain Rule, but apply it without using the Leibniz notation, make sure to watch the videos.  There are a number of applications where the d/dx notation becomes necessary.

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.

We introduce the derivative as the limit of the slope of secant lines. This will be one of the most important practical and theoretical tools available to you as an engineer.

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.

We now begin calculus itself. In this unit, we look at limits and try to figure out what they are and how to calculate them.

• Definitions of functions and related terms
• Inverse functions and logarithms
• Trigonometry (with inverse trig)