Math 1220 - Calculus II - Section 3

MTWF 9:40 - 10:30 AM, JFB 103

Office Hours: Wed 10:30-12:30, Thurs 11:00-12:00, JWB 314.


Syllabus for Math 1220

ANNOUNCEMENTS

December 2

Practice Final: Practice Final
Solutions: Solutions
Topics that are not on the final: Topics

November 27

The schedule has been updated through the end of the semester. Some things to note here:
1) The syllabus said there are 4 midterm exams and a final. This was a mistake, there are only 3 midterms and a final (and we have already taken all the midterms). This changes the exam weighting so that each exam is 25% (HW opt out) or 20% (with HW). Sorry for any confusion caused by this.
2) There are two more homework assignments due. There is one due next Monday, and another that I will collect the day of the Final. All of the new material will be tested on (unless I specify otherwise).
3) I originally thought next Friday (the 7th) was part of Finals week but it appears we have another day of class that day. This will be an extra final review day if this is true.
4) This weekend I will make a practice final that covers most of the new stuff. Study the previous tests and practice tests to review old stuff. Also the practice final will list things that will NOT be tested on.

November 18

The Exam 3 Solutions are available here: Exam 3 Solutions

This solutions sheet explains all the exam problems in addition to giving a few extra notes at the end. The extra notes cover:
- "The Hierarchy"
- The Alternating Series Test
- The nth Term Divergence Test
- Some comments about interpreting results of tests

Even if you did well on the exam I recommend reading theses notes at the end of the exam solutions for your information.

With the end of class coming up now, I have a few other things to say about the coming weeks:
- *** UPDATE NOV 19 *** The "Bonus Day" before Thanksgiving break will be a review session where you are allowed to ask any questions you choose from Chapter 9.
- There will be a practice Final available at some point. Note that the practice final will consist mostly of new material, and I will refer you to old practice exams for practice on the older material.
- The final will be about 50% new material and 50% stuff from previous tests. The previous test stuff will mostl hit the main points and most imporant things from each section.
- If you would like to know your grade either see me in my office or email me and I can give you a break down of your current grade and what you need on the final to get your desired result in the class.
- For those who picked their tests up late, Exam 3 is being curved up by 4 points. Also the HW score and the final class grades may be curved up. I will try to put the class average between 78 and 80.

November 2

Last week's bonus problem will be accepted on November 5 as well as the new bonus problem for this week

The practice Exam solutions will be posted ( Practice Exam 3 Solutions ) no later than Monday afternoon next week.

October 30

Practice Test for Exam 3:
Practice Exam 3

October 25

Section 9.2 has been completely deleted from HW set 9. That assignment will be due as part of next week's Homework. Also problem 35 from section 9.1 has been removed. The rest of the 9.1 homework will still be due on Monday.
Also it is looking more and more likely that Exam 3 will be moved back a day, to November 7 .

October 19

The Solutions for Exam 2 are now available:
Exam 2 Solutions
This was done hastily so I will check it later for accuracy.

October 5

The HW set on 8.1 and 8.2 was changed slightly to reflect a problem I did not have time to cover in class:
From the assigment previously posted on this website, 8.2 # 16 and #24 have been removed. These are limits of type 1^(infinity), which is the last indeterminate form to cover. As it happens the method for solving them is exactly the same as for the other two exponential forms we made it to in class, if you are interested.
The rest of the assignments will still be due Monday, October 15 after the break.

Also, the assignment which was due on the 1st, and Exam 2 should be returned to you Monday after the break.

September 25

Practice Exam is now available for Exam 2:
Practice Exam 2
Solutions

Note that on Exam 2, the format will be the following: You will be given something like 8 integrals to do (this number may change), and you will be asked to choose any 6 of them to do completely (this may also change) and leave the other two alone.

Also a bonus problem for HW Set 6 has been posted at the bottom of the page.

September 23

Exam Solutions are now available:
Exam 1 Solutions

If you have any further questions regarding the exam please let me know by email.
The practice exam for Exam 2 will be available early this week, then solutions shortly after.

Also, the next homework assignment has been posted.

September 18

To answer some common questions:
1) Exams will be handed back Friday unless something bizarre happens in my schedule. HW will hopefully be handed back that day as well.
2) The fire alarm should not change our schedule significantly. If anything, the time will be deleted from Section 7.5 once we get there, and none of the homework assignments should be affected.
3) A Bonus Problem has been posted for HW set 5. It is at the bottom of this page.

September 4

Practice exam solutions are now available. Also there were changes to problems 2c and 4c on the practice exam. 2c had a formatting error and 4c was not solvable using methods we know. Both should be fixed on the links on the site (the new one says Version 2).
Practice Exam 1 Solutions

September 3

The practice exam for Chapter 6 is now available. Solutions will be available by no later than Wednesday evening. Also a bonus problem for Set 3 has been added.
Practice Exam 1 - Chapter 6

August 27

A Bonus Problem has been added to HW set 2. Also office hours for this semester are now listed here as well as on the syllabus, which has been updated.

August 24

I mentioned at the end of class that you should ignore some of the homework problems for assignment #1, as I was not able to finish that part of the lecture.
To be very clear, this is your homework assignment now, to be due Monday morning in class:
Sec 6.1 # 4, 5, 6, 15, 16, 18, 19, 23, 31, 32, 40
Sec 6.2 # 2, 3, 8, 12, 17, 22
In other words, problems 37-39 from section 6.2 have been removed.
Problem #38 from 6.2, which we began in class on Friday, will be completed on Monday.

August 21

It occurs to me I did not give you my office location. It is in room JWB 314. This will be corrected on the syllabus as well.

August 19

Welcome to class!

You should decide in the first few days whether you would like to turn in the homework. You MUST turn in something on Monday, August 27, whether it be your homework or a slip of paper saying your homework will not be graded this semester. If you do not turn anything in, I will assume you are having homework graded and put you down for a 0 for the first assignment.

My schedule will not become set until after the first week, so I will list office hours in class on Monday, August 27. If you would like to set up an appointment before then, email me and I will schedule some time for you.

HOMEWORK SETS

Set 1 (Due Monday, August 27):
Sec 6.1 # 4, 5, 6, 15, 16, 18, 19, 23, 31, 32, 40
Sec 6.2 # 2, 3, 8, 12, 17, 22

Set 2 (Due Tuesday, September 4):
Sec 6.3 # 11, 12, 13, 15, 21, 29, 34, 37, 38, 40
Sec 6.4 # 1, 3, 4, 13, 17, 19, 23, 24, 31
Sec 6.6 # 1, 2, 3, 5, 7, 12, 13
Bonus Problem (optional) at bottom of page

Set 3 (Due Monday, September 10):
Sec 6.8 # 1, 3, 5, 6, 29, 43-46, 61, 63, 66, 67, 69
Sec 6.9 # 1, 5, 13, 17, 18, 20, 27, 29, 32, 34, 38
( Practice Exam 1 - Chapter 6 )( Practice Exam 1 Solutions )
Bonus Problem (optional) at bottom of page
If you need additional practice, try doing the odd-numbered problems 1-33 in Section 6.10 "Sample Test Problems" in the book.

Set 4 (Due Monday, September 17):
Sec 7.2 # 3, 4, 6, 9, 10, 12, 13, 15, 19, 21, 25, 28, 30, 35, 37, 39, 41, 43, 46

Set 5 (Due Monday, September 24):
Sec 7.3 # 1, 2, 5, 12, 13, 14, 19, 21, 26, 27
Sec 7.4 # 1, 3, 6, 9, 10, 13, 17, 18, 20, 21, 23
Bonus Problem (optional) at bottom of page

Set 6 (Due Monday, October 1):
Sec 7.5 # 1-6, 14, 15, 17, 21, 31
Sec 7.6 - Problems for Section 7.6
Bonus Problem: Bonus Problem
( Practice Exam 2 )( Solutions ) - Note, these are NOT to be turned in, they are for your own practice!
You may also do Review Section 7.7, #1-41 odd, if you would like more practice (do NOT turn these in)

Set 7 (Due Monday, October 15):
Sec 8.1 #1, 3, 5, 8, 10, 14, 18, 22, 30
Sec 8.2 #2, 5, 9, 12, 13, 15, 21, 22, 23, 25, 27, 32, 36

Set 8 (Due Monday, October 22):
Sec 8.3 #2, 3, 5, 8, 10, 12, 14, 18, 19, 31, 37
Sec 8.4 #1, 3, 5, 7, 14, 16, 19, 23, 27, 29, 35, 47, 48
Bonus Problem: 8.4 #58

Set 9 (Due Monday, October 29):
Sec 9.1 #1, 2, 4, 7, 10, 13, 21, 22, 24, 27 (NOTE: 35 used to be in the assignment but has been removed)
Bonus Problem: Bottom of page

Set 10 (Due Monday, November 5)
Sec 9.2 #1, 2, 5, 7, 8, 10, 15, 18, 23, 27, 30, 39
Sec 9.3 #1, 3, 5, 6, 11, 12, 16, 20, 21
Sec 9.4 #1, 2, 5, 10, 12, 14, 15, 20, 25, 31, 32, 42
Bonus Problem
Also, last week's bonus problem will be accepted this week too.

Set 11 (Due Monday, November 12)
Sec 9.5 #1, 3, 6, 7, 8, 9, 13, 15, 17, 19, 20, 24
Bonus Problem

Set 12 (Due Monday, November 19)
Sec 9.6 #1-4, 9, 12, 14, 15, 16, 22, 23, 24
Sec 9.7 #1, 2, 4, 7, 13, 15, 18, 23, 27
Sec 9.8 #3, 7, 11, 12, 19, 20, 27

Set 13 (Due Monday, November 26)
Sec 9.9 #1, 3, 5, 6, 10, 14, 16, 62
Sec 10.1 #1, 2, 4, 6, 7, 9, 10

Set 14 (Due Monday, December 3)
Sec 10.2 #1, 2, 5, 7, 10, 12, 13, 20, 24, 47
Sec 10.3 #1, 3, 6, 7, 9, 12, 15, 17, 20, 24, 43 (46 is now a bonus problem)
Bonus Problems: 10.3, #46 and #53

Set 15 (Due Tuesday, December 11 at Final Exam)
Sec 10.4 #1, 9, 10, 14, (22, 25, 30 only find dy/dt), 34, 36, 39, 40, 47
Sec 10.5 #2, 9, 14, 15, 25, 28
Sec 10.7 #1, 3, 5, 9 (do not worry about graphing, just look in the back).
Hint: Integrate from 0 to 2pi for #1, 3, 5. For #9 integrate from 0 to pi/2 and multiply your result by 2 to get both "petals". This is necessary because for theta between pi/2 and pi, r is imaginary.
Bonus Problem: Section 10.7, #33 (See bottom of page for hint)

CLASS SCHEDULE

Day Sections Covered Extra announcements
Week 1
August 20 Review Syllabus handed out
August 21 Review, 6.1
August 22 6.1
August 24 6.2
Week 2
August 27 6.3
August 28 6.4
August 29 6.6
August 31 6.8
Week 3
September 3 No Class - Labor Day
September 4 6.8
September 5 6.9
September 7 Test Review
Week 4
September 10 Exam 1 ( Practice Exam 1 - Chapter 6 )( Practice Exam 1 Solutions )
September 11 7.2
September 12 7.2
September 14 7.3
Week 5
September 17 7.3
September 18 7.4
September 19 7.4
September 21 7.5
Week 6
September 24 7.5
September 25 7.5/7.6
September 26 7.6
September 28 Test Review
Week 7
October 1 Exam 2 ( Practice Exam 2 - Chapter 7 )( Solutions )
October 2 Limit Review (Ch. 1), 8.1
October 3 8.1/8.2
October 5 8.2
Week 8
October 8-12 Fall Break - No School!
Week 9
October 15 8.3
October 16 5.7/8.3
October 17 8.4
October 19 8.4
Week 10
October 22 9.1
October 23 9.1
October 24 9.2
October 26 9.2
Week 11
October 29 9.2/9.3
October 30 9.3
October 31 9.4
November 2 9.4/9.5
Week 12
November 5 9.5
November 6 Test Review
November 7 Exam 3 ( Practice Exam 3 )( Practice Exam 3 Solutions )
November 9 9.6
Week 13
November 12 9.6/9.7
November 13 9.7
November 14 9.8
November 16 9.8
Week 14
November 19 9.9
November 20 10.1
November 21 Bonus Day
November 23 Thanksgiving Break, no class
Week 15
November 26 10.2
November 27 10.3
November 28 10.3
November 30 10.3/10.4
Week 16
December 3 10.4
December 4 10.5
December 5 10.7
December 7 Final Review
Finals Week
December 11 FINAL EXAM Time 8:00-10:00 AM ( Practice Final )( Solutions )

BONUS PROBLEMS

Remember that on these problems, you must show all work and complete all parts of the problem to receive credit. The grading will be harder on these than on normal homework!

HW Set 2 Bonus (Due Tuesday, September 4)
The Lemon Juice Problem. In early 2004 I sat down at a restaurant in Cincinnati on vacation and became quickly bored with the rest of my group's conversation. Then the waiter brought me a glass of water with a lemon in it. I hate it when restaurants do this as I do not like the lemon flavor.
I decided to model the situation as follows: The glass began with 400 mL of water in it. The lemon adds 2 mL of lemon juice to the glass per second (assume it is at all times evenly mixed). Meanwhile I am drinking 4 mL of the mixture per second through my straw.
QUESTION: Find an equation for the percentage of liquid in the glass that is lemon juice at time t. At what point is the liquid 20 percent lemon juice (for which I consider it undrinkable)?
Hint: Call the amount of lemon juice in the glass Y, and note that it satisfies a first order differential equation.

(Side comment: After formulating the problem it took me 2 years to learn how to solve it!)

HW Set 3 Bonus (Due Monday, September 10)
The Art Gallery. A painting at an art gallery is 3 feet tall, and it is hung so that its bottom is 1 foot above your eye level. How far away from the wall should you stand in order to get the best view of the painting (i.e, so that the painting fills up the maximum angle, "theta", of your total vision)?
Hint: Draw a picture. Write a function with y = the angle, and x = your distance from the wall. Then differentiate to find the minimum.

HW Set 5 Bonus (Due Monday, September 24)
Trig Type "5c". Integrate sec^3 (x) dx.
Hint: Begin with integration by parts before doing anything else. Also, you will eventually need to know the integral of sec(x) dx, which I told you in class (also in back of book).

HW set 6 Bonus (Due Monday, October 1)
A mess of an integral. Bonus Problem
No Hints this time!

HW set 8 Bonus (Due Monday, October 22)
Mystery of Convergence (8.4 #58). Determine what numbers p and q would make the integral converge. This will amount to there being some relationship between p and q that you need to describe. It may be helpful to use the Comparison Test!

HW set 9 Bonus (Due Monday, November 5)
Infinitely Nesting Square Root. ( Bonus Problem ).
Hint: Problems 37-39 in section 8.1 outline the process you will need to follow to solve the problem.

HW Set 10 Bonus (Due Monday, November 5)
Sequence with a slowly vanishing tail. Bonus Problem

HW set 11 Bonus (Due Monday, November 12)
Chaotic Conditional Convergence Bonus Problem

HW Set 14 Bonus Problems (Due Monday, December 3)
That Problem In Class I Couldnt Do Do problem #46 from section 10.3. The key is to never actually find the angle theta. Use the cot(2*theta) equation to draw a triangle with the angle 2*theta. Then determine cos(theta) and sin(theta) by using your triangle and half-angle formulas.
3 Points determine a Conic? Do problem #53 (all three parts) from section 10.3. 3 points in the plane is not quite enough information to determine a conic, but it is with a little extra information about what type of conic we're looking for. A hint: All three parts can be solved by setting up a standard (up to translation) equation for the conic and solving a system of equations with 3 variables and 3 unknowns.

HW Set 15 Bonus Problem (Due Tuesday, December 11)
"First Old Goat Problem" . Do problem #33 from section 10.7.
Hint: Split the shaded region into the left semicircle (which you dont need calculus to find the area of) and the right region. In the right region each slice will be a slice of the ka-circle minus a slice of the a-circle. You will need to solve for the intersection point of the two circles to determine your limits of integration.