Overarching Goals

As a result of your efforts in this course, you should strengthen your skills in:

**Critical and Creative Thinking****Problem Solving****Communication****Questioning, Problem Posing, and Conjecturing****Working Collaboratively**

The course is unlike most courses offered in high
school math. You will be asked to work in some new ways, do more reading of
text (i.e., words),
and
do more
writing.
While
technical
skills remain important, there is **more emphasis on interpretation and
understanding**.
Homework problems are less likely to closely resemble problems worked out in
the text or in class, and the questions being asked may require interpreting
and refining.

Central Theme

The
central theme to this course concerns a most miraculous relationship: the
relationship between the *instantaneous rate of change in a function* and
the *accumulation of a function*. You will not neccesarily know
now what the two expressions in italics mean - learning them is an essential
part of this course! (A very rough example of what the expressions mean
is the following: Water flows over a dam at a *rate* that is continually
varying and *accumulates* in a basin. If the rate were constant,
we could answer questions like, "How much water accumulates in the basin
over a
period of 3 hours?" But if the rate varies, the question becomes one that
calculus is designed to answer; moreover, the very idea of varying rate
is one that differential calculus describes. Much of the power of calculus
lies in the fact that it answers not just one question, like the water
accumulation problem, one context at a time, but it answers many questions
set in many different contexts. To do so, calculus must have very general
methods - this is the beauty and the difficulty of calculus. I hope you
find it beautiful - and not so terribly difficult!

Chapters/Topics

Chapter
1: Functions and Limits (**The limit concept is what, in a way, distinguishes
calculus from algebra. We'll take an intuitive look here.**)

Chapter 2: Derivatives (**This is the first
of the biggies: Instantaneous Rate of Change!**)

Chapter 3: Inverse Functions (**with
special attention to logarithm functions, which are the inverses of exponential
functions**)

Chapter 4: Applications of Differentiation (**A
whole chapter on applications - We
will have already seen applications and now do a couple in detail.**)

Chapter 5: Integrals (**Now for the second
of the biggies: The Definite Integral!**)