Mat 221 Daily Log Please press F5 to refresh your page. If this page is more than two class days out of date, please send me an email reminding me to update it.


Day 51: Tuesday, 4/22: Handed out copies of the end of semester calendar with notes on it. (Extras in the box outside my door). Handed out information on using the Success Strategy Points, with an Example of the 3 Possibilities. Worked on problem 32 from section 5.2, emphasizing that the definite integral did NOT always represent the area bounded by the curve and the x axis. In the case of the second interval, since the curve is below the x axis, the definite integral over that interval represents the opposite of the area. Reviewed several times what a definite integral was.... the limiting value of the Riemann Sums.... and reviewed what the Riemann sum was as a way to try to help students see why some definite integrals will produce negative values. We will continue to work on this tomorrow, and will also introduce the Evaluation Theorem. 

Day 50: Monday, 4/21: Teacher out  
Day 49: Friday, 4/18: Reviewed what we had done so far. Showed students how to use the RSums Program on their calculator. Created a table with n increasing to show that the RHS and LHS did seem to have a limiting value. Defined this limiting value as the definite integral. Discussed notation and terminology.  
Day 48: Wednesday, 4/16: Handed back plans for final project along with a rubric showing the essential components. Handed out the final project. There is to be NO COLLABORATION with anyone on this project. Spent time making sure that each student got the function correctly entered into Mathematica. Loaded the programs we use in Calc 1 and 2 on the calculators. Had students continue working on creating Left Hand Sums and Right Hand Sums for the function and interval we considered yesterday using 8 partitions. 

Day 47: Tuesday, 4/15: Talked briefly about the problem we were working on in class yesterday, and gave final answers. Began Chapter 5. Discussed section 5.1, and took students through approximating the area under a curve with a left hand sum and a right hand sum using 4 partitions.  
Day 46: Monday, 4/14: Continued work on applied problems. Collected Plans.  
Day 45: Friday, 4/10: Worked on Section 4.2 with the Extreme Value Theorem, as well as section 4.6 with the applied problems. We will do more applications on Monday, and will start Chapter 5 on Tuesday.  
Day 44: Wednesday, 4/9: Worked with the students on Mathematica as we analyzed a cubic function with a polynomial denominator from section 4.4 Showed all the "issues" that can arise, and how to work around them by using NSolve, indicating Reals, using the Together command, etc.  
Day 43: Tuesday, 4/8: Handed back tests. Handed out Planning for Project  which is due in on Monday, 4/14. Talked a little about how I have been reviewing all of the key ideas with them, and with what I have discussed in class, and their first Mathematica project, they should have a clear pathway through analyzing a function fully. Worked on another function  emphasizing how important it is to summarize all the key behavior at the end. We can use the key points (CP, POI, discontinuities) to create a table of intervals and points where we consider the first and second derivative behavior to determine what is happening for the function. Worked on constructing this table.... will finish this tomorrow.


Day 42: Monday, 4/7: Test on Chapt 3, Chapt 4 sections 3, 5. 

Day 41: Friday, 4/4: Answered a question on implicit differentiation. Continued to work on analyzing functions, looking at an example that had a vertical asymptote. Emphasized that we would explore the behavior at the undefined points by using tables for the final project. Showed clearly that a function CAN change behavior on either side of a point where it is undefined. 

Day 40: Wednesday, 4/2: Reviewed exercise 8, handing students the Mathematica work on this problem, and emphasizing how we gave a summary of function behavior at the end of the problem based on the key points. Upon request, agreed to move the test until Monday, 3/7 

Day 39: Tuesday, 4/1: Quickly reviewed what the test on Friday would cover. Finished ideas from the Mathematica Sheet that was handed out yesterday. Created a summary of the material using the "Key Points"  which are the collection of the Critical Points and the possible Points of Inflection. Key points would also include any points where the function was undefined if there were any. Had students work together on exercise 8 from section 4.3. This is the type of problem that could be on the test. Asked students to complete their work tonight. We will review the ideas tomorrow at the beginning of class. 

Day 38: Monday, 3/31: Handed out Practice Exercises that will be used for Success Strategy Points at test on 3/4. That test will cover all of chapter 3, and sections 4.3 and 4.5. Handed out a Summary of Key Ideas in Chapter 4. Handed out a Mathematica sheet for Problem 10 Section 4.3 that we used as a basis to begin discussing the process of analyzing a function. As we covered ideas for the particular example, I continued to focus student's attention to the gold sheet. 

Day 37: Friday, 3/28: Reviewed ideas on Linearization, and extended using locally linearity to help understand L'Hopital's Rule (Section 4.5). Did a number of examples using L'Hopital's rule for the cases of 0/0 and inf/inf. Test will be next Friday, 3/4 

Day 36: Wednesday, 3/26: Worked with students on material in Mathematica that will help them think about what it means for a differentiable function to be locally linear. Talked through these ideas for 2 different functions from a geometric and numeric point of view. Handed out GW 7 

Day 35: Tuesday, 3/25: Showed the derivatives of inverse sin, cos and tan. Did not derive the formulas for inverse cos and tan. Showed an example of using these formulas. Developed the rules for derivatives of log functions. Also developed the idea behind logarithmic differentiation. Announced that the next test will be Friday, April 4th. It will cover derivatives, L'Hopital's rule, and some early ideas in Chapter 4. 

Day 34: Monday, 3/24: Handed back quiz, and talked some about how to work on improving at taking derivatives. Pointed out a few common mistakes that I saw. Worked on find the derivative of the inverse sin function. Started by reviewing key ideas about the inverse sin function... restricting the domain of sin of x so that it was one to one. Used implicit differentiation and trig identities to establish the rule for the derivative of inverse sin. Did not have time to do an example. Will pick up there tomorrow. 

Day 33: Friday, 3/21: Did an example of implicit differentiation. Gave quiz. 

Day 32: Wednesday, 3/19: Answered a few questions on homework. Began discussing Implicit Differentiation. Will do another specific example of this on Friday. Quiz on Friday!! Practice Exercises are due then. 

Day 31: Tuesday, 3/18: Continued work with Chain Rule. Did a number of exercises. 

Day 30: Monday, 3/17: Handed back tests, and talked about issues with really knowing the material. Began section 3.4  chain rule. Did a number of examples. Will continue this work tomorrow. Quiz on Friday on sections 3.1 through 3.4. I will look at Practice exercises then. 

Day 29: Friday 3/7 Presented rules for derivatives of Trig functions. Used this as an opportunity to review drawing a graph of the derivative from the graph of a function to conjecture the derivatives for Sin(x) and then Cos (x). Developed derivative of Tan(x) using the quotient rule. Likewise developed the derivative of Csc(x) using the quotient rule. Happy Spring Break!!!! 

Day 28: Wednesday 3/5: Test on Unit 2 and sections 3.1 and 3.2 

Day 27: Tuesday 3/4: Review for test tomorrow. 

Day 26: Monday 3/3: Presented the product rule and quotient rule  Section 3.2. Did a number of examples. 

Day 25: Friday, 2/28: Handed back GW 6 with answer key. Discussed that writing about this type of material took some getting used to, and that students would improve throughout the semester as long as they thought carefully about the difference between an answer that they lost points for and an answer on the answer key. The language is essential. Presented all the "rules" for derivatives in section 3.1, and then did a series of examples that helped exemplify these rules in action. Handed out Practice Exercises for Unit 3. Please notice that I will be looking at these practice exercises in "chunks", with the first couple of sections due at the beginning of the test on Wednesday, March 5th. Test will cover material from PE Unit 2 sheet, as well as 3.1 and 3.2. 

Day 24: Wednesday, 2/26:Quickly reviewed the last question from yesterday  where we find a graph of the function from a graph of the derivative. Encouraged students to think very systematically about the process. Worked on computers with a worksheet on Exponential functions. (See Angel, Learning Modules, Classwork, Exponential Worksheet.) Discussed what the derivative of an increasing exponential function would look like, and then used the worksheet to see that the graph did seem exponential. Showed by using the limit definition of derivative that the derivative would be exponential, times some constant multiple. Used the worksheet to find an approximation for this limiting value. Showed that it was almost ln(base). Discussed a decreasing exponential function, and saw that the same pattern held. 

Day 23: Tuesday, 2/25: Handed out additional sheets that worked more with finding graphs of derivatives based on graph of function. Also worked on finding the graph of a function from the graph of the derivative. 

Day 22: Monday, 2/24: Finished material on the yellow sheets from Friday. 

Day 21: Friday, 2/21: Collected GW 6. Handed out some yellow sheets for working with derivatives. Extra copies are outside my office. We worked through ideas on the first page, and saw how that information related to the statements on the back of the Gold Sheet on Derivative Facts. We also worked on the back of the first sheet, and discussed the second derivative and what it told us about the function. Told students to complete work on the back of the 2nd sheet. We will continue to work on this material in the next class. Discussed that I might not be in class on Monday. I will post on MyDCC by Noon on Monday if I will not be in class. Students should continue work on practice exercises. 

Day 20: Wednesday, 2/19: Handed back GW 6 with answers. Talked briefly about some of the common issues with the homework. Many of the assignments were definitely moving in the right direction. Make specific reference to the answer key, and explained what it was that I was looking for. Picked up with the algebraic definition of derivative. Showed the work and notation to algebraically find the derivative of our function f(x) at x = 1. Then showed how we can find the derivative as a function of x. We discovered that the derivative function for our function x^2 + 2 is 2x. Showed that we did get an answer that matched what we decided was the limiting value of the difference quotients at x  1. Showed that we got what we expected when x =2. Students will have to be able to work through algebraic definition with a quadratic function 

Day 19: Friday, 2/14: Snow Day. Students should be working on GW 6. We will pick up with work on derivatives on Wednesday, 2/19. 

Day 18: Wednesday, 2/12: Colleceted GW 5. Students worked on Sections 16 and 17 from their Mathematica Manual. If I did not check your work in class, you MUST attach your file in the dropbox in Angel, Learning Modules, Graded Work, Graded Work 6  Preliminary Tutorial. This will count as 5 points towards the GW 6 grade. As students finished, handed out GW 6. This is due on Friday, 2/21. 

Day 17: Tuesday, 2/11: Handed out tables relating to what we were talking about yesterday  using average rates of change to consider instantaneous rate of change. Walked students through what the first table represented, making MANY notes on verbally expressing what it represented, as well as symbolically representing what information we got from the table. Picked a particular value in the table and emphasized what that represented  each output is an AVERAGE RATE OF CHANGE. The language absolutely matters here! Showed the specific difference quotient that represented our value. Defined the instantaneous rate of change as the derivative. Discussed that it was the slope of the tangent line to a curve at a point, whereas the ARC was the slope of the secant line between two specific points on the curve. Handed out a GOLD SHEET on DERIVATIVE FACTS. This sheet is VERY important for students to make sure they understand completely! 

Day 16: Monday, 2/10: Handed back tests and answers (pink). Talked about the potential of doing a Test Analysis, and what that would/could entail. Emphasized the importance of reading the notes, and seeing how the notes lined up with the practice exercises. Doing the practice exercises mindfully is KEY! Talked about the graded work 5, and answered a number of questions. Postponed the due date until Wednesday. Began discussing section 2.1: Used the idea of Average Rate of Change to help us consider what an instantaneous rate of change was. We will do more work with this tomorrow. In the meantime, students need to focus on reviewing their tests, and work on the graded work 5. 

Day 15: Friday, 2/7: Test # 1 

Day 14: Wednesday, 2/5: Snow Day. DCC canceled all classes. 

Day 13: Tuesday, 2/4: Worked on section 2.4. Emphasized the definition of continuity at a point, and told students that they needed to know the three pieces for the test on Friday. Did a number of examples, clearly showing how we checked each of the three pieces of the test until we found one that was not satisfied. 

Day 12: Monday, 2/3: Handed back GW 4, and talked briefly about the results for WebAssign. I will continue to post Practice Exercises for the course, and students can elect to either do the practice through WebAssign, or from the book. Handed out Graded Work 5, which is due next week. Emphasized that it is similar to the problem we did together in class, and similar material will be on the test on Friday. Students must be able to articulate information about limits from a verbal, symbolic, and graphical point of view. Discussed that "large commands"  i.e. to create plots and tables  must be moved to a "Background Page" in order to not have them interrupt the flow of the presentation of the material. While they are necessary for making Mathematica produce material we need, they are not necessary to see in the presentation of the core ideas. Continued section 2.3. Did an example where we have to multiply by a form of 1 involving the conjugate of an expression containing a radical. Also did another problem where we had to factor using the pattern of the difference of squares twice. 

Day 11: Friday, 1/31: Handed back quizzes with answers, and addressed a couple of common mistakes. Overall quizzes showed that most students were processing many of the key points. Discussed the difference between evaluate and solve. Evaluate means that you are given an input, so you put it in for the variable, and compute the answer  so you are getting the output for the function. (When you use an input of 0, you are finding the y intercept of the graph of the function.) Solve means that you have an output, and you want to find the values of the variable that get mapped to that output. (You are essentially finding x intercepts for the graph of the function when you solve for where the output is 0), Began section 2.3  Algebraically computing limits. Got through one example. Will continue this work on Monday. Announced: Test on Unit 1 on Friday, 2/7 

Day 10: Wednesday 1/29: Quiz on Mathematica. After the quiz, students began work on creating tables in Mathematica. 

Day 9: Tuesday, 1/28: Handed back Graded Work 3, and handed out a list of the hours that tutors who have had me in Calc 1 are available in the lab. Finished the material from section 2.5 that I had started in class. Handed out a worksheet that gave a problem similar to what the students will be working with on Mathematica next week. Asked students to work together on it, and I went around to answer specific questions. We will review this quickly at the beginning of class on Friday before moving into section 2.3. Reminder: Quiz on Mathematica tomorrow. Then students will be working with section on tables from the Mathematica manual. 

Day 8: Monday, 1/27: Handed back Graded work 2, and explained that 3 of the points were for correctly submitting an electronic copy in Angel Graded Work folder. The other 22 points were for the work from the Mathematica manual. Reminded students to enter their grades on the back of their pink sheet so they would have an accurate record of their grades for the semester. Collected Graded work 3. there will be a quiz on the Mathematica material in the lab on Wednesday. Students need to be able to complete the major components of the work they have been doing without using any resources. Here is the quiz I gave last semester: Quiz from Fall 2013 with the answers. Continued work on limits, discussing Long Term Behavior (Section 2.5). Again, we considered numerical, verbal, symbolic and graphical components. Showed an example of a function that did have a limit, and one that did not. We will finish up this material tomorrow. 

Day 7: Friday, 1/24: Teacher out. Students should be working on GW 3 (Mathematica) and GW 4 (WebAssign) 

Day 6: Wednesday, 1/22: Collected Graded Work 2. Handed out Graded Work 4  which students should be working on during class time on Friday. This assignment involves going into WebAssign, and working with the material included there for section 2.2 Finished talking about the examples I had begun yesterday. We discussed one sided limits from a numerical, verbal, graphical and symbolic point of view. We discussed a two sided limit, as well as a scenario where a limit did not exist because we had evidence of a vertical asymptote. Students should work on the reading and the practice exercises for this material in WebAssign, though they can also work with reading the book, and work on the practice exercises from the book. Worked with students on using the Solve command in Mathematica. Emphasized that students needed to be working with Mathematica on a regular basis, and needed to make sure that they could complete the work without having to look things up in the manual. Next Wednesday, there will be a quiz on the sections that students addressed in GW 2 and GW 3. GW 3 is due on Monday. Reminded students to submit GW 2 in the dropbox in Angel. This is NOT the same as emailing me the file. 

Day 5: Tuesday, 1/21: Handed out the Practice Exercises for Unit 1 (purple). Explained that as we cover each section, students should be working on the practice exercises from that section. Handed out the Bonus Opportunity for meeting with my student leader (gold) (or a student tutor who took Calc 1from me). This allows a student to get double the points that I typically give for meeting with a tutor. The form must be submitted no later than Friday, January 31st. Handed out the Quick Start Guide to WebAssign (white  copies in folder outside my door) with the class key: sunydutchess 3231 1822. Asked students to get signed into that program. I will be asking students to work with the material in that area during class time on Friday. The next graded homework assignment will be asking for students to complete certain work, as well as give me feedback to the program. Began section 2.2. Discussed concept of a one sided limit. In one case, we approached a point. In another case, the outputs decreased without bound. We will continue exploring this idea tomorrow before our continued work on Mathematica. 

Day 4: Friday, 1/17 Showed students how to find the "help options" in the link to Mathematica on the MyDCC page. Handed out notes on Automatic Positioning in Mathematica (gold). I had shown students this issue in lab on Wednesday. Handed out new schedule (tan) with a change in my office hours. Handed out How to Save to the Angel Toolbox (gold). Handed out the Success Strategies Grade Sheet (pink) Extras are in the box outside my office door. Reviewed what students should have in their blue books. I will be collecting these books next week with Graded Work 2. Reminded students that Graded Work 1 is due by 5 PM today. Answered questions on Success Strategies Grade. Reminded students that I have purposefully not gotten into more of the course material, or given them much else to do outside of class so that they have the time to get up and running with Mathematica. Students MUST be working with that program on a regular basis for the next couple of weeks. 

Day 3: Wednesday, 1/15: Worked with students on Mathematica, showing them how to create a text region, enter a function in a math region, set up a definition for creating the graph of a function. We then moved the definition to a "Background Page" so that it won't interrupt the flow of a presentation. Gave students some time to begin working on Graded Work 2 (green sheet), which is due at the beginning of class on Wednesday 1/22. Blue books will also be due then, and will count as 10 points. Emphasized again how important it was for students to be working regularly with learning Mathematica. 

Day 2: Tuesday 1/14: Have students say hello to students they met yesterday. Find new groups to work with. Continue discussing the questions that were assigned from page 80 in their text. Towards the end of class, I discussed question 12 with the entire group, as this seemed to be the problem that most students had questions on. Showed students how to login to the nsflab account, with the password: reason. Showed them how to open Mathematica and go to a new Notebook. Tomorrow, all students should immediately log in to the nsflab account, and have Mathematica up and open so that we can begin right at the start of class. 

Day 1: Monday 1/13: Handed out Syllabus (white), Info on Textbook (white), General Information package (gold) and Graded Work 1 (green) which is due no later than 5 PM on Friday, January 17th. Had students fill out Course Information cards. Had students meet some other students in class, and begin to discuss review material from page 80 in their text books. (Questions 6, 8, 11, 12) Students should have notes in the blue books provided for each of these questions. At the end of class, had students add to their "To Do" list in their Blue Books, and handed out Homework and Notes After Class 1(purple) 