Tuesday, August 31st

We began class with a reading entitled Why Do We Study Calculus? This led us to a brief discussion of the historical context for calculus and the derivative.

We defined the derivative as a rate of change. In particular, the derivative of a function at a point can be thought of as the slope of its tangent line at that point. Defining a tangent line was a little tricky, but we looked at one in Geogebra for the function

at the point (4, 3). We saw that as we zoomed in on the point (4, 3), we observed that the function was locally linear, and the tangent line and function were virtually indistinguishable. Thus, we defined a tangent line for a function to be the line that the function approaches as we zoom in closer and closer.

We then tried to find a tangent to the function

at the point (2, 5) using only our graphing calculators. While we found several lines that appeared to be tangent, the only line that was truly tangent was

We obtained this line by first finding the slope of the tangent by zooming in on the point (2, 5) and then tracing step to obtain a point very close to (2, 5). We used the slope formula of rise over run to calculate (5 – Y)/(2 – X) which was approximately –4. We used the point-slope formula

with the point (2, 5) and the slope m = –4 to obtain the equation of the tangent.

We then stepped back and admired our work on the first day of calculus class: the derivative, tangent lines, local linearity. Impressive. For a different take on the tangent line, take a look at this website.

We talked a little about the structure of class. After each Red day class, the obligation is to attempt each problem in the assignment. The scribe will post the notes from class (scribe does not need to attempt each problem). At the start of the White day lab class, we will first revise the scribe's notes, and then we will go over the day's questions. Lab days will be the opportunity to finalize assignments which are submitted every two weeks.

Some changes from last year:

• homework should be less
• if you prefer not to count homework in your grade at the end of the quarter, you don't need to (the Tom Clause)
• Mr. O'Brien has a Google Voice number to which you can text or call questions

Period 2 finished with this video of President Kennedy announcing that the U.S. would fly to the moon- think of this as we progress through the year!

Assignment #1:

• p. 29/9, 10 and commit to memory the trig functions at the numbers 0, π/6, π/4, π/3, π/2, and their multiples (this unit circle may help and here are all 198 values in a quizlet)
• Please complete this student information sheet (if I taught you last year, you only need to complete the first part).
• Read the course methodology (it is very similar to last year's; a copy is available on the website home page)
• Read the family letter and then give it to your parent/guardian (a copy is available on the website home page).
• Have your parent/guardian sign the Student Release Form and return it next class.
• Cover your text book.
• Explore the class website- it would be a good idea to bookmark it.

Welcome!

Welcome to AP Calculus- this is going to be a wonderful year! If I didn't have you in class last year, please first read this opening post in our Honors Pre-AP Calculus blog last year.

This year, our blog will form the textbook for our class (especially since our real textbook is quite old!). It will feature links to current calculus websites and dynamic calculus explorations- all from you. For an explanation of how blogging will work this year, please take a look at the blogging rubric here.

I will write the first scribe post today. Please post a comment below to let me know that you've logged into Blogger successfully.

Here's to a great year!