|
Calculus I |
|
|
Date
|
Activities |
| ANN: You will see Chapter O (Orientation) Homework and 1.1, 1.2, 1.3, Chapter 2 Skills Check Homework, 2.1, and 2.2 HW assignments are all due on MML on Monday, Jan. 27. The first is an introductory assignment that will help familiarize you with the interface of MML. The chapter 1 assignments are a review covering functions. We will likely finish sections 2.1 and 2.2 this week and so they will come due the following Monday. In class, I introduced the class by referring to the syllabus and mentioning a few extra tidbits. Read it and make sure you understand what is expected of you. I referenced the Math Resource Center which is our tutoring location and gave out a handout with their information. They are available online and in-person this semester. I talked about MyMathLab (MML) which is described on the syllabus. You should thoroughly read the syllabus and get MML set up before next class. I handed out the first 30 pages of The Manga Guide to Calculus (not available online here) as a fun introduction. We started the Class Notes for 2.1, only getting halfway done. Once finished, I post the Notes here and also under Class Notes. | |
Jan. 22 |
ANN: Remember that Chapter O (Orientation) Homework and 1.1, 1.2, 1.3, Chapter 2 Skills Check Homework, 2.1, and 2.2 HW assignments are all due on MML on Monday, Jan. 27. Students completed First of Semester Quickie Survey so that I may know a bit of your histories. In class, we finished the Class Notes for 2.1 and then went on to start the Class Notes for 2.2. Once finished, I post the Notes here and also under Class Notes. |
Jan. 23 |
ANN: Remember that Chapter O (Orientation) Homework and 1.1, 1.2, 1.3, Chapter 2 Skills Check Homework, 2.1, and 2.2 HW assignments are all due on MML on Monday, Jan. 27. ANN: Please do not use Messages in Blackboard; email me at soleary@lc.edu instead. In class, we finished the Class Notes for 2.2. Once scanned, I post the Notes here and also under Class Notes. |
| ANN: Remember that Chapter O (Orientation) Homework and 1.1, 1.2, 1.3, Chapter 2 Skills Check Homework, 2.1, and 2.2 HW assignments are all due on MML tonight. In class, we worked through another example we put in 2.1 notes. It had to do with finding the average velocity of a function in the interval [0, h]. Students asked me about one in the homework like it and I thought I should add it. We then worked on the Class Notes for 2.3, getting some rules written down but not doing many examples. Once finished, I post the Notes here and also under Class Notes. I handed out Trigonometry Identities and All-in-One Cheat Sheet (author, Paul Dawkins) which can be found at http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf and Limits and Their Properties Cheat Sheet (author, Paul Dawkins) which can be found at https://tutorial.math.lamar.edu/pdf/calculus_cheat_sheet_limits.pdf. |
|
Jan. 28 |
ANN: I explained the late policy for worksheets. If you turn in a worksheet after I collect it at the beginning of class, the grade will start at 8/10 after a late penalty. If you are absent when a worksheet is due, email me a picture of it to get full credit and then turn in the paper when you return. ANN: I will not announce MML due dates. Just know that if we finish a set of notes, the MML homework will be due the following Monday. The exception will be when I curtail due dates to accommodate an exam. In class, we worked on the Class Notes for 2.3, finishing most of the rules and doing many examples. We have the Squeeze Theorem yet to discuss but then we will be done. Once finished, I post the Notes here and also under Class Notes. I handed out a 2.3 worksheet called Have you reached your limit?. It will be collected next time. |
Jan. 29 |
I collected the 2.3 worksheet Have you reached your limit?. We finished the Class Notes for 2.3. We then started the Class Notes for 2.4, getting through a discussion of these infinite limits and starting number 25 from the book. Once finished, I post the Notes here and also under Class Notes. |
Jan. 30 |
[January 31 is the last day to drop and receive a full refund.] I gave out better copies of the Limits handout from a couple of days ago; if you want a darker copy, tell me, I have extras. We discussed a problem from 2.3 homework (number 18) that utilized a factoring formula you may not have been familiar with. We finished the Class Notes for 2.4. We then started the Class Notes for 2.5, getting through only me handing out two pages from my College algebra, Math 131, class to fill in the end behavior of polynomial functions and rational functions (called horizontal or oblique asymptotes). |
| I showed students the College algebra resources on my Website and also plugged Khan Academy which is great for picking up review topics. We worked on the Class Notes for 2.5, getting through the introduction and limits at infinity and their connection with horizontal asymptotes. We did a few examples. We are just now beginning our examples and rules concerning polynomials. I handed out the 2.5 worksheet Limits as x approaches infinity 2 with the intent to collect it later this week (Wed. or Thurs.). | |
Feb. 4 |
ANN: As a reminder, you can do late MML work for half credit. There is a strict deadline of March 31. In class, we worked on the Class Notes for 2.5, getting through some examples and theorems concerning polynomials and rational functions as well as one involving a radical in the denominator. I will collect the 2.5 worksheet Limits as x approaches infinity 2 Thursday. |
Feb. 5 |
ANN: Exam 1 over 2.1-2.6 is coming up. It will be held Tues., Feb. 11. It will be paper-and-pencil in the classroom. Bring your notes, homework notebook, and calculator. You will see that 2.6 HW (Homework) in MML will come due Monday even though that is the day we will finish the section's notes. Be aware of that quick turnaround. ANN: Also due soon in MML, Chapter 3 Skills Check will be due midnight, Feb. 11 to help prepare for chapter 3 notes the next day. In class, we worked on the Class Notes for 2.5, finishing them. We then started the Class Notes for 2.6, getting through the informal and formal definitions of continuity as well as drawing a lovely little picture for our next example. I will collect the 2.5 worksheet Limits as x approaches infinity 2 Thursday. |
Feb. 6 |
ANN: Exam 1 over 2.1-2.6 is coming up. It will be held Wed., Feb. 12. [After class, and seeing how much more 2.6 we have to go, we need to move the exam back one day. Wednesday is the new day. I have emailed students.] It will be paper-and-pencil in the classroom. Bring your notes, homework notebook, and calculator. You will see that 2.6 HW (Homework) in MML will come due Monday even though that is the day we will finish the section's notes. Be aware of that quick turnaround. ANN: Also due soon in MML, Chapter 3 Skills Check will be due midnight, Feb. 11 to help prepare for chapter 3 notes the next day. In class, I collected the 2.5 worksheet Limits as x approaches infinity 2. We worked on the Class Notes for 2.6, getting through identifying points of discontinuities, types of discontinuities, algebraic analysis of limits, theorems 2.9-2.12, and an example of theorem 2.12. |
| ANN: Exam 1 over 2.1-2.6 is coming up. It will be held Wed., Feb. 12. [I moved it back one day last Thursday.] It will be paper-and-pencil in the classroom. Bring your notes, homework notebook, and calculator. You will see that 2.6 HW (Homework) in MML will come due Tuesday even though that is the day we will finish the section's notes. Be aware of that quick turnaround. I have not made those changes yet to MML but will tomorrow morning. ANN: Also due soon in MML, Chapter 3 Skills Check will be due midnight, Feb. 12 to help prepare for chapter 3 notes the next day. In class, we worked on the Class Notes for 2.6, getting through left and right continuity, continuity on an interval, and Theorem 2.13 with examples. | |
Feb. 11 |
ANN: Exam 1 over 2.1-2.6 is coming up. It will be held Wed., Feb. 12. It will be paper-and-pencil in the classroom. Bring your notes, homework notebook, and calculator. You will see that 2.6 HW (Homework) in MML will come due tonight even though that is the day we will finish the section's notes. Be aware of that quick turnaround. ANN: Also due soon in MML, Chapter 3 Skills Check will be due midnight, Feb. 12 to help prepare for chapter 3 notes the next day. In class, we finished the Class Notes for 2.6. Today, we looked at the continuity of trig functions, exponential and log functions, and inverse functions. We also explored the Intermediate Value Theorem. |
Feb. 12 |
No class, snow day. Due dates will get pushed back. |
Feb. 13 |
ANN: In MML, Chapter 3 Skills Check will be due Sunday, Feb. 16 at midnight to help prepare for chapter 3 notes the next day. In class, we took Exam 1. If you missed, expect an email from me. |
| ANN: Exam 2 will cover chapter 3. In class, we started the Class Notes for 3.1, getting through an introduction of the derivative as an instantaneous rate of change found with a limit, with an example (#13) including finding the equation of the tangent line at a given point. We completed another example (#16) as well. We started the alternative definition on page 135 and will need to finish that next time. The example numbers are from the homework given in the textbook. | |
Feb. 18 |
We Zoomed class due to snow day. In class, we finished the Class Notes for 3.1. This copy of the notes will differ from what was done in class but is equivalent. |
Feb. 19 |
We Zoomed class due to snow day. In class, we started the Class Notes for 3.2. |
Feb. 20 |
Class cancelled due to teacher illness. |
| We finished the Class Notes for 3.2. (This copy of the notes will differ from what was done in class but is equivalent.) I handed out the 3.2 worksheet Differentiability and continuity to be done for next time. We started the Class Notes for 3.3. I handed out the first page of the Paul Dawkins (derivatives) handout http://tutorial.math.lamar.edu/pdf/Common_Derivatives_Integrals.pdf. On this handout, we circled the formulas that are introduced in the section. (It's the first four and the one (near bottom) for the derivative of the function y = e^x.) We got through three examples, numbers 21, 23, and 28. | |
Feb. 25 |
I collected the 3.2 worksheet Differentiability and continuity. I handed out a worksheet that will help you internalize the formulas for chapter 3. It is Differentiation Rules Worksheet and it will not be collected. In class, we completed the Class Notes for 3.3. |
Feb. 26 |
We worked on the Class Notes for 3.4, getting through the product rule with examples and starting some examples for the quotient rule. Here is the partial set of notes. I gave out a 3.4 worksheet Product and Quotient Rules which will be collected Monday. |
Feb. 27 |
ANN: The last day for late MML work from chapters 1-3 is March 31. ANN: I did give a trig handout to students. Do not forget about it. In class, we finished the Class Notes for 3.4. We then started the Class Notes for 3.5. We only got through writing down theorem 3.10 and doing one example, number 11 from the book. |
| ANN: I had to change the MML due date for Section 3.5 homework; it is now due next Monday. In class, I collected the 3.4 worksheet Product and Quotient Rules. (I had emailed you about number 1 on this worksheet as it needed the chain rule, which we have not covered. I gave you the needed derivative to complete the question.) We finished the Class Notes for 3.5. We then started the Class Notes for 3.6, only getting the introduction started. | |
Mar. 4 |
We worked on the Class Notes for 3.6, getting through numbers 15 and 25 as examples. We will finish next time. |
Mar. 5 |
ANN: Exam 2 will cover 3.1-3.9 and is set for next Thursday, March 13. ANN: You can do late MML work for half credit. However, there is a strict deadline of March 31 after which you may not do any work from chapters 1-3. In class, we finished the Class Notes for 3.6 and then started the Class Notes for 3.7. We got through an introduction and a first example using the chain rule. |
Mar. 6 |
ANN: Exam 2 will cover 3.1-3.9 and is set for next Thursday, March 13. You can use your class notes, homework notebook, and calculator. ANN: In MML, Chapter 4 Skills Check will be due Sunday, March 23 to prepare us for Monday's class. In class, we almost finished the Class Notes for 3.7. We got through everything but our last example which is an application. These notes here are the partial 3.7 notes we have so far. |
| ANN: Exam 2 will cover 3.1-3.9 and is set for Thursday, March 13. You can use your class notes, homework notebook, and calculator. There are curtailed due dates since the test is Thursday and normally the MML homework would be due next Monday. ANN: In MML, Chapter 4 Skills Check will be due Sunday, March 23 to prepare us for Monday's (after Spring Break) class. In class, we finished the Class Notes for 3.7. We then started the Class Notes for 3.8. We got through a couple of examples. We are now in the middle of doing number 32 which uses both the product rule and chain rule. | |
Mar. 11 |
ANN: Exam 2 will cover 3.1-3.9 and is set for Thursday, March 13. You can use your class notes, homework notebook, and calculator. There are curtailed due dates since the test is Thursday and normally the MML homework would be due next Monday. ANN: In MML, Chapter 4 Skills Check will be due Sunday, March 23 to prepare us for Monday's (after Spring Break) class. ANN: The last day for late MML work from chapters 1-3 is March 31. ANN: I reminded students of the late paper worksheet policy as well. If you turn in a worksheet after I collect it at the beginning of class, the grade will start at 8/10 after a late penalty. If you are absent when a worksheet is due, email me a picture of it to get full credit and then turn in the paper when you return. Know that the last day to turn in late paper worksheets from this unit (meaning chapter 3) is exam day. In class, we finished the Class Notes for 3.8. We started the Class Notes for 3.9. We got through a brief introduction and an example. |
Mar. 12 |
ANN: Exam 2 will cover 3.1-3.9 and is set for Thursday, March 13. You can use your class notes, homework notebook, and calculator. There are curtailed due dates since the test is Thursday and normally the MML homework would be due next Monday. ANN: In MML, Chapter 4 Skills Check will be due Sunday, March 23 to prepare us for Monday's (after Spring Break) class. We finished the Class Notes for 3.9. |
Mar. 13 |
[No school March 17-22 for Spring Break.] We took Exam 2. If you missed, look for an email from me. |
| ANN: Exam 3 will cover 4.1-4.9 and be sometime at the end of April. In class, we started working on the Class Notes for 4.1. We got through our major definitions and theorems. We will outline a procedure for finding the abolute extrema and do examples next time. | |
Mar. 25 |
ANN: Calculus II is offered at LC in the summer but not in the fall 2025. Plan your classes accordingly. In class, we finished the Class Notes for 4.1. |
Mar. 26 |
We started the Class Notes for 4.2. We covered Rolle's Theorem with two examples. We then started our work on the Mean Value Theorem with its statement and an example. I handed out problem #42 photocopied from the book but we did not start the problem. We will continue next time. |
Mar. 27 |
We finished the Class Notes for 4.2. We then started the Class Notes for 4.3. I handed out part of a handout from Paul Dawkins that gives lots of good information; pages 4 and 5 of this handout gives us a write-up of the rules from this section. The first two pages were already given out for limits. Some of the other pages are a nice overview of what we have studied. In class, I handed out the first six pages of his cheat sheet. |
| ANN: Calc II is offered in the summer but not in the fall. ANN: IDOT is hiring Engineering Technicians from the student body. More information can be gotten from emailing Jennifer.Boster@Illinois.gov or visiting their Commons Cafe table on April 3 anytime from 10 am - 2 pm. In class, we worked through a 4.1 homework problem (4.1.35) from a student question and we worked on the Class Notes for 4.3. We covered increasing and decreasing functions with two examples. We started discussing minimums and maximums. | |
Apr. 1 |
We worked on the Class Notes for 4.3. We covered local mins and maxes, the first derivative test, and theorem 4.9 with some examples. |
Apr. 2 |
In class, we worked on the Class Notes for 4.3. We covered an example for theorem 4.9. We went on to discuss concavity and inflection points with an example. We started an example that has a nasty derivative to find. You will see one very much like it in the MML homework. |
Apr. 3 |
ANN: We have been doing well. Keep up the good work and work hard to the end. Spend real time on the homework and work for understanding. We are getting to more difficult material that demands more attention. In class, we finished the Class Notes for 4.3. We then started the Class Notes for 4.4 which will have three examples. We did a quicky example and then started a more extensive example of graphing a polynomial function by hand. We are partly through that and will continue next time when we also get an example of a rational function. |
| We almost finished the Class Notes for 4.4. We will get through a total of three examples. We have to finish up the last tomorrow. | |
Apr. 8 |
We finished the Class Notes for 4.4. We then started the Class Notes for 4.5. We got halfway through an example (number 17) and will continue next time. I handed out the Guidelines from page 282 as they make a nice plan of attack. |
Apr. 9 |
We worked on the Class Notes for 4.5, completing number 17 and getting a good start on 30 (number from textbook). We will continue next time. |
Apr. 10 |
We finished the Class Notes for 4.5, adding number 48 to our notes. |
| We worked on the Class Notes for 4.6. We got through an introduction of the idea of linear approximation with the definition of the function L(x). We worked an example (number 20), looking at it more deeply than the instructions needed to understand our estimate better and how the concavity of f(x) matters. We are working on how the absolute value of the second derivative at x=a will tell us how good of an estimate we got. We will continue next time. | |
Apr. 15 |
We almost finished the Class Notes for 4.6. We discussed how the absolute value of the second derivative is related to error, estimating change with linear approximation, and wrote most of what we need for differentials. We will complete a small example next time and we'll be done with 4.6. |
Apr. 16 |
We finished the Class Notes for 4.6. We then started the Class Notes for 4.7. We got through the introduction of l'Hopital's Rule (for the indeterminate form 0/0) with its proof and a couple of examples. One example had us perform l'Hopital's Rule twice (joy!). We were able to start the discussion of the indeterminate form infinity/infinity with an example. We will check that one by graphing next time. |
Apr. 17 |
We continued to work on the Class Notes for 4.7. We looked through examples for the indeterminate forms "0 times infinity" and "infinity minus infinity". We went on to the forms 1^infinity, 0^0, and infinity^0. We started this discussion but the examples will wait 'til next Monday. I will be posting (with these notes) other annotated examples I did but do not have time to cover in class. |
| NN: Exam 3 over 4.1-4.9 is set for Monday, April 28. You will be allowed your full set of notes as always. [I did not mention this in class but sent an email right after class.] In class, we finished the Class Notes for 4.7. I am also posting a few extra 4.7 examples that I did but were not included in the lesson. We started the Class Notes for 4.8 by introducing the topic and looking at the pictures on page 313 and copying the procedure on page 314. We will continue next time. | |
Apr. 22 |
We continued our work on the Class Notes for 4.8. We did a few examples, using online calculators for the repetitive calculations. We did go through an example of finding the formula for "x sub (n+1)". However, if you use an online calculator to find the root, you likely do not need this. Certain MML questions will ask for the formula directly. We did examples showing how to find roots, local extrema, and the intersections of two functions. Next time, we will wrap up 4.8 with a discussion of the method's pitfalls. We have already seen two pitfalls so that will not take long. We did use an online calculator ( https://www.desmos.com/calculator/pjxjvdbt7i) for most calculations. |
Apr. 23 |
A substitute finished up the Class Notes for 4.8 and taught the first part of section 4.9. You covered an introduction to antiderivatives with rules and exmaples. |
Apr. 24 |
[April 25 is the last day to withdraw and receive a grade of W.] ANN: Exam 3 will be held next Monday, April 28. It will cover 4.1-4.9. In class, we worked through the rest of the Class Notes for 4.9. We covered an introduction to differential equations and an example involving the motion of an object (position, velocity, and acceleration). |
| We took the exam. If you missed, look for an email from me. | |
Apr. 29 |
I had to cancel class for personal reasons. |
Apr. 30 |
ANN: Exam 4 over 5.1-5.5 is set for Thursday, May 15 (with May 16 being the end of the semester). In class, we started the Class Notes for 5.1, getting through the idea of approximating the area under a curve for a function with several examples. We just got done writing the Riemann Sum definition from page 341 and will continue from there next time. |
May 1 |
We finished the Class Notes for 5.1. We completed the 5.1 worksheet Riemann Sums as an in-class activity. We then covered most of a packet of Notes I got from another professor. This completes our lesson on 5.1. |
| NN: Exam 4 will cover 5.1-5.5 and is scheduled for Thursday, May 15. You will be allowed your full set of notes as always. In class, we worked on the Class Notes for 5.2 (written by Nikki Munden). We covered net area with an example and the definite integral and its connection to net area. For this second topic, we started an example (#32, page 365) but will need to finish next time. | |
May 6 |
ANN: Exam 4 will cover 5.1-5.5 and is scheduled for Thursday, May 15. You will be allowed your full set of notes as always. ANN: You can still work on late MML work for half credit through May 16. In class, we almost finished the Class Notes for 5.2. We finished the example we were on last time by doing the right Riemann sum. We then covered more examples for definite integrals. We will do a final example next time that uses geometry to find the value of an integral. I gave out pages 7 and 8 of the Paul Dawkins Calculus Cheat Sheet (link) for 5.2 and 5.3. |
May 7 |
We finished the Class Notes for 5.2. We then started the Class Notes for 5.3. We covered the introduction of the area function with a few examples and a good example of finding an area under a function by using geometry (area of a trapezoid). This example blew our minds as it revealed the Fundamental Theorem of Calculus. We then read over the Fundamental Theorem of Calculus and did an example using it to find an integral. |
May 8 |
ANN: Exam 4 will cover 5.1-5.5 and is scheduled for Thursday, May 15. You will be allowed your full set of notes as always. ANN: You can still work on late MML work for half credit through May 16. In class, we finished the Class Notes for 5.3. We then started the Class Notes for 5.4. We covered Theorem 5.4 for even and odd functions and a couple of examples. |
| ANN: Exam 4 will cover 5.1-5.5 and is scheduled for Thursday, May 15. You will be allowed your full set of notes as always. ANN: You can still work on late MML work for half credit through May 16. In class, finished the Class Notes for 5.4. We then started the Class Notes for 5.5. We covered the main theorem which shows us how to use the Chain Rule to find complicated looking integrals. I personally do not think about these problems how the theorem states it. I think about finding inside the integrand (thing I am supposed to take the integral of) one bit I can let be u such that the remaining bit of the integrand is the derivative of u (or something related). We are covering indefinite integrals so remember to attach a constant to the end of those answers. We did a few examples. | |
May 13 |
ANN: Exam 4 will cover 5.1-5.5 and is scheduled for Thursday, May 15. You will be allowed your full set of notes as always. ANN: You can still work on late MML work for half credit through May 16. In class, we worked on the Class Notes for 5.5, completing more examples. |
May 14 |
ANN: Exam 4 will cover 5.1-5.5 and is scheduled for Thursday, May 15. You will be allowed your full set of notes as always. ANN: You can still work on late MML work for half credit through May 16. In class, we wrapped up the Class Notes for 5.5. We did example 10 differently than I did earlier (on my own) and I showed my work for a slightly different method. The point is that you can define differently than what MML suggests and often you are fine. Both methods are shown in the posted notes. |
May 15 |
[Friday, May 16 is the last day of the semester.] |