- This session will be conducted only on
Zoom, due to the shuttering of our building because of water
problems.
Reminder: hit record on that Zoom session! (Although this is the last time I plan to do a Zoom, barring further challenges caused by Covid.)
Here's a menu of our past zooms...
- I'm assigning another IMath exercise for you to undertake. Those will come about once a week, and you'll typically have a week to do them. How is that going?
Any questions about the worksheets you've been working on? Anything you'd like to bring to our attention?
- Your homework last time was to carry out the following two
exercises: Section 1.1, #8; Section 1.2, #7 (sorry, I haven't
graded these yet -- and some of them are prisoners in my
office, which I may not be able to get back into until
Monday!:).
We'll start with a short discussion of those.
- Section 1.1, #8 (no freedom...)
- Section 1.2, #7 (freedom!)
- For today, as a preview, you were to "Explore" two of the
"GeoGebra" examples mentioned in this section:
Let's take a look at those. - I had asked you to come prepared to use Desmos in class today (or
something similar, so that you can do some graphing); a
laptop or tablet.
Presumably you're on such a device now!:) So let's get into it.
- We're going to be using a worksheet today created by Dr. McGee in
our department. He's fond of Desmos! He's also fond of Word
(which I'm not); so I'm going to put a link here to two
versions of our Section 1.3 Activity: Derivatives at a point:
one version in Word, the other a pdf:
One note on vocabulary: Dr. McGee talks about "forward
difference"; that means that you take $h$ as positive (you look
for a point to the right); we could just as well ask for
"backward differences", meaning take $h$ negative (a point to
the left).
I want you to carry out this exercise, and whenever you're asked for a screenshot, capture that and then add it to an entry in a discussion on Canvas that I created.
So you'll be able to see other students' work.
We'll see how that goes! It may be a model for other worksheets, going forward
- One thing that we're doing in this exercise is confirming that all of our methods -- graphical, numerical, algebraic -- are giving consistent answers. (If they're not, we've got to figure out what's going on!)
- Another thing that's a focal point of this exercise is "place where the derivative is 0". You'll notice that these tend to be "extrema" -- maxes or mins, for smooth functions -- and we're awfully fond of finding these extremes (maximizing profits, for example, or minimizing costs).
- My freshman physics professor at Miami University, Prof. Don C. Kelly wrote The Little Book of Calculus. Self-Help Guide to Calculus. I found this on his website, and it's a neat "little" (50 some pages) resource produced by him and his kids/grandkids. Check out page 12, limits....