Week #4

Where should you be? At the beginning of course, we're back again looking at secant and tangent lines. This week we will look more closely at the process to figure out the 'derivatives', that is we are going to take the slope of the secant line as a difference quotient and then move the points together to find a new function that we call the derivative, because it is derived from the original function. Essentially the two points on a function f(x) will be:
(x, f(x)) and (x + h, f(x + h)), then the difference quotient or slope of a line containing those points, finally a limit as h -> zero. Sounds easy, but there's much more detail to come.

Oh, also, almost everyone got a perfect score on quiz #2. The actual quiz and solutions are posted. I'll give back your papers on Monday.

But a warning too. IT IS UNACCEPTABLE TO LOOK AT YOUR NEIGHBOR WHILE TAKING THE QUIZ! I saw many people looking at their neighbor's property. That is a BIG NO-NO! For some, that's a warning shot over your bow, next time I see it I will send in a direct hit, and yes, your boat will sink. I don't take prisoners and will not throw out a floatation device.

Week #3

You should be finished with the limit law problems in Stewart's textbook, and we'll move forward from here, but you better have limits under control before moving on.

I realize that I put up the assignment during the quiz, and many may have missed it, so here it is: Section 2.3 , Problems: 11 - 29 odd, 33, 37 - 47 odd, optional 51, optional 59.

As for quiz number 1, it was a near disaster (score = 1) for some, easy as pie (score = 10) for others. Most depressing, is that many of you cannot evaluate a function (second problem) using a calculator! The function problem (first problem) may have appeared to be new, but it was pretty easy algebra. Solutions to this quiz are posted on this blog --- just look at the section under "Course Files", it's to your right. You should be prepared to stretch your brains on occasion. Please post comments, especially if you have something constructive to say, or you just want to share your frustrations/elations.

Okay, so this week we'll probably do the precise definition of the limit, continuity, and then finish off chapter 2, including finishing the Squeeze Theorem. Then it's onto the meat of calculus, THE DERIVATIVE AND ITS APPLICATIONS.

Week #2

We'll start where we left off, at the tangent. Last week we took a careful look at the unit circle (centered at the origin) and several lines tangent to key points on this circle. A sequence of secant-slopes were then computed, and their computed values formed a predictable sequence. I hope you all agree that this sequence of secant-slopes moved towards our 'predicted' slope of the tangent.

This week we will look at the concept of limits, and we'll start with a predictable sequence that moves towards a fixed number. For example if we want to move towards one, from values smaller than one, a predictable sequence could be:

0.9, 0.99, 0.999, 0.9999, . . . , 0.9999999999, . . .

Or move towards one, from values bigger than one, a predictable sequence would be:

1.1, 1.01, 1.001, 1.001, . . . , 1.00000000001, . . .

You'll need a way to compute quickly, so please bring your calculators!

Week #1

We'll spend some time on review, but it should be very familiar. Again-and-again, I need to remind everyone that they should know pre-calculus. Also, you need to read the book, do the homework, and constantly review. This is not a hard course, but it can be if you decide to slack-off.

We're almost there . . .

I hope you're all ready for a new year at ECC. Welcome aboard.