Calculus I Early Content Assignments
We will start with the model of depth vs. time for water flowing from a hole
in a uniform cylinder,
as demonstrated on some of the GEN1 video clips. On the DVD, you will view the clips that are relevant to your
course.
- This model involves simultaneous linear equations and their solution and quadratic
functions, and the work we do here constitutes a pretty good review of these ideas.
The process of analyzing data and relating to what we actually see in the real world by
the mathematical modeling process allows us to see how calculus is used in many real-world
situations.
The flow-and-depth model will serve throughout the course as a paradigm for
understanding the main concepts of calculus.
The Randomized Problems all go into a problem bank from
which major quizzes and tests are constructed. These problems are therefore doubly worthy
of your attention.
There is no text
assignment for Week 1. However, you might want to begin your work on
Chapter 1.
- It is essential that you
fully understand chapter 1, which is a review of what you should have learned in Precalculus.
Few students, however, actually learn precalculus in a precalculus
class. If you don't understand the Chapter 1 material by the time we start applying the Calculus to it, you will probably find at that time that you
are lost with little hope of catching up. Unless you have a math IQ over 150 or so you
are just not likely to
be able to learn both the calculus and the prerequisite precalculus at the same time. Review the precalculus
now so you have it when you need it.
Our review of Chapter 1 will take us through the fifth week of the term.
During this time we will be developing, in the context of the flow model and other
models, the main ideas of the subject. This will allow us to move quickly through
Chapters 2-5.