MATH 191, Sections 1 and 3: Calculus I

Continuing a long-standing tradition, here's a bad joke to start things off: did you hear that the recent Asian number puzzle convention was called off because of an overflying of a large messy flock of seagulls? You could say that dung flew over the Sudokufest.

Assorted class resources:

Syllabus and course description:
- Section 1
- Section 3
Course schedule
Homework assignments
Turnabout is fair play: here is my completed information form, for all you nosy nellies out there.
Here are the lists of team members for the first few team quizzes and the first team project:
- Teams for Section 1, with role assignments!
- Teams for Section 3, with role assignments!
Tips of the Trade : hints from your peers on creating high-quality homework solutions!
How will I be grading your written projects? To find out, take a look at my rubric for such projects, Assessing the Quality of Math Writing: The Four Cs.
You want practice exams? Here they are!:
- Practice Exam 1, and... solutions.
- Practice Exam 2, and... solutions.
- Practice Exam 3, and... solutions.

Recent class notes and Mathematica files:

Monday, August 20th. Hello, hello! Welcome, one and all, to the brand new Fall 2007 semester! Today we will spend a bit of time working with some fun on-line software, and seeing exactly what the heck it has to do with calculus.
Wednesday, August 22nd. We will spend the first half of class today discussing what it is we will expect from one another during the coming semester. Come prepared to discuss matters of consideration and common courtesy as we work together to design a class environment we will all get the most from. After this discussion, we will spend some time discussing functions: what are they? You may wish to follow along, with these notes from Section 1.1 of your text. Also, here are sites dealing with the various examples of functions we began considering in class:
- Craters on the moon
- Distribution of nitrogen isotopes
- The boiling point of water
- Interest in a Jane Austen novel
Thursday, August 23rd. Today will be dedicated to functions and their properties, first in general terms and then more specific ones as we talk about the models you were supposed to have read about for the discussion today.
Friday, August 24th. Here are my notes from Section 1.2 of your text, which we will discuss today. We will also make use of the Mathematica notebook, LogisticPlot to help us visualize a particular model for population growth.
Monday, August 27th. We will spend most of today talking about creating new functions from old, the subject of Section 1.3 of your text.
Wednesday, August 29th. We wrap up our discussion of compositions and whatnot, and continue by paying a little attention to exponential functions, the topic of Section 1.5 of your text.
Thursday, August 30th. After finishing off exponential functions, we spend the rest of today discussing inverse functions in general, and logs and inverse trig functions in particular; all of this is contained in Section 1.6 of your text. We will be making use of the Mathematica notebook NewtonsLaw in class; feel free to bring this file up in the Math Lab and use it there to gain better intuition regarding exponential graphs.
Friday, August 31st. We continue with our conversation on inverse functions; see the previous entry for the notes. Zowie!
Monday, September 3rd. Labor Day! No class, silly billy!
Wednesday, September 5th. Back to school. Today, after finishing off Section 1.6, we begin our exploration of calculus itself; after a motivating exercise along these lines, we break, allowing you to let the notion of a limit sink in overnight.
Thursday, September 6th. Today we (finally!) address the idea of limit, the content of Section 2.2 of your text. Fun, fun, fun!
Friday, September 7th. Today, after a quick quiz and a capping off of Section 2.2, we move on to Section 2.3, where is contained a passel of limit laws. Come prepared to do a bit of algebra!
Monday, September 10th. After finishing off Section 2.3, we might begin to tackle the precise definition of a limit, the topic of Section 2.4 of your text. Are you ready to play Name That Delta?
Wednesday, September 12th. For sure we will cap off Section 2.3 today, and continue with Name That Delta!
Thursday, September 13th. Continuity is the name of the game today, the topic of Section 2.5 of your text.
Friday, September 14th. Today we wrap up our discussion of continuity, begun yesterday: see the previous link for class notes.
Monday, September 17th. To infinity, and beyond! This is where we head today, in talking about limits at infinity, the topic of Section 2.6 of your text.
Wednesday, September 19th. We move to a discussion of instantaneous rates of change: what are they? how do we find them? And what in the heck do they have to do with tangent lines?!? All this, and more, in Section 2.7 of your textbook!
Thursday, September 20th. Exam 1, covering Chapter 1 and Sections 2.2 through 2.6!
Friday, September 21st. We get going in earnest on Section 2.7, encompassing the definite of the derivative. Look two entries back for a link to the class notes! Also, here is a link to the Mathematica notebook, SecantsTangents60, illustrating the behavior of secant lines as they approach the tangent line to the graph of a function at a given point. Enjoy!
Monday, September 24th. More on tangents, secants, and rates of change! We continue with the note set from this past Wednesday and Friday, available above. By the way, in case you wanted another look at that donut-filled Mathematica notebook, here it is: GrowingTori.
Wednesday, September 26th. After a quiz, we tackle Section 2.8, in which we envision the derivative of a function as a function itself. It might not be a bad idea to take a look at the Mathematica notebook, DerivativeAsAFunction, allowing you to plot a function and its derivative alongside one another for quick and simple comparison!
Thursday, September 27th. Time to build some formulas: today we derive (no pun intended!) formulas for the derivatives of various simple functions like polynomials and exponential functions, read all about it in Section 3.1 of your text.
Friday, September 28th. The first course on the menu du jour is a team quiz, the last you will take with your current teams (how sad!). Then, a fun-filled romp through calculus with the Product and Quotient Rules, the subject of Section 3.2 of your textbook. Come along for the ride, I save you a seat! (You might want to take a look at the Mathematica notebook, DerivativesInMathematica, which shows you how this software deals with derivatives.)
Monday, October 1st. We continue with derivatives of products and quotients; see the notes from the previous entry. You might also have a hankering to look at the Mathematica notebook, GrowingTrees, the second in the Fun with Mathematica series.
Wednesday, October 3rd. We wrap up the Product and Quotient Rules with a few rounds of Derivative Jeopardy! And hey, check it out: yet another installment of Fun with Mathematica: PitchingPenniesForPi!
Thursday, October 4th. After the fifth quiz (on the Product and Quotient Rules), we spend a bit of time deriving the formulas for trigonometric derivatives, the content of Section 3.3 of your text.
Friday, October 5th. First, a team quiz with your new teams! Then, the Chain Rule, discussed in Section 3.4 of your text. This one is big, folks, you will not want to miss it! Moreover, I will be assigning the new teams, and handing out the first part of the new team project, Newton v. Leibniz. Be there!
Monday, October 8th. No class! Fall Break! Rejoice!
Wednesday, October 10th. Back in the swing of things! Are you ready to differentiate?!? We continue with the Chain Rule (see above for the class notes).
Thursday, October 11th. Howdy! We will spend today talking about implicit differentiation, the topic of Section 3.5 of your textbook. Come ready to be sneaky! (You may like a look at the Mathematica notebook Tschirnhaus, graphing one of the examples we consider in class.
Friday, October 12th. Today we tackle logarithms and related functions: how to differentiate them? Take a look at Section 3.6 of your text.
Monday, October 15th. We are jumping ahead a few sections today; we will return to applications of the derivative later in the week. To start with, though, I hoped to discuss related rates problems, the topic of Section 3.9 of your textbook.
Wednesday, October 17th. We will continue talking about related rates of change; the notes are in the previous entry.
Thursday, October 18th. After the team quiz, we will finish up our work with related rates and move on to talking about some applications of exponential and logarithmic functions, topics covered, in part, by Section 3.8 of your textbook.
Friday, October 19th. We will continue talking about exponential and logarithmic models. One of the models we discuss relates to the growth of the internet, the topic of the latest episode of Fun with Mathematica: MoreTrees.
Monday, October 22nd. We spend a little bit of time talking about one last application of derivatives, linear density (this is described in Section 3.7 of your text), before getting a preview of Chapter 4.
Wednesday, October 24th. Today comes the first of several days in which we discuss the way in which the derivatives of a function tell us something about the function itself, starting with determination of extreme values, the topic of Section 4.1 of your text.
Thursday, October 25th. Exam 2, including material discussed in Sections 2.7 and 2.8, as well as 3.1 through 3.9. I will have your exams graded and handed back to you on Monday, at which time you will have a few days to effect revisions and earn a few points back, if you so desire.
Friday, October 26th. No class! I will be out of town. However, as I have mentioned before, this period would make a splendid time at which you could meet with your team. After all, you know you will all be free at this time!
Monday, October 29th. We will finish up talking about maxima and minima; see the link to the notes above.
Wednesday, October 31st. Happy Halloween! The topic of the day is the Mean Value Theorem, the subject of Section 4.2 of your text. By the way, here is a link to a potentially useful Mathematica notebook I whipped up to help us visualize the Mean Value Theorem: behold, the MVT Randomizer!
Thursday, November 1st. Happy Day After Halloween! We will likely finish up the Mean Value Theorem today, and begin talking about the way derivatives describe the behavior of a function, the topic of Section 4.3 of your text.
Friday, November 2nd. We will keep working on the various and nefarious ways that the derivative informs us of the original function. See the notes in the previous entry.
Monday, November 5th. Today is all about taking it to the Hospital! Check it out as you make your way through Section 4.4 of your text.
Wednesday, November 7th. More time in the Hospital. The notes are in the previous entry, and we will also make use of Mathematica to investigate indeterminate limits. Check out the handout, Indeterminate Forms for more on this in-class exercise.
Thursday, November 8th. We will finish up with our investigation of indeterminate forms.
Friday, November 9th. Sketch that graph! The relevant section from your text is Section 4.5.
Monday, November 12th. Today is the day you have all been waiting for! Newton v. Leibniz gets re-enacted!
Wednesday, November 14th. We spend a little more time on Section 4.5 (note set above) before turning to the topic of optimization, the topic of Section 4.7 of your text.
Thursday, November 15th. More on optimization! See the previous entry for notes. Here is a link to Exam 3, due on Monday, November 19th.
Friday, November 16th. We spend a bit of time today talking about antiderivatives, about which you can read in Section 4.9. Whaddaya think: can you do it all backwards ?
Monday, November 19th. I will also hand out your last writing assignment of the semester, asking you to write a mathematical poem. This will be due on the last day of class. Please remember that your third mid-semester exam is due on this day, at 1:00 p.m.!
Wednesday, November 21st through Monday, November 26th. Thanksgiving Break! No class! You lucky dogs, you! (Note that classes do resume on Monday, but I will not be back in town until Tuesday, so we will not have class on that day.)
Wednesday, November 28th. Today will be spent talking about areas, motivating our definition of the definite integral (to come later in the week). For those of you keeping score at home, this comes from Section 5.1 of your text. You may want to play around with the Mathematica notebook, Riemann Sums, designed to help you better understand the way Riemann sums are built as we set about trying to compute areas of curvilinear figures.
Thursday, November 29th. Today we wrap up our computation of areas and define the definite integral, the topic of Section 5.2 of your text.
Friday, November 30th. One day to go after today! Today we finish our discussion of the definite integral and pave the way for the Fundamental Theorem. Here is the second set of notes on Section 5.2 of your text. Also, I will be handing out the Final Exam in class today...this will be due on Friday, December 7th, at 5:00 p.m.
Monday, December 3rd. Last day of class! What a total bummer! Today we discuss what the FTC means to us in terms of computing definite integrals (this is the topic of Section 5.4 of your text). (Please remember: your poem will be due on this day, along with revisions for Exam 3.)