Mat 222 Daily Log

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Day 49:  Thursday

Have students work on directions for parametric curves and arc length in class using Mathematica Directions.  Hand out take home problems on work and arc length.

Day 48:  Wednesday, 4/16

Review for test.

Day 47:  Monday, 4/14

Had students do course evaluations.

Did a third type of problem on work.  Test will be Thursday.  Spent some time talking about what the test will cover.

Day 46:  Friday, 4/11

Students worked on problems from Work, as well as continued work on other material in Chapter 6.

Day 45:  Thursday, 4/10

Did two complete problems for Work (section 6.6)

Day 44:  Wednesday, 4/9

Handed back take home test on power series, and spent some time discussing some key elements of the work.

Had students work together on some problems involving volumes of revolution as well as arc length.  Handed out answers to the problems at the end of class.

Day 43:  Monday 4/7:

Collected GW 7 on Taylor Polynomials.

Presented section 6.4 - arc length.  First talked about parametric equations.  Then developed the length of a typical line segment by calling on local linearity, and showing that change in the output variable = derivative * change in input variable.  We used this idea with x = f(t) and y = g(t) to create a Riemann Sum for the lengths of the line segments.  Set the integral up for problem 15, after showing students how to get the graph for the function on their calculators.

Day 42:  Friday, 4/4

Presented section 6.3 - Shells.  Emphasized that we would be using shells if we made our typical slice parallel to the axis of revolution.  Have to switch our perspective to finding the surface area of a cylindrical shell.... which would be 2*pi*r*h, and then multiply this by the width to get the volume of a typical shell.  Emphasized that r and h had to both be given in terms of the same variable.  Worked through 2 examples.

Day 41:  Thursday, 4/3

 Answered some questions for the Taylor Polynomial project. 

Continued work on section 6.2.  Did an example of using washers.

Day 40:  Wednesday, 4/2

Began section 6.2 - volumes of revolution using washers and disks.  Emphasized what would lead you to use one of these methods.... having a typical slice be perpendicular to the axis of revolution.  If the axis is a boundary for the region, we would use disks.  If the axis is not a boundary, we would use washers, where we subtract the area of the inner disk from the area of the outer disk, so that the surface area we are considering is in the form pi(outer radius squared - inner radius squared).   Did an example of disks.

Day 39:  Monday,3/31

Collected the Take Home Test on Power Series.  Began Chapter 6.  Discussed the two orientations for our typical rectangle when considering the area between two curves.  Set up a particular situation, and worked through the integration.

Day 38:  Friday, 3/27

Finished discussion on Taylor Series by looking at a function that does not have an elementary derivative, showing how we could develop the taylor series quickly by using a known pattern, and then discussing how we could use Taylor Polynomials to help us determine the value of a definite integral for the original function.

Day 37:  Thursday, 3/26

Gave students time to work on Mathematica - working with material on Taylor Polynomials.

Handed out GW 7

Day 36:  Wednesday, 3/25

Talked more about the assignment on Power Series.

Reviewed key ideas about Taylor Series.  Worked with students to develop the Taylor Series for Cos (x) at 3pi/2 by hand.

Handed out information on generating Taylor Polynomials with Mathematica, and talked about why we might want to center the Taylor Polynomial at a particular center (like 3pi/2) if we were interested in approximating a particular function value.

Day 35:  Monday, 3/24

Answered questions about Power Series project.

Showed how we could develop the Taylor Series for Cos x by taking the derivative of the Taylor Series for Sin x.  Developed the Taylor Series for e^x centered at a = 3. 

Day 34:  Friday, 3/21

Began work with Taylor Polynomials.  Developed the procedure for developing a Taylor Series.  Worked through this process for e^x and sin(x).  Showed how to develop the summation formula for each of these series.

Day 33:  Thursday 3/20

Collected GW 6 if students felt they had done a sufficient job with it.  I am going to count this as a quiz...rather than giving the same type of questions as a take home.  Students could elect to continue refining their work... and hand the papers in to me tomorrow.

Handed out a yellow sheet that established a process for considering power series convergence using Mathematica.  Discussed the results in detail, and then gave students time to work on Mathematica to create the material.

Handed out Take Home Test on Power Series.  This is to be done by individuals, with no help from others in the class, or in the math lab.

Day 32:  Wednesday 3/19

Talked about the endpoints for the power series we worked with on Monday.  Completed another example, and handed out a Mathematica worksheet on Power Series to help in exploring the concept of convergence over an interval.

Day 31:  Monday 3/17

Handed back GW 5.  Spent a little time talking about the answers that I handed out as an example of what I was looking for.

Began section 8.5 - Power Series.  Did one complete example, leaving the test of endpoints to the students.  We will pick up from there on Wednesday.  Students should focus their energy on GW 6.

 Day 30:  Friday 3/7  Finished section 8.4 by doing a couple of examples.  Handed out GW 6.  Students should enjoy their break, but also spend some time working on material with series.
 Day 29:  Thursday 3/6  Started discussing section 8.4.   Covered alternating series and did two examples.
 Day 28:  Wednesday 3/5  Asked students to work on Practice Exercises.  I had to be at a mediation session for part of class.
Day 27:  Monday, 3/3  Worked more on section 8.3.  Discussed the p series, and showed an example using the comparison test.
Day 26:  Friday, 2/28

Answered a number of questions from material we had covered earlier.

Told students to look at GW 5 at link from yesterday.  I added a new section in that document that shows how to get the first n terms of a series written out.  This will be useful in terms of explaining the behavior of some of the series in GW 5.  I STRONGLY suggest that students incorporate this into their work.

Began section 8.3, talking about the integral test.  Had a lively discussion of why you needed to show your sum was above a known diverging integral  to say the series diverged, and below a known converging integral to say the series converged.

Handed out the Practice Exercise Sheet for Unit 2.

Day 25:  Thursday, 2/27

Worked in lab on GW 5 .  Helped students see how to work with summation notation.  Worked with them to understand how to look at tables of partial sums and think about discussing what they see.

Day 24:  Wednesday, 2/26

Answered questions (LOTS of them!) about what we had covered so far.  Worked through one of the practice exercises on a telescoping series.

Day 23:  Monday, 2/24

Continued with section 8.2, showing a telescoping series, as well as the harmonic series.  Talked about the fact that if a series converges, the terms of the underlying sequence MUST go to 0.  However, if the terms of the underlying sequence DO go to 0, the series does not necessarily converge.  

Emphasized the notation we had encountered so far, and worked with students to understand the differences.

Day 22:  Friday, 2/21

Collected GW 4. 

Continued with Chapter 8.  Started section 8.2, and distinguished between a sequence and a series.  Focused on the notation.  Worked with several examples of series, and worked to determine whether they converged or diverged.  Again, it is essential that students be reading the book to make sure they are reading and writing the theorems that we incorporate in our discussion in class.

Developed the pattern for a geometric series, and discussed when it converged, and when it diverged. 

We will continue with this work next week.

Day 21:  Thursday, 2/20

Began Chapter 8.  Discussed sequences, noting that students MUST be reading the book to process some of the theorems and definitions.  My class approach will be to do as many examples as I can,  while integrating the core ideas from the theorems...but students should be writing out the theorems and definitions in their notes.  The notation is essential.

Did a number of examples of finding patterns for sequences, and determining whether sequences converged or diverged.

Day 20:  Wednesday, 2/19

Test on integration techniques and improper integrals.

Day 19:  Friday, 2/14

No class.  Snow Day.  Students should be studying for test next week, and working on the GW.

Day 18:  Thursday, 2/13

No class.  Snow Day.  Students should be studying for test next week, and working on the GW.

 Day 17:  Wednesday, 2/12

 Handed back quiz.  Results were not very good.  Will give a test on Wednesday, 2/19 that covers this same material, and includes 3 additional questions:  one on partial fractions, one on the concept of improper integrals as well as the proper notation, and one that students have to complete to decide if it diverges or converges.

Handed out GW 4.  This assignment should help students understand that some improper integrals that appear in the same form converge while others diverge, and should emphasize which behavior in each manner.  (The assignment at the link is the slightly modified assignment from the paper copy handed out in class.  Students should address the extra parts in this link.)

Day 16:  Monday, 2/10

Worked on several examples where the integrand was boundless.  Again, emphasized the notation, and how to make final conclusions.

Day 15:  Friday, 2/7

Did another example of an improper integral with one of the limits of integration being boundless. 

Gave most of the period for the Quiz.

Day 14:  Thursday, 2/6

Started section 5.10:  Improper Integrals.  Explained the two types of scenarios:  One or more limits of integration are boundless, or the integrand is boundless at some one of the limits, or at some point within the interval.

Did an example of a function where one of the limits was boundless.  Emphasized the notation.

Day 13:  Wednesday, 2/5

Snow day.  DCC canceled all classes.

Day 12:  Monday, 2/3

Continued work with Partial Fractions, and reviewed some of the key ideas with this technique.  Worked out a problem with powers of trig functions that required making use of trig identities.  These can be time consuming, and can take a while to figure out a pathway through.  It is important for students to understand the historical significance of this type of work, however, Computer Algebra Systems now make it easy to obtain answers quickly.

Downgraded the test on Friday to a quiz that will cover sections 5.4, 5.5 and 5.6.

Day 11:  Friday, 1/31

Collected GW 3.

Worked on section 5. 7 - worked on technique involving partial fractions.  Got all the way through an example where we have only non repeating linear factors in the denominator.  Began a second problem where we have two quadratic factors.

Showed students where vital information in the textbook was for the different cases that could arise.  Emphasized that they need to be reading the book!

Announced test on Friday.

Day 10:  Thursday, 1/30

Picked up with the example we were working on yesterday, and completed that work. 

Showed students how they could use the free form entry option in Mathematica to access Wolfram Alpha, which provides extensive help on solving problems like the one we just did. 

Worked on another example, and showed how to check the result just using Mathematica.

Day 9:  Wednesday, 1/29

Talked some about GW 3.

Walked students through the presentation in the book developing the formula for integration by parts (Section 5.6).  Emphasized the u dv notation, and did 2 examples carefully discussing how to think about the selection of u and dv.  Left off in the middle of another example where we had to use integration by parts twice.  

Here is the "gold sheet" material that I have referred to a number of times:  Calculus 1 info on Derivatives 

Day 8:  Monday, 1/27

Answered some questions on GW 3.

Presented the rest of section 5.5 - working with definite integrals.  Showed two approaches:  1)  Changing the limits of integration by using the u substitution, and 2) Temporarily suspending the definite integral until we come back to an antiderivative in terms of x, and then using the original limits of integration.  Did a couple of examples.

Day 7:  Friday 1/24

Teacher out.  Students should be working on Graded Work 3.

Day 6:  Thursday, 1/23

Answered some questions from section 5.4.  Collected GW 2.

Presented some of the material from 5.5.  Did several examples using u substitution.  Will deal with the definite integrals next week.

Handed out GW 3 - due on Friday, 1/31.

Day 5:  Wednesday 1/22

Presented material from section 5.4 - showing that a function can be defined as an integral, and also showing that the derivative of that function will involve the integrand.  Showed the case of having to use the chain rule.

Handed out Practice Exercises for Unit 1 (purple).  Handed out Bonus Tutor opportunity (gold) - extra copies in the folder for this class outside my door.

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), and showed students how that worked in Mathematica.  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.

Answered some questions on GW 2.  Discussed the Evaluation Theorem of the Fundamental Theorem of Calculus, and what it represented.

Walked students through their blue books, reiterating what I expected to see when I collected them next week.  The answers from the yellow sheet on  Remembering Some Calculus will count as 6 points.  This is where students should start from in terms of creating the answers for the collaborative assignment.

Next week we will begin with the more traditional pattern for class.  We are up and running!

Day 3:  Thursday 1/16

Students met in groups to work on Graded Work 2 (green).  The end goal is to create 1 document that all group members agree says what they want in terms of answering the questions.

Showed students how to go through the 4 steps to create the table of values.

Answered questions as they arose.

Day 2:  Wednesday 1/15

Had students say hello to the people they had met on Monday.  Get together with a new group, and review answers to the rest of the derivative problems on the yellow sheet from Day 1.  I reviewed the answers quickly with the entire class.

Handed out Remembering Some Calculus and Running again with Mathematica (yellow sheet), and had students begin discussing material that had to do with some of the derivative concepts, as well as concepts about integrals.  Had students jot down answers in their blue books

Explained how our day in the computer lab would run on Thursday.

Students should complete the explanations asked for on the Remembering sheet in their blue books so that they have a starting point to work from when they meet in a group on Thursday.

Day 1:

Monday

1/13

 Handed out Syllabus (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.  Students should have names of the people they met, and some common ground indicated on the second page of their blue books.  Had students  begin to discuss Review material on Derivatives (yellow).

At end of class, had students write what they should do before next class in their "To Do" list in their Blue Books.  Each student should complete the work on the yellow sheet, and be prepared to discuss it with their classmates at the beginning of the next class.

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