We’ll use this page to keep track of what has happened each day in class. It won’t contain any of the nitty-gritty details, but will instead serve to summarize what has transpired each day.

Week 1

  • Monday, August 31: First day! We spent the majority of the time doing the Setting the Stage activity, which generated lots of great discussion. The last 10-15 minutes of class were spent discussing the syllabus and surfing the course webpage.
  • Wednesday, September 2: The first few minutes of class were devoted to reviewing some key aspects of the syllabus. Next, we divided the class into groups A-F and each group was tasked with putting their proposed solution to a particular problem from Daily Homework 3 up on the white board. During this time, Hannah and I circulated around the room listening and chiming in when necessary. We spent the last 10 minutes having a few groups share out. NH presented Problems 3 and 4, MM3 presented parts of Problem 5, and RF presented Problems 7 and 8. I am thrilled with how the first set of presentations went! I apologize that more students did not get to present.
  • Thursday, September 3: After some announcements, we played around with WeBWorK and chatted about Weekly Homework 1. The last 20 minutes of class was reserved for students taking the Calculus Readiness Quiz.
  • Friday, September 4: Class began with a few brief announcements and then I did a quick mini-lecture on function transformations. Next, we split the class up into four groups. While each group discussed one of the homework problems, Hannah and I milled around to see what questions people had. The last 15 minutes of class was devoted to students presenting their group's work. AG and HD presented Problems 10 and 11, respectively, that were left over from Daily Homework 3. Then NH and BL showed us Problems 12(d) and 14(b), respectively. We wrapped up with a presentation of Problems 15(f), 17, and 19 by SM. A great end to the first week.

Week 2

  • Monday, September 7: Labor Day. No classes!
  • Wednesday, September 9: After synthesizing some ideas about average rate of change, secant lines, and tangent lines, we launched into some presentations. MM3 and TB presented Problems 21 and 22, TR discussed Problem 26, and finally TM walked us through Problem 31.
  • Thursday, September 10: Today was aimed at synthesizing ideas and solidifying concepts. We postponed doing any presentations and I lectured over the intuitive approach to derivatives.
  • Friday, September 11: Great day! Maybe it was because the radiator thing in the back of the room was finally quite, but I think it was because the student presentations were awesome. First, EB did an excellent job discussing Problem 40. Next, LL walked us through Problems 34 and 37, which spawned some great discussion. Lastly, after announcing that she knew that she made a mistake, VK presented Problem 41 and addressed her mistake along the way. With the few minutes we had left, I starting discussing limits and did a few quick graphical examples.

Week 3

  • Monday, September 14: We did a lot today...maybe too much. After passing last time, MM2 presented the big picture of Problem 43. Next, we had JC, SR, EB, and BB present Problems 45, 47/48, 50, and 51, respectively. After the student presentations, I spent time discussing to applets from Calculus Applets with GeoGebra and then cranked out some examples involving limits.
  • Wednesday, September 16: I had a lot of fun today. We slowed the pace a bit and had students present problems live at the board. We kicked off with PD presenting Problem 53. This resulted in a quick conversation about notation. Next, we had JE present Problem 54 (without his notes!). This led to a discussion about limits that don't exist and how sometimes we can be more specific about how they don't exist if they march off to $\infty$ or $-\infty$. Utilizing the discussion that followed Problem 54, SC was able to quickly dispense with Problem 52. With the little time we had left, I drew a picture that captured the essence of Problems 56-58.
  • Thursday, September 17: Yay! Great presentations by CW, JC, and EB, who did Problems 66, 67(a), and 67(c), respectively. I also spent some time discussing limit laws and the Squeeze Theorem.
  • Friday, September 18: Today I spent a good chunk of time lecturing over a proof that $\lim_{\theta\to 0}\frac{\sin(\theta)}{\theta}=1$ using the Squeeze Theorem and then discussed one-sided limits. As I was about to kick off discussing one-sided limits, HD volunteered to do an example for us. Cool. The last few minutes of class was spent on having students discussing Problems 72-75 with a partner while Hannah and I walked around and helped.

Week 4

  • Monday, September 21: Today was a little chaotic and I think I'll take the blame on this one. While likely entertaining, I probably spent too much time discussing my bike race that took place over the weekend. Once we got started on doing calculus, I blitzed through solutions of Problems 73-75. After that, MG walked us through various parts of Exercise 2.4.16 from "Calculus I Lecture Notes." This would have gone better if the graph for the problem was displayed (unfornately, I couldn't get the doc camera working). I totally lost track of time and when a few minutes over. We decided to postpone the due date of Daily Homework 12 with the intention of wrapping up discussion of Daily Homework 11 on Wednesday.
  • Wednesday, September 23: Ah, that was better. The first half of class was devoted to be cranking out some examples involving limits at infinity while the second half was a free-for-all for the students. Hannah and I milled around while students worked on problems from Daily Homework 11, Daily Homework 12, or one of the reviews.
  • Thursday, September 24: We spent the whole day reviewing for Exam 1.
  • Friday, September 25: Exam 1!

Week 5

  • Monday, September 28: Fun day! After handing back exams (which the class did very well on as a whole), I did a mini-lecture on the formal definition of the derivative and highlighted what is to come over the next couple weeks. With the 25 minutes that we had left, students worked in small groups on Daily Homework 13.
  • Wednesday, September 30: We accomplished a lot today. We split the class up into 6 small groups and had each group work on a specific problem or two. Afterwards, we had MM3, EB, JE, HD, SM, and JC present Problems 80, 81/84, 82(a), 82(b), 86, and 88/89, respectively. SM's proof of the Product Rule was impressive!
  • Thursday, October 1: I spent a good chunk of class reviewing and setting the stage for what is to come. Together as a class we proved the Power Rule (in the case that the exponent is a positive integer) and then we did a few examples. With the few minutes we had left in class, folks started working on Daily Homework 15.
  • Friday, October 2: Class began with a quick review of our current derivative shortcuts and a brief discussion of what's to come. Next, TR crushed Problem 134 (Quotient Rule). Then we took a step backwards and had the class help me tackle an alternate approach to Problem 132 using the Quotient Rule. This was followed by AG and TM presenting solutions to Problems 136(a) and 136(b), respectively. With help from the class, I presented solutions to Problems 139 and 141. Class concluded with SC taking a crack at Problem 142. I'm really happy with how the whole week went, but I need to find a way to get more students persevering a bit longer on the harder problems.

Week 6

  • Monday, October 5: We accomplished a lot today. After a quick review, we divide the class up into 6 small groups to work on problems from Daily Homework 16. We had TR, BB, HD, PD, and MM2 present solutions to Problems 125, 126, 137, 127/128/129/136(c), and 138, respectively.
  • Wednesday, October 7: After a few quick announcements, we reviewed our current list of derivative shortcuts. This was followed with some motivating examples for the Chain Rule, which led us to the statement and "proof" of the Chain Rule. Next, we cranked through a few short examples. We didn't have too much time before our derivative quiz, so instead of having students present, we discussed the definition of the irrational number $e$ and then proved $d/dx[e^x] = e^x$. The last 10 minutes of class was reserved for students working in small groups (if they so chose) on our very first derivative quiz.
  • Thursday, October 8: I was out of town for a conference and David covered for me while I was gone. Hannah informed me that JE, NH, BL, SR, and CW presented.
  • Friday, October 9: Sarah covered for me while I was gone. JC, JE, VK, BL, MM1, and TM presented.

Week 7

  • Monday, October 12: Today was a review, catch-up, and synthesize day. I spent most of the class period reviewing the derivative rules with focus on exponential and log functions that required use of the Chain Rule. In addition, we discussed the use of logarithmic differentiation (aka, the "log trick"). Towards the end of class, TR presented Exercise 3.11.1(a).
  • Wednesday, October 14: Today was mostly a review day. We spent quite a bit of time discussing how to combine the Chain Rule with the derivative formulas for logs, exponentials, and inverse trig functions.
  • Thursday, October 15: We reviewed for Exam 2 the whole class meeting. This mostly consisted of me running my mouth and doing examples.
  • Friday, October 16: The students took Exam 2.

Week 8

  • Monday, October 19: Class began with handing back and briefly discussing Exam 2. Next, we decided to postpone discussing Daily Homework 22 and worked through a series of examples on implicit differentiation. This included some historical discussion of the Folium of Descartes.
  • Wednesday, October 21: Today was productive and we had quite a few students present. In particular, we had EB, RF, LL, MG, TB, and MM1 show us solutions to Problems 167, 168, 169, 170, 173, and 175, respectively. We had a few minutes at the end to start discussing what it means for a function to be increasing/decreasing on an interval and we briefly discussed local versus global maximums/minimums.
  • Thursday, October 22: I know I've said it before...but today was a good day! I spent the first 10-15 minutes reviewing the definitions of increasing, decreasing, strictly increasing, strictly decreasing, local max/min, and critical point. We then worked through a graphical example, where we examined each of these definitions. With the time we had left, we divided up into 5 small groups. The last 15 minutes of class was spent having SC/RF, SR, HD, KP presented Problems 97/98/99/100, 102, 103, 104, 105, respectively.
  • Friday, October 23: We had a very productive week. Class started with a short review, which was followed by a brief introduction to second derivatives and concavity. As usual, we divided the class up into small groups to discuss the current homework problems. MM2, RF, AG, EB were the spokespersons for Problems 106, 108/109/110, 111, 112, respectively. SC was prepared to present Problem 113, but we ran out of time.

Week 9

  • Monday, October 26: Today felt a bit rushed to me. Perhaps we tried to do too many different things. Class began with me providing a summary of all the recent connections between increasing/decreasing, local max/min, critical points, First Derivative Test, etc. I also introduced the Extreme Value Theorem and we discussed a method for finding absolute max/min of a continuous function on a closed interval. Next, we split up into 5 small groups to discuss the homework problems that were due today. All we ended up having time for was EB and SM to share their proposed solutions to Problems 114/115 and 116, respectively. Class ended with me explaining the pros and cons of the First Derivative Test versus the Second Derivative Test.
  • Wednesday, October 28: Again, we started with a short review and then launched into students discussing homework problems in small groups while Hannah and I walked around to listen in and help out. MM3, sC, BL, and CW presented Problems 1, 2/3, 4(a), and 4(b), respectively, from Daily Homework 26.
  • Thursday, October 29: I spent most of class working through a couple applied optimization examples using applets from [Calculus Applets with GeoGebra](http://dcernst.github.io/CalculusApplets/) (made by Hannah!). With the time we had left, the students started working on some exercises from an [Applied Optimization](/teaching/mat136f15/AppliedOptimization.pdf) handout.
  • Friday, October 30: The students spent the entire class session working on the problems on the [Applied Optimization](/teaching/mat136f15/AppliedOptimization.pdf) handout.

Week 10

  • Monday, November 2: The whole class meeting was devoted to me presenting examples from the [Function Analysis](/teaching/mat136f15/FunctionAnalysis.pdf) handout.
  • Wednesday, November 4: We split the class up into several small groups and had them discuss the homework due today. When all was said and done, we had SM, MM1, and TM present Problems 1, 2, and 3, respectively from Daily Homework 29.
  • Thursday, November 5: After a quick introduction to L'Hospital's Rule together with a prove of the 0/0 case, I cranked through a bunch of examples.
  • Friday, November 6: We kicked off with a few quick presentations by MM2, MG, BB. They presented Exercises 4.1.6(1), 4.1.6(6), and 4.1.6(11), respectively. The rest of the class was spent reviewing for Exam 3. This consisted mostly of me working through a few optimization problems.

Week 11

  • Monday, November 9: The students took Exam 3.
  • Wednesday, November 11: No class due to Veteran's Day!
  • Thursday, November 12: After handing back Exam 3, I presented solutions to Problems 5 and 8(b) from the exam. The rest of the class session was spent doing some related rates exams from the [Related Rates Handout](/teaching/mat136f15/RelatedRates.pdf).
  • Friday, November 13: We had MM2, TB, MM1, and BB present Problems 180, 181, 182, and 183, respectively. With the time we had left, I introduced Rolle's Theorem and the Mean Value Theorem.

Week 12

  • Monday, November 16: Busy day! We split the class up into 8 small groups, where each group worked on a separate problem or two from the homework. Before launching to presentations, I got philosophical while standing on the desk. We got through most, but not all of the problems. When all was said and done, we had HD, SC, PD, KP, LL, and MG present Problems 185/186, 189/190, 191, 192, 193/194, and 196, respectively.
  • Wednesday, November 18: I was surprised how much we got done today. Very productive. To help synthesize some ideas the students were already grappling with, I did a mini-lecture on antiderivatives and indefinite integrals. One thing we did was write down a bunch of integral formulas that we now know are true. Next, we split the class up into 8 small groups, where each group worked on one of the problems from the homework. TB, NH, BB, PD, and CW presented Problems 200, 201, 202, 203, and 204, respectively.
  • Thursday, November 19: After Joe's reminder, I spent some time discussing Problem 188, which no one had previously figure out. Cool problem! Then I presented Problem 207, which we didn't get to last time. The whole rest of the class session was spent cranking out examples of indefinite integrals where the method of substitution was handy. All the examples came from the [Substitution Handout](/teaching/mat136f15/Substitution.pdf).
  • Friday, November 20: Today was productive. We had AG, LL, MM3, MM2, BL, HD, EB, MM1, and TM present Problems 211, 212, 213, 214, 215(a), 215(b), 215(c), 216(a), and 216(b), respectively.

Week 13

  • Monday, November 23: I was really sick, but managed to make it to class. With an extremely raspy voice, I lectured over definite integrals as a limit of Riemann sums.
  • Wednesday, November 25: I was a bit disappointed in today's attendance. Yes, I know that it was the day before Thanksgiving, but only a few of you that missed class informed me that you would be missing. Thanks to the people that showed up. We spent the first few minutes of class chatting about what everyone was doing for Thanksgiving. Next, I summarized where we currently are in the course and where we are headed. After that, I cranked out another example of computing a definite integral using a limit of Riemann sums. The last few minutes of class were devoted to answering some questions that students had on the homework from a few days ago.
  • Thursday, November 26: Thanksgiving! No class.
  • Friday, November 20: Thanksgiving recovered day. No class.

Week 14

  • Monday, November 30: We spent the whole class session discussing the First Fundament Theorem of Calculus (FTC1). This included its proof and a bunch of examples. The notes are available [here](/teaching/mat136f15/FTC.pdf).
  • Wednesday, December 2: The first 10 minutes or so were spent discussing questions from the homework. After that, we discussed the Second Fundament Theorem of Calculus (FTC2). After a motivating example, we stated and proved FTC2. Next, we cranked through several examples.
  • Thursday, December 3: We reviewed for Exam 4.
  • Friday, December 4: The students took Exam 4.

Week 15

  • Monday, December 7: We crushed some integrals involving integration by parts. We followed the [Interation by Parts Handout](/teaching/mat136f15/IntegrationByParts.pdf).
  • Wednesday, December 9: After a quick discussion of Exam 4, we launched into student presentations. We had CW, RF, LL/JE, SR, AG, TB, PD, and TR present Exercises 5.7.5(1)-5.7.5(4), 5.7.7(1)-5.7.7(3), and 5.7.10, respectively from "Calculus I Lecture Notes".
  • Thursday, December 10: Most for the class session was spent having students work either independently or in a a small group on previous exam problems. Towards the end of class, we had NH, MG, MM3, and SM present Problem 1 on Exam 4, Problem 4 on Exam 1, Problem 12 on Exam 1, and Problem 3(f) on Exam 4, respectively.
  • Friday, December 11: Last day of classes! Today was more or less the same as yesterday. In the midst of students studying, we had SR and KP present Problem 7(b) on Exam 1 and Problem 4 on Exam 3, respectively. What a great semester! Thanks.

Dana C. Ernst

Mathematics & Teaching

  Northern Arizona University
  Flagstaff, AZ
  Google Scholar
  Impact Story

Current Courses

  MAT 431: Intro to Analysis
  MAT 526: Combinatorics

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Land Acknowledgement

  Flagstaff and NAU sit at the base of the San Francisco Peaks, on homelands sacred to Native Americans throughout the region. The Peaks, which includes Humphreys Peak (12,633 feet), the highest point in Arizona, have religious significance to several Native American tribes. In particular, the Peaks form the Diné (Navajo) sacred mountain of the west, called Dook'o'oosłííd, which means "the summit that never melts". The Hopi name for the Peaks is Nuva'tukya'ovi, which translates to "place-of-snow-on-the-very-top". The land in the the area surrounding Flagstaff is the ancestral homeland of the Hopi, Ndee/Nnēē (Western Apache), Yavapai, A:shiwi (Zuni Pueblo), and Diné (Navajo). We honor their past, present, and future generations, who have lived here for millennia and will forever call this place home.