Overarching Goals

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

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!



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!)