Mat 222 Daily Log

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Combined File of Test/ Quiz questions - This is the BEST place to start to prepare for the piece of the final on Monday, May 6th!

Handed out the Take Home part of the Final on Chapter 11, and spent some time going through what was being asked for each of the questions.

Collected the Graded work on chapter 8.

Finished the exercise we had started in class.  Showed how this problem related to the take home questions.

 Began chapter 11.  Discussed what a Differential Equation was, and how we could test to see if a specific function was a solution to a differential equation.

Handed out Graded Work on Chapter 8.

Finished section 8.2 - Did a problem of building a set of semicircles on a particular region, and finding the volume of that solid.  Also developed the concept of arc length - developing the formula with the class - and then applying the formula for a specific exercise.

Handed out the Practice Exercise Sheet for Unit 5.  Handed out End of Semester Notes.

Continued work on section 8.2.  Did another exercise involving washers - revolving around a horizontal line.

Had students complete the Survey of Teaching forms at the beginning of class.

Students worked on Graded Work 6 in the lab.

Extended the due date for Graded Work 6 until Monday, 4/22.

Began section 8.2.  Worked on several examples, showing how to find volumes of solids of revolution by the disk method.  Began one problem that involved a washer.  Will complete that problem on Friday, as well as begin the problems dealing with arc length.

Covered section 8.1 by doing several exercises.

Students should work on project.  Teacher out at wedding.

Students should work on project.  Teacher out at wedding.

Handed out Mathematica instructions for creating Taylor Series and working with them to identify good intervals where they gave us good approximations for the function.

Handed out Graded Work 6.  Students should be working on this material during class time while I am away.

Students spent the remainder of the class working on the quiz.

Discussed section 10.2 and 10.3 more, showing a demonstration on mathematica that helped us see the error in the TP approximation compared to the function value.  Showed how to determine if a Taylor Series converges or diverges by using the ratio test.

Discussed Sections 10.1 and 10.2, showing students the pattern for how you generate a Taylor Series centered at a.  Worked through exercise 2 from section 10.2.  We will continue to discuss Taylor Series on Monday. 

Quiz/Test on Chapter 9 will be on Wednesday - worth 60 points.  It will contain 6 problems, a different type of test for each problem.  We have covered 7 types of test.  The problems will be in random order, not in the order that we covered the tests.

Finished discussing exercise 12, showing how to prove that the series converged for a finite interval.

Gave students time to work together on the sheet of series.  Handed out my solutions to these problems.

Discussed Power Series.  Emphasized how power series differed from our numerical series.   Handed out a sheet that showed tables for Exercise 12.  Focused on 3 specific values for x, and showed clear evidence of convergence for two of them, though the power series clearly converged more slowly for one point than the other.  For the third x value, the series clearly diverged. 

Test on Chapter 9, sections 1 - 4 will be next Wednesday.

Day 37:  Thursday, 3/28

Started section 9.4.  Handed out a gold summary sheet of the Convergence Tests.  Discussed the series comparison test, and the limit comparison test.

Day 36:  Wednesday, 3/27

Collected Graded Work 6.  Finished section 9.3.  Emphasized the requirements for the integral test. Did a number of examples.

Day 35:  Monday 3/25

Discussed section 9.3.  Worked through the harmonic series, and showed how you can compare to an improper integral that diverges.  Spent a lot of time helping students see how they had to thoughtfully read the book to pick up some of the essential details.

Day 34:  Friday, 3/22

Handed back GW 4 and partial answers.  Discussed question 3 in some detail.

Answered some questions from practice exercises in section 9.2.  Lively discussion of # 17!   Will start section 9.3 on Monday.  Students should make sure they are working on graded work and practice exercises from 9.1 and 9.2.

Day 33:  Thursday, 3/21

Students worked on GW 6.

Day 32:   Wednesday, 3/20

Gave students a chance to review and redo the mathematica part of graded homework for Friday, in case the feedback from the test would influence their explanations to the homework.

Continued discussion of Geometric series.

Day 31:  Monday, 3/18

Collected GW 4 & 5.  Handed back tests and answers.

Began discussion of section 9.2:  Geometric Series.

Handed out GW 6

Day 30:  Friday, 3/8

DCC cancelled afternoon classes due to weather.

Day 29:  Thursday, 3/7

Gave students time to work on GW 4 & 5.  Circulated and helped students as they had questions.

Day 28:  Wednesday, 3/6

Test on Chapter 7 material.

Day 27:  Monday, 3/4

Began Chapter 9.  Discussed 9.1:  Sequences.  Pointed out some key ideas in the text book, and then worked on a number of examples.

Handed out Practice Exercises for Unit 4. 

Day 26:  Friday, 3/1

Reviewed material on Improper Integrals by doing several examples.

Changed test to Wednesday!  GW 4 will be ALL due on Friday, 3/8.   We will start Chapter 9 on Monday.

Day 25:

Thursday 2/28

Worked in computer room on GW 4.  Showed students how to work with tables in the most effective way in terms of presenting their work in a professional way.  Created the first set of tables together with the class.

Students continued work on the second set of tables.

Day 24:  Wednesday 2/27

Worked through one of the practice exercises from section 7.7.

Answered some other conceptual questions that students had about the material.

Talked about the composition of the test on Monday.

Handed out GW 4 & 5.  Spent some time talking about what I was looking for.  Please notice that the material is due in two pieces.  Only question 4 must be done using mathematica.

Worked on another problem from section 7.8.

Day 23:  Monday 2/25

Finished working on the third scenario for the general improper integral below.

Walked through section 7.8, asking students to pay particular attention to key information.

Worked on some examples from section 7.8.

Encouraged students to begin working on discovering the patterns of convergence and divergence of the integral from 0 to 1 of 1/x^p.  This proof will follow the same type of pattern as our work for the integral from 1 to infinity.  There will again be 3 cases to consider.  This will be part of the next turn in homework assignment.

Day 22:  Friday 2/22

Answered some questions from section 7.7.

Completed # 18 from section 7.7 - which was an improper integral that diverged.

Began working through Example 3 from section 7.7 to consider what happens to the improper integral from 1 to infinity of 1 / x^p.  Showed that there were three distinct cases.... when p > 1, when p < 1 and when p = 1.  We got through the first two cases, and will finish this work on Monday.

Day 21:  Thursday 2/21

Began section 7.7.  Walked students through the section pointing out some very important ideas.  Students should take additional notes from the book, as the work I will do in class will be to clearly demonstrate the core ideas - but I will not be writing out all the the definitions and background material.

Worked on two specific exercises # 6 and # 16.  #6 was improper because one of the limits was infinite.  # 16 was improper because the integrand was boundless at one of the endpoints.  We will continue work with these ideas tomorrow.

Day 20:

Wednesday, 2/20

Handed back tests and answer key.

Handed out Practice Exercises for Unit 3

Reviewed material we had covered for section 7.5 on approximation techniques.  Continued to work with this material.  Did an example from section 7.5 and and example from 7.6.

 Day 19: Friday, 2/15

 Test # 1.

Day18:

Thursday

2/14 

 Spent the class reviewing by answering questions students had on practice exercises.  Test # 1 tomorrow.

Day 17:

Wednesday

2/13

Answered several questions on the practice exercises.

Presented the core ideas in section 7.4 on the use of Left and Right hand rectangle sums, Midpoint Rectangle sums, and sum of areas of trapezoids.  Discussed which were overestimates and which were underestimates, and  what controlled that - i.e. increasing, decreasing, or concavity.

Showed how to use the Integral program on the calculator to create the results for these rules.

Day 16:

Monday

2/11

Handed back GW 3 with answers to the written components (pink).

Handed out Practice Exercises for Unit 2. 

Notice, there will be a test on Friday that covers chapt 6 and chapt 7 sections 1, 2, 4.

Answered some questions on practice problems.

Discussed Integration by partial fractions, showing two examples:  One with 2 linear factors in denominator, and one with a linear factor and a quadratic factor.

Day 15:

Friday

2/8

Class cancelled due to impending snow storm.

Day 14:

Thursday

2/7

Collected GW 3.

Began section 7.2 - Integration by Parts.  Showed how the formula was developed by working from the derivative of a product.  Showed the short cut form.

Did problems 10 and 4.  Then showed students how to access Wolfram Alpha, and how they could use this with the "Show Steps" feature to help them work their way through integration problems that caused them trouble.

We will do a problem with a "repeated integral" in the next class.

Day 13:

Wednesday

2/6

Spent some time reviewing some of the questions that students had asked me during my office hours in relation to the turn in assignment which is due tomorrow.

Answered several questions on the practice exercises from 7.1, pointing out that not every problem that was presented could be done by substitution, and that students needed to be aware that they might have to use other approaches, including simplifying the integrand before doing the integration.

Finished section 7.1 - discussed two different approaches to completing a definite integral problem when using substitution.  One approach changes to u, and changes the limits of integration accordingly.  The problem is then completed using the variable u.  The other approach uses u to help find the antiderivative, but then reverts to the original variable, and uses the original limits of integration.

Students should work on exercises 47 - 53 odd, and then 55, 59, 63, 67.  I will get the next practice exercise sheet out as soon as possible.

Day 12:

Monday

2/4

Finished discussing # 30 from section 6.4.

Began section 7.1 - Integration by substitution.  Pointed out key ideas in the book, and discussed how the book structured the examples, giving the first few worked out by trial and error, and then honing in on the actual technique of substitution.

Students should work on exercises 3 - 39 odd.  We will continue with this section on Wednesday.

Day 11:

Friday

2/1

Went over the GW 3 sheet, making some points to students about what level i was looking for, and where on the sheet they would be using the capabilities of Mathematica other than as a word processor.

Worked on section 6.4, doing problems 10, 16, and almost finishing 30.  I will put the finishing touches on #30 on Monday, and will be starting Chapter 7.

Day 10:

Thursday

1/31

Quiz on sections 6.1 and 6.2.

Handed out GW 3, and reminded students that they should first work through Section 17 of Part 3 Mathematica instructions before trying to work on the table asked for on the assignment.

Day 9:

Wednesday

1/30

Handed back GW 2 with answers.  Discussed what students should do each time they get a graded assignment back.  If anyone has questions on their paper, please come and talk to me about it as soon as possible. 

Handed out Part 3 mathematica instructions, and asked students to make sure to bring the packets with them to lab tomorrow.  After the quiz, students should go through section 17 of these instructions in preparation for the next graded homework assignment.

Quiz tomorrow will cover sections 6.1 and 6.2.  The practice exercises for Success Strategies will NOT be due tomorrow.  I will let you know a future date for that material, since we are not where I predicted we would be because of the storm on Monday.

Answered some questions on practice homework.

Began section 6.4.  Did exercise 6.  Will finish the discussion of this section on Friday.

Day 8:

Monday

1/28

Answered some questions on 6.2.  Spent time doing work with some of the definite integrals in this section, emphasizing the notation used, and need to make sure that parentheses were used appropriately.  Worked on 3 specific practice problems.

Reminded students that there was a quiz on Thursday on sections 6.1 and 6.2.

Handed out attendance cards with grades indicated for GW1 to make sure that all students agreed with their grade.  Asked students to write their grade on the back of their Success Strategies grade sheet ( turquoise).

Day 7:

Friday

1/25

Answered some questions on section 6.1 practice problems.

Discussed the concept that a general antiderivative or indefinite integral resulted in a family of functions that were only different by the constant.

Went over how to find the antiderivative of a power function where the exponent was not equal to -1.

Discussed the situation where the exponent was -1, so the integrand would be 1/x.  Showed that the antiderivative would be ln |x| + C.

Students should read the material in 6.2 and work with the practice exercises from this section.

Day 6:

Thursday

1/24

Collected GW 2.

Worked on section 6.1.  Talked about the examples that were in the text book, pointing out some specifics that students should focus on as part of their work for this material.

Worked through Exercises 4, 6 and 10 in class, emphasizing what the examples were demonstrating, how they were similar and how they were different.  Students should work on some of the practice exercises from the Practice Exercises for Unit 1 sheet for tomorrow.

Day 5:

Wednesday

1/23

Answered questions on GW 2. 

Worked on problem 4 from the review sheet on integrals. 

Day 4:  Friday

1/18

Reviewed the last question on the Derivative Review Material from the first day.  Handed out a Review Sheet on Integration, and gave students time to discuss some of the material together.  Reviewed questions 1 and 3 together as a class. 

Students should work on 3 things before the next class:  1) Continue work on Graded Work 2.  2) Complete problem 4 on the review sheet on Integrals, and 3)  Work on the specific exercises listed on the Practice Work for Week 1 sheet.  On Wednesday, I will answer any questions on review material, and also begin Chapter 6.

Day 3:

Thursday

1/17

Meet in Lab.  Handed out Graded Work 2 (Green).  Handed out Part 1 and Part 2 of Basic Instructions for Mathematica. (Extra copies in bin outside my door.)  These instructions have been significantly revised from the ones you may have received last semester, so you should use these as reference.

Gave students time to work on Graded Work 2 in the lab.  The intent of the assignment is to have you review key ideas from Calculus 1 while also honing your skills on Mathematica.

Day 2:

Wednesday 1/16