Mat 221 Daily Log

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Mat 221 – 03       PM Section

Combined Tests and Quiz :   Use this as the first resource in preparing for the final exam.

Day 60:  Wednesday, 5/8

Day 59:  Tuesday, 5/7

Day 58:  Monday, 5/6

First part of final exam.

Handed out Notes and Example 1 and Example 2 of Computing Grade with Success Strategies.

Day 57:  Friday, 5/3

Day 56:  Wednesday, 5/1

Day 54:  Monday, 4/29

Day 53:  Friday, 4/26

Completed the 2nd and 3rd problem on the yellow sheet, reinforcing what the FTC was all about. 

Reviewed the theorems and ideas presented in section 5.4, and briefly discussed what they were allowing us to say and do, and why they made sense.

Day 52:  Wednesday, 4/24

Collected the final project part 2.  Reviewed what a definite integral was from both a numerical and geometric viewpoint.  Reviewed what the FTC was all about.

Handed out a yellow sheet with three problems on it.  Discussed the first problem in detail (this is # 36 from section 5.3).  Tried to help students see how this problem connected to what the FTC was all about.

Day 51:  Tuesday, 4/23

 Handed back the first part of the final project, and spent a little time in class discussing the results.

Discussed the Fundamental Theorem of Calculus, and tried to help students understand it from a contextual point of view (change in position if you are integrating a velocity function) as well as from a geometric point of view (accumulating the signed areas bounded by a curve and the x axis.)  Showed how to apply the Fundamental theorem to the function we started the chapter out with:  f(x) = x^2 + 2 over the interval from 1 to 3.   Showed that for this case, we did get the exact value of the area bounded by the curve and the x axis over the interval.

Day 50:  Monday, 4/22

Worked on several exercises that helped emphasize the concepts behind what a definite integral represented. Showed clearly that a definite integral DOES NOT always represent the area bounded by a curve and the x axis.

Wrote out 5 statements that help address the questions:  What is a definite integral of f(x) over the interval [a,b]?

Day 49:  Friday, 4/19

In response to a student question about a practice exercise, worked most of the way through a practice exercise from chapter 4.  Used this as an opportunity to tie into the 2nd part of the project, showing where Mathematica was "doing the grunt work", but how we actually had to understand what to do and why.

Presented the formal definition of a definite integral from section 5.2, and walked through the 3 different scenarios of what a definite integral could represent from a geometric point of view.

Day 48:  Wednesday, 4/17

 Handed out End of Semester Notes - outlining the plan for the next couple of weeks.

Gave students time to fill out Survey of Teaching Forms.

Students spent the remainder of class time working on Part 2 of the Final Project.

Day 47: Tuesday, 4/16

Worked through two problems from section 5.1:  Exercise 16 and then exercise 8.  Emphasized how to create estimates from a table, and how to use the formula on page 261 to determine the size of the partition if you want your left hand and right hand sum to be within a certain amount of each other.  For exercise 8, reviewed how you would create the values by hand for a small number of subdivisions, and then how you would use the RSums program for a larger number of subdivisions

Day 46:  Monday, 4/15

Began chapter 5.  Discussed how to systematically find the area under a curve and above the x axis over some interval of x values.  Showed how we could use left and right hand rectangles to approximate area, and how area approximations got better and better as we increased the number of partitions.

Handed out a revised Practice Exercise Sheet for Unit 4 which reflects that we will cover chapter 4 and 5 for the next (and last) test.

Day 45:  Friday, 4/12

Day 44:  Wednesday, 4/10

Gave students time to work on project Question 1 in lab.

Day 43:  Tuesday, 4/9

Spent some time discussing the final project.  Handed out Problem 2 for the project.  Took students to the MathLab, and had them continue working on Problem 1.

Day 42:  Monday, 4/8

Discussed ideas of family of functions.  Worked on # 24 from section 4.1. Began work for # 43.  Handed out sheets for how you would approach these problems in mathematica.  Pointed out some of the key ideas on these sheets.

Day 41:

Friday, 4/5

Covered section 4.2 - Extreme Value Theorem.

Quiz during second half of class.

Day 40 Wednesday 4/3

Handed out Mathematica work for Ex. 6 from section 4.1.  Worked on this problem with students, walking them through the instructions on page 3 and 4 for using the List Plot command and the Show command to have the Critical Points and Points of Inflection show up on the graph.

Day 39:  Tuesday 4/2

Handed back Test on Chapter 3, with answer key.  Discussed fact that I had not counted question 4, since students seemed to struggle so much with it.  That material will be covered again on the test including material for Chapter 4. 

Handed out Final Project part 1 and spent some time discussing it. 

Worked on Exercise 6 in section 4.1 on board, showing students how to use the sign chart to employ the First Derivative Test in order to determine whether critical points were local max or min.

Day 38:  Monday 4/1

Teacher out sick.

Asked students to continue working on practice exercises.  Quiz delayed until Friday.

Day 37:  Friday 3/29

Handed back GW 5, and used this a springboard to discuss L'Hopital's rule, which is based on local linearity.  Went through the justification, and worked through a number of examples.  Quiz on Wednesday, 4/3 - covering inverse trig derivatives and L'Hopital's rule.  May also cover some ideas if there are issues with material from test 3.

Day 36:  Wednesday, 3/27

Test on Chapter 3

Day 35:  Tuesday, 3/26

Handed out Practice Exercises for Unit 4.  Handed out gold sheet on Key Ideas in Chapter 4.  Spent the class talking through the ideas on the gold sheet in preparation for the work we will do in the chapter.

Students should complete the practice exercises from section 3.9, and bring any questions they have to class on Friday.

Day 34:  Monday 3/25

Review for test.

Finish developing formula for derivative of arcsin(x).

Day 33:  Friday 3/22

Reviewed information about inverse functions and trig as we worked to develop the formula for the derivative of arcsin(x).

Test on Chapter 3 on Wednesday, March 27th

Day 32:  Wednesday, 3/20

Answered some questions on practice exercises.

Reviewed the derivative rule for cos (x), and had students compute the derivative of tan(x) using the quotient rule, and the fact that tan(x) = sin(x)/ cos(x).  Worked on a number of exercises using the rules of derivatives of trig functions.

Presented how to find the derivative of ln(x).

Day 31:  Tuesday, 3/19

Students had class time to work on GW 5.

Day 30:  Monday, 3/18

Handed out GW 5, with a yellow sheet demonstrating how you could effectively build a background page, and then set up a clean and clear presentation page for a similar type of problem.

Worked together on considering the derivative of sin (x) graphically and then by creating an approximation using a difference quotient on the calculator with h = .0001.  Asked students to follow a similar method for conjecturing what the derivative of cos (x) is.

Day 29:  Friday, 3/8

Classes cancelled due to wintry weather!

Day 28:  Wednesday, 3/6

Worked on section 3.4:  Chain Rule.  Did a couple of specific examples.

Showed Students how to access Wolfram Alpha by typing the equal sign into a Mathematica Notebook.  Wolfram Alpha allows you to enter your request in plain English, and will return a wealth of information to you.  In order to access Wolfram Alpha, you must have a connection to the internet.

Day 27:  Tuesday 3/5

Worked on section 3.3 - Product rule and Quotient rule.  Did a number of examples.

Day 26:  Monday 3/4

Finished discussing the material on the Derivative of Exponential function sheet.  Worked on a number of questions from section 3.2

Day 25:  Friday 3/1

Handed out GW 5 - Due on Wednesday, 3/6

Handed back Test 2 with answers.  Asked students to compute their midterm grade over the weekend, counting any success points as another grade. For example, if a student has 25 success points, they should insert a grade of 25/25 in the computation box on the back of their success strategies grade sheet.

Finished exercise 54 and did exercise 56 from section 3.1.

Began section 3.2.  Worked through the algebraic definition of derivative for an exponential function a^x, and showed that the derivative of an exponential function will be a constant multiple of that exponential function.  Worked through the first page of the Derivative of Exponential function sheet (yellow).  Asked students to complete the work on that sheet for Monday.

Handed out Practice Exercises Unit 3.

Day 24:  Wednesday 2/27

Test 2

Day 23:  Tuesday 2/26

Covered section 3.1.  Showed 5 rules for derivatives:  1) Derivative of a constant, 2)  Derivative of a linear function, 3) Constant Multiplier rule, 4) Derivative of a sum or difference, and 5) Power Rule.  Did a number of even exercises to show how to work with these rules.  Worked through exercise 54, and part way through exercise 56.

Day 22:  Monday 2/25

Review for test 2 on Wednesday, 2/27.  Handed out Exploring Derivatives Sheet 5 with answers on back.  (Copies are in the box outside my door).

Day 21: Friday 2/22

Handed out Working with Derivatives Sheet 6. (yellow)  Went through the front of the sheet with students - showing how to use the graph of a derivative to reconstruct a possible graph of the function.

Had students work on the back of the sheet on a graph.  Handed out answers at the end to show a possible function.(pink)  Answers are included at the end in file above.

Day 20:

Wednesday,

2/20

Answered some questions on GW 4. 

Reviewed with class all key ideas about derivatives.

Handed out Exploring Derivatives Sheet 3.  Worked with class to graph the derivative function on the front following 3 key steps - 1) identifying the zeros of the derivative by considering turning points of functions, 2) determining where the derivative was positive or negative by considering where the function was increasing or decreasing. and 3) determining where the derivative was increasing or decreasing based on concavity of the function.

Worked on back of Exploring Derivatives Sheet 3 with numerical data.  Reviewed core information about g(x) based on the derivative of g(x), and also based on the second derivative data.

Handed out Exploring Derivatives Sheet 4, and had students complete the graph. 

Students should be working on practice exercises from 2.3 and 2.5

Week 5

Day 19:

Friday

2/15 

 Handed back GW 3 with answers, and discussed how students need to think about their homework assignments.  You MUST make use of the resources provided to you.

Handed out GW 4 - Due Friday, 2/22

Reviewed idea of derivative as a function, and built from there...pulled in idea of a second derivative.

Handed out Exploring derivatives Sheet 2, and discussed core ideas from graph of function to concepts about derivative, and then from table, from numerical data about derivative to ideas about function.

Students should start GW 4, review GW 3, and read sections 2.3 and 2.5.

Day 18:

Wednesday

2/13

Spent time in lab showing an alternative way to work with cube root functions.

Also built tables for difference quotients (average rates of change) to help explore the derivative of (x-1)^(1/3) at x = 1.  We discussed the behavior we saw, and why there was no derivative at x = 1.  Students will be explaining these ideas as part of the next turn in homework, so I encouraged students to make sure they saved a copy of the assignment.

Day 17:

Tuesday

2/12

 Reviewed what we had done so far, trying to connect ideas more firmly in student minds. 

Began working with derivative as a function of x, not just considering the derivative at a particular point x = a.  Showed how to derive the general derivative for our function x^2 + 2.

Began to work with the idea of derivative as a slope of a tangent line, and showed that if a function is decreasing, the derivative will be negative, if a function is increasing the derivative will be positive, and if the derivative is 0, the function will be turning or flattening out.

Considered concavity of a function, and saw that if a curve is concave down, the derivative is decreasing, and if a curve is concave up, the derivative is increasing.

Handed out Sheet 1 on Working with Derivatives (yellow) , and reiterated this behavior while looking at the specific data values.

Day 16:

Monday

2/11

Handed back tests with answer key.  Talked briefly about results, and asked students to make sure they looked at their results carefully, and sought help for any trouble spots.

Collected GW 3.

Handed out a gold Bonus Tutor Opportunity.  This can be used between now and February 22nd.  Extra copies are in the bins outside my door.

Handed out a write up by a student that explored the number of digits given in a numerical answer using Mathematica.  Encouraged students to do similar work for Success Strategies points if they found something new and helpful, or had suggestions for helping improve the Mathematica instructions.

Answered some questions from the practice material.

Discussed the questions "What is a derivative of f(x) at x = a?" and discussed numerical, geometric and algebraic answers for this question.  Handed out a gold sheet on Derivative Facts that has the "answers" to this question so that students could actively listen, rather than trying to write the full detail out.

Week 4

Day 15:

Friday

2/8

Class cancelled due to impending snow storm.

Day 14:

Wednesday

2/6

Test on Unit 1

Day 13:

Tuesday

2/5

Quickly reviewed what we had discussed in terms of ARC.  Worked to change the notation so that we were using the points (a, f(a)) and (a + h, f(a+h)).  This allows us to let h go to 0 from both sides in order to bring the two points closer and closer, and allows us to consider if there is a limiting value.  If the limiting value exists, we call this the instantaneous rate of change of f(x) at x = a.

Worked with students to create tables of ARC with the focus point of x = 2, and described the behavior of the tables both verbally and symbolically.

Gave students a sheet (yellow) to consider the ARC with the focus point of x = -3, and gave them time to complete the table.  The answers for this work are on the back of that sheet.

Handed out sheet for Practice Exercises for Unit 2.

Day 12:

Monday

2/4

Handed back Mathematica Quiz.  Showed students the issue with using just an = sign, for example f(x)=5.  Reviewed how to clear the function, and then to Evaluate Notebook to get Mathematica to read down again from the top.  Discussed that you could not use the same function name in a given notebook to define two different functions.

Began Chapter 2, reminding students of the notation and ideas behind Average Rate of Change (ARC).

Week 3

Day 11:

Friday

2/1

Handed out GW 3 (Green), and spent some time in class talking about the resources people had to refer to, and how to think about some of the parts of the assignment.

Corrected # 4 on the pink sheet from Day 10.  The last table is incorrect, and should  have shown inputs decreasing without bound.  You will then see the outputs decreasing without bound, as the graph shows.  Please make an adjustment to that last part.

Reviewed the answers to the questions on continuity, discussing them as a class.

Discussed the set up for the test next Wednesday .  Also discussed expectations and procedures for students submitting Practice Exercises for a Success Strategies Grade.   I will ONLY accept Practice Exercises at the beginning of the test on Wednesday, and will not look at them at any other time.

Day 10:

Wednesday

1/30

Quiz on Mathematica took up most of the class. 

Handed out Unit 3 for Mathematica Instructions (Yellow) .  Students should work on Sections 15 and 16 in preparation for the next graded homework.

There will be an in class test next Wednesday on Unit 1.  Practice Exercises will be due at that time if students want Success Strategy Points for that work.

Day 9:

Tuesday

1/29

Handed back GW 2 with answers of work done by 2 students in the class.  Spent some time talking about what students should do now that they have their paper back, and how I selected student work to copy.  Talked briefly about how to discuss solving the exponential equation algebraically, either referring to property of logs, or using the fact that you form the composition of inverse functions.

Had students meet briefly to check where they had questions on the practice problems for limits for inputs increasing or decreasing without bound.  Answered a few questions on this material.  Gave students answers to these problems (pink).

Discussed Continuity of a function at a point.  Handed out some notes (yellow) from another book as well as a page of 4 practice problems (purple).  Both of these papers are available in the bin outside my office door for anyone who was not in class.

Day 8:

Monday

Gave students a chance to meet with each other briefly to look over the practice exercises on limits as input approaches a particular point.  Answered questions from this material.  Reminded students that when they were working with trig functions, their calculator had to be set in radian mode.  Also reminded them that the absolute value function was under the Math menu.  Completed the notes referencing the graphs that I had drawn on the board on Friday.  Discussed when a two sided limit existed.

Presented material on limits as input increases or decreases without bound.  Again, developed numerically, graphically, symbolically and verbally.  Discussed how students should be able to work with this information from any of those starting points.

Handed out notes on limits for inputs increasing/decreasing without bound. (yellow)  Handed out practice exercises for these ideas (purple).

Week 2

Day 7:

Friday

1/25

Finished discussing material on limits, which we started on Tuesday.  Stressed the need to understand the material from a numerical, graphical, symbolic and verbal point of view.

Handed out Practice Exercises for Approaching a Specific Point. (Purple)

Reminded students that they MUST be working on Mathematica.

Day 6:

Wednesday

1/23

 Met in computer lab W -240.  Had students get up and going with what they had been working on in Mathematica.  Handed out Mathematica Part 2 (in box outside my office ) instructions.

Students MUST be very proficient with Section 1, 2, 6 and 7 of the instructions as soon as possible.  There will be a quiz on these sections next Wednesday.

Students should work completely through the packages of instructions by next Wednesday.  We will begin with Part 3 next Wednesday, which covers some advanced graphing techniques as well as creating tables in Mathematica.

Graded Homework 2 is due in at the beginning of class on Friday. 

 Day 5:

Tuesday,

1/22

 Handed out Practice Exercises for Unit 1 (Purple) and discussed how these sheets fit into the Success Strategy option for Practice Exercises.  Handed out the Success Strategy Grade Sheet (Turquoise) with Record of Grades on the back.  Briefly discussed the Success Strategy Grade.

Answered some questions on Graded Work 2, and reminded students that the due date was the beginning of class on Friday, 1/24 since students did not get the work until last Friday due to the snow day.

Began work on limits as we approach an input point.  Got through approaching a point from the left.  Will continue with work on approaching from the right on Friday.

Tomorrow is lab day.  Students should have worked through at least sections 1, 2 and 3 of Mathematica Basics Part 1

WEEK 1

Day 4: 

Friday

1/18

 Handed out Homework After Day 2 , and had students meet to work on the problems on Exponential Functions.  Handed out answers to these problems , and spent some time discussing the 2nd problem, and showing an algebraic solution.

Talked about students accessing Mathematica, and downloading it on their own machines.  Since we missed class on Wednesday, students must begin working through the Part 1 package on Mathematica outside of class.

Handed out Graded Work 2.   Adjusted the due date to Friday, 1/24 because there was no class on the 16th. 

Students should focus on 3 things before the next class:  1) Work on Graded Work 2, 2) Work with Mathematica instructions, and get through as much of Part 1 Instructions as possible before lab on Wednesday, and 3) Make sure that they carefully read through the solutions handed out in class to become comfortable with the expectations for turn in assignments.

 Day 3:

Wednesday

1/16

 No Class - SNOW

 Day 2:

Tuesday,

1/15

 Had students continue to work together to get familiar with who else was in class.  Handed out Answer to # 40 on page 9 (Pink).  Handed out sheet to Review Exponential Functions (Purple).  Did a quick review of Exponential Functions as a class.  Had students work in pairs on the problem on the sheet.  Handed out answer to Problem 18 page 15 (Pink) at the end of class.  Handed out Part 1 of Mathematica Instructions (Yellow)  Students should read as much of this as possible before Lab.                    

Day 1:

Monday

1/14

Handed out General Information Package (Gold), Syllabus (Gold), Graded Work 1 (Green), and In Class Work for Day 1 (Purple).  Had students fill out attendance cards.  Briefly discussed handouts.  Had students begin work with review material.  At end of class, handed out Answers for Day 1 Work (Pink), and Homework after Day 1 (Purple).