# MATH 131 - Fall 2015 Calculus II

Professor: Erika L.C. King
Email: eking@hws.edu
Office: Lansing 304
Phone: (315) 781-3355

Section 2 Class: MWF 10:10-11:05am in Napier 202
Section 2 Lab: Th 11:55am-1:20pm in Gulick 206A

Section 3 Class: MWF 11:15am-12:10pm in Napier 101
Section 3 Lab: Th 1:30-2:55pm in Gulick 206A

Office Hours: T 12:45-2:15pm, W 1:30-3:30pm, Th 3:30-4:30pm, F 1:30-2:30pm, and by appointment
Math Intern Hours with Tasha Williams in Lansing 310: Su: 2-5pm, 7-10pm; M-Th 3:00-5:30pm and 7:00-10:30pm

Course Syllabus for Section 2
Course Syllabus for Section 3
***Note that these syllabi are essentially the same -- the main difference is the Final Exam schedule.***
Course Homework Guidelines

Review Session: Monday, December 14th 2:00pm-3:30pm in Napier 201. Bring questions!

Office Hours:

• Monday, December 14: 11:00am-Noon
• Tuesday, December 15: 1:30pm-3:30pm
• Wednesday, December 16: 11:30am-1:30pm
• Thursday, December 17: 11:00am-Noon
• By appointment

Section 2 Final Exam: Wednesday, December 16th 7:00PM-10:00PM in Napier 202 (our classroom).

Section 3 Final Exam: Thursday, December 17th 1:30PM-4:30PM in GULICK 206A (our lab room).

• Here is the Lab Key for the Week 14 Lab. Be sure to read it to make sure it makes sense and that you understand what level of detail is necessary.
• Here is the Main Exercises Key for the Week 14 Main Exercises. Be sure to read it to make sure it makes sense and that you understand what level of detail is necessary.
• Here is the Lab Key for the Week 15 Lab. Recall that this only has final answers (and a few hints), not full solutions.

### WEEK 15: December 7-December 11

Homework due Monday, December 7:

• Review your notes from Friday's class. I think everyone was a little out of focus after the quiz and with the cloudy weather. Be sure to work through the details and come to class with any questions you have about the material on Direct and Limit Comparison Tests. Section 3, be sure to fill in the blanks for the last example.
• Start working on the groupwork sheet I handed out at the end of class. Try to guess what series to compare each of the four series to, and complete at least the first question. Head directly to your groups when you get to class on Monday so that you can compare answers and start sharing ideas.
• Remember how most of the techniques we have been learning will only help us tell the convergence or divergence of a series and not what it converges to if it converges? Some of you wondered about how to figure out the sum in these instances. It isn't easy! But it is neat! Check out problem 66 in Section 8.4 on page 639! Here they show one way to find out the sum of the $p$-series, when $p=2$.
• Week 14 Lab is due at the beginning of Monday's class! One from each group. Be sure you meet with your group to review each other's final write-ups prior to Monday's class, so that everyone agrees that each group member's set of solutions is a good one. Email me if you have questions. I will roll the die to see which group member will turn in hir/his/her paper. Be sure you send your lab to class with someone else if there is a reason you cannot be there!!!
• Work practice exercises on Section 8.5 on WeBWorK. BE CAREFUL!!! ALL of these questions allow only one or two attempts! Be very careful of AUTOFILL and check your answers carefully before you submit them. This is due Monday at 9:00am online.
• Complete the Reading Assignment for Section 9.1 on this handout. Remember to use complete sentences in your responses!!! This is due Monday at the beginning of class.

Homework due Wednesday, December 9:

• Remember to think about what you might like to bring to the lab party on Thursday.
• Review the series exercises that we did in Monday's class. Since each group worked a different problem, and not everyone worked through the details of all the problems, be sure that you work through problems that other groups did. Make sure they make sense and you see how to apply the two different comparison tests used in these exercises!
• Read about the Ratio Extension Test on the handout I gave you. This will be especially helpful as we discuss absolute and conditional convergence.
• Note that there are not many practice problems in WeBWorK for the Ratio and Root Tests without looking at absolute convergence, which we started discussing Monday. (Note I assigned a problem that did have the absolute value of the ratio last week, but you can essentially ignore the absolute value for those questions since the terms are all positive anyway.) Thus to get some extra practice with those two tests, you should also do some of the odd problems from 9-25 in Section 8.5 on pages 647-648 in your textbook. Remember that answers are in the back of the text. I will not be collecting these, but it is to your advantage to spend some time with these!
• Work practice exercises on Section 8.6 on WeBWorK. BEWARE! You are only allowed ONE attempt for the most of these problems!!! Why does including $\cos(n\pi)$ in your general term make the series alternating? When coming up with a formula for your general term, remember to look at each part separately: the numerator, the denominator and the sign; then put all the parts together! This is due Wednesday at 9:00am online.
• Complete the Reading Assignment for Section 9.2 on this handout. Remember to use complete sentences in your responses!!! This is due Monday at the beginning of class.

Homework due Thursday, December 10:

• Bring your book, notes (if you have more than one notebook, bring them all!!!) and snacks to lab! We will do evaluations, some work on the group work and Taylor polynomials, we will review for the final and share tasty treats.
• Work on and try to finish the problems we were working on in groupwork today. We will put these on the board.
• Bring a laptop or other devise, if you have one, on which you can complete the course evaluations.

Homework due Friday, December 11:

• Complete the Main Exercises Assignment for Week 15 on this handout. This is due Friday at the beginning of class.
• Work practice exercises on Section 8.6 on WeBWorK. BEWARE! You are only allowed ONE attempt for the fifth problem and TWO attempts for the first problem!!! This is due Friday at 9:00am online.
• What would you like to see an example of or discuss when we have our review session on Monday, December 14th (this will be a joint review session with both of my sections of calculus)? Bring a piece of paper with your requests written on it to class or send me an email. Want some BONUS points? I will offer you up to 7 bonus points for giving a nice presentation of a problem I assign you at the review session. Let me know by email by Friday at 3:00pm if you would like to do this.
• Unfortunately, we will not have time to discuss Section 9.3, but it is REALLY NEAT! and leads us to exciting things in Section 9.4! So, if you would like to earn up to 5 BONUS points: Complete the Reading Assignment for Section 9.3 on this handout. This is due Friday at the beginning of class. To earn all five bonus points your assignment must be VERY thorough and contain complete sentences.

### WEEK 14: November 30 - December 4

Have a great Thanksgiving Break!!!

On Wednesday, December 2nd at 4:45pm in Napier 201, there will be a colloquium given by Alyssa Newman, William Smith class of 2016, mathematics and studio art major, about her work doing an independent study on fractals with Prof. Vaughn. Refreshments will be served at 4:30pm. I hope you can make it!

There will be a 20-30 minute quiz at the beginning of class on Friday covering sections 8.1-8.5. Be sure to be on time! Extra time will not be given to those arriving late! Remember that complete solutions involve full sentences!!!

Homework due Monday, November 30:

• THERE IS NO LAB ASSIGNMENT DUE THIS WEEK!!! :)
• Work practice exercises on Section 8.4 on WeBWorK. The first is about the Test for Divergence, the middle four about the Integral Test, and the last is a review. Although we did not do an example applying the Integral Test, these questions involve all concepts that you have used before together with the statement of the Integral Test. So in many ways, the bulk of these problems are a review (of calculus I as well as previous topics in calculus II)! This is due Monday at 9:00am online.
• Do extra practice problems from the book!!! Remember that odd answers are in the back of the text so you can check your work!

Homework due Wednesday, December 2:

• Review the series exercises that we did in Monday's class. Since each group worked a different problem, and not everyone worked through the details of all the problems, be sure that you work through problems that other groups did. Make sure they make sense and you see how to apply each of the different tests each used!
• Work practice exercises on Section 8.4 on WeBWorK. Some of these will ask you to apply your new theorem from the handout in class on Monday. Remember that finding a way to express a rational number as a fraction can be done using geometric series! Cool! This is due Wednesday at 9:00am online.
• Monday we briefly discussed the Harmonic Series. There is a beautiful proof that it is divergent using the idea of looking at a subsequence of the sequence of partial sums of the series. If a subsequence of a sequence diverges, so does the original sequence. Check out this article. Specifically read the intro on page one and Proof 1 on page 2 to get an idea of how this method works. Isn't it neat! Ask if you have questions!
• Review past WeBWorK questions and do extra exercises from the textbook to practice for Friday's quiz!

Due to a doctor's appointment, I will need to cancel my office hours on Thursday. Please be sure to see me in office hours or make an appointment before that time if you have questions!

Homework due Thursday, December 3:

• Try to finish the groupwork exercises I put on the board in Wednesday's class from Section 8.5: 11, 19, 15, 21, 17 and 23. Go directly to your groups at the beginning of lab and start discussing them. Really spend some time on all six questions!!! The more time you spend before lab, the more time we will have to spend on working on the lab in class.

Homework due Friday, December 4:

• Prepare for your quiz! The quiz will be roughly the first 20-30 minutes of class and will cover Sections 8.1-8.5.
• Complete the Main Exercises Assignment for Week 14 on this handout. This is due Friday at the beginning of class.
• Work practice exercises on Section 8.5 on WeBWorK. This is a short one! This is due Friday at 9:00am online.
• Complete the Reading Assignment for Section 8.6 on this handout. This is due Friday at the beginning of class.

### WEEK 13: November 23 - November 24

Homework due Monday, November 23:

• FINISH the groupwork exercises on the handout from Friday's class. Many of you did most of these questions in class, but all of you have something more to do. You should make sure that you have all the details that you would need to put on the board, not just rough notes for the solution. If I ask you, you should be ready to show me your complete work on these problems when you walk in the classroom. I will ask groups to put solutions to specific questions on the board.
• THERE IS NO LAB ASSIGNMENT DUE THIS WEEK!!! :)
• Work practice exercises on Section 8.3 on WeBWorK. Some of these should be relatively quick, and others will take more thought. This is due Monday at 9:00am online.
• Complete the Reading Assignment for Section 8.5 on this handout. This is due Monday at the beginning of class.
• Make a flow chart or list for the methods you know to decide the convergence or divergence of sequences. (Note that doing this for series is part of your reading assignment!)

### WEEK 12: November 16 - November 20

Remember to start your work as soon as possible so that you have the opportunity to ask questions if you have them!

Our third exam, covering sections 7.1-7.6 and 7.8, will be on Thursday, November 19th in Gulick 206A, our normal lab space.

Homework due Monday, November 16:

• Work on the groupwork exercises I put on the board in Friday's class. These included determining if two sequences were convergent or divergent as well as the following exercises from Section 8.2: 45, 47, 49, 55 and 61. You should start working on all of them. Go directly to your groups on Monday morning when you arrive in class and start discussing them. Really spend some time on all seven questions!!! You do not have a Reading Assignment and the WeBWorK is not long!
• Week 11 Lab is due at the beginning of Monday's class! One from each group. Be sure you meet with your group to review each other's final write-ups prior to Monday's class, so that everyone agrees that each group member's set of solutions is a good one. I will roll the die to see which group member will turn in hir/his/her paper. Be sure you send your lab to class with someone else if there is a reason you cannot be there!!!
• Work practice exercises on Section 8.2 on WeBWorK. Beware! Some of the problems only allow you one or two attempts! These questions are trying to help you visualize sequences and think carefully about how they converge or diverge. This is due Monday at 9:00am online.
• Practice, practice, practice for the exam!

On Wednesday, November 18th at 4:45pm in Napier 201, there will be a colloquium given by Dr. Robert Fiete, Chief Technologist for the Harris Corporation. He will be giving a talk entitled: "Image Chain Modeling with Applications in Space Imaging and Photofakery". Refreshments will be served at 4:30pm. I hope you can make it!

Homework due Wednesday, November 18:

• Review the exercises on sequences that we did in Monday's class. Be sure that you work through ALL the problems. Make sure they make sense and let me know if you have any questions.
• Work practice exercises on Sections 8.1-8.2 on WeBWorK. Some of these are similar to past examples, but they are good practice! The last one is a review problem. Although you do not need to show details to do your WeBWorK exercises, remember you do when you turn work in! Thus it is good practice to write down the details for yourself even if you can see the end result ahead of time. Remember to ask if you have questions!!! This is due Wednesday at 9:00am online.
• Complete the Reading Assignment for Section 8.4 on this handout. This is due Wednesday at the beginning of class.
• Carefully read this Review Sheet. Work on the suggested problems on that sheet and/or use any odd problem from any of the sections included on the exam to practice. Remember that you can go back to redo WeBWorK problems too! I will give you a hard copy of the review sheet in class on Wednesday. Also bring questions to class on Wednesday! We will discuss Section 8.3, do some groupwork problems, and then discuss the review sheet and other questions you have.
• The Week 10 Lab Key has been taken off line now. If you have questions about it, please send me an email.

Homework due Thursday, November 19:

• Prepare for Exam 3! Have confidence in your abilities!!!
• Be sure to review the lab keys for Week 10 and Week 11 posted above and directly below.
• The Week 11 Lab Key has been taken off line now. If you have questions about it, please send me an email.
• Arrive on time to lab in Gulick 206A. Use all the tables and space yourselves out!

Homework due Friday, November 20:

• Work practice exercises on Section 8.3 on WeBWorK. This is due Friday at 9:00am online.
• THERE IS NO MAIN EXERCISES ASSIGNMENT DUE THIS WEEK!!! :)

### WEEK 11: November 9 - November 13

Remember to start your work as soon as possible so that you have the opportunity to ask questions if you have them!

Our third exam will be Thursday, November 19th instead of this week!!! Don't wait to prepare! Make sure your questions are answered now!

Homework due Monday, November 9:

• Continue solving the groupwork exercises on the handout that we were started in Friday's class. Be sure that you have tried all of them. Go directly to your groups on Monday morning when you arrive in class and start discussing them. I will ask specific groups to put up specific problems before or soon after class begins.
• Week 10 Lab is due at the beginning of Monday's class! One from each group. Be sure you meet with your group to review each other's final write-ups prior to Monday's class, so that everyone agrees that each group member's set of solutions is a good one. I will roll the die to see which group member will turn in her/hir/his paper. Be sure you send your lab to class with someone else if there is a reason you cannot be there!!!
• Work practice exercises on Section 7.8 on WeBWorK. This is due Monday at 9:00am online.
• Complete the Reading Assignment for Section 8.1 on this handout. This is due Monday at the beginning of class.

Homework due Wednesday, November 11:

• Review the Type 1 Improper Integral exercises that we did in Monday's class. Be sure that you work through problems that other groups did. Make sure they make sense and let me know if you have any questions.
• Work practice exercises on Section 7.8 on WeBWorK. These are mostly problems on Type 2 Improper Integrals, though you will see a Type 1 in there as well! Remember to ask if you have questions!!! This is due Wednesday at 9:00am online.
• Complete the Reading Assignment for Section 8.2 on this handout. This is due Wednesday at the beginning of class.
• OPTIONAL HOMEWORK BONUS: Interested in adding a few points to your homework grade and getting some good practice on some challenge problems along the way? Try this. This is due Wednesday at the beginning of class.
• The Week 9 Lab Key has been taken off line now. If you have questions about it, please send me an email.

Homework due Friday, November 13:

• Remember to start your homework as early as possible so that you can ask me questions! Come to office hours or send me emails about ANY of it: WeBWorK, Main Exercises, Reading Assignments, Labs, Class Notes...you name it! ASK!!! The sooner you start your homework the more time you have to ask me questions!
• At the beginning of Thursday's Lab we will work on some groupwork problems from Section 8.1. They are numbers 15, 21, 24, 35, 47, 63 and 81. Be sure that you have reviewed our work from Thursday's lab, that you have worked through all of the problems before Friday's class, and that they make sense to you or you have specific questions that you can ask about them.
• Complete the Main Exercises Assignment for Week 11 on this handout. This is due Friday at the beginning of class.
• Work practice exercises on Section 8.1 on WeBWorK. The first three problems are about sequences, but the last two are review! This is due Friday at 9:00am online.
• Complete the Reading Assignment for Section 8.3 on this handout. This is due Friday at the beginning of class.

### WEEK 10: November 2 - November 6

Homework due Monday, November 2:

• Review the groupwork exercises on the handout that we were working on in Friday's class. Finish working on the problems on that worksheet. With your group, choose a problem to put on the board when you arrive in class on Monday!
• Week 9 Lab is due at the beginning of Monday's class! One from each group. Be sure you meet with your group to review each other's final write-ups prior to Monday's class, so that everyone agrees that each group member's set of solutions is a good one. I will roll the die to see which group member will turn in her/hir/his paper. Be sure you send your lab to class with someone else if there is a reason you cannot be there!!!
• Work practice exercises on Section 7.4 on WeBWorK. This is due Monday at 9:00am online. The first six problems are about trigonometric substitution, and the last one is to get you started thinking about partial fraction decomposition.
• Complete the Reading Assignment for Section 4.7 (yes, we are reviewing!) on this handout. This is due Monday at the beginning of class.

Homework due Wednesday, November 4:

• Work on the problems I put on the board in Monday's class (Section 7.5: 30, 31, 51, 60 and 62. These are on pages 549-550 in our text.). Be sure that you have tried all of them. Go directly to your groups on Wednesday morning when you arrive in class and start discussing them. I will ask specific groups to put up specific problems before or soon after class begins.
• Work practice exercises on Section 7.5 on WeBWorK. This includes four problems on the material from Section 7.5, and one review question from Section 4.7. Be sure to read the directions!!! The order matters in how you key in your answers to WeBWorK. This is due Wednesday at 9:00am online.
• Complete the Reading Assignment for Section 7.8 on this handout. This is due Wednesday at the beginning of class.
• OPTIONAL HOMEWORK BONUS: Interested in adding a few points to your homework grade and getting some good practice on some challenge problems along the way? Try this. This is due Wednesday at the beginning of class.

Homework due Friday, November 6:

• Remember to start your homework as early as possible so that you can ask me questions! Come to office hours or send me emails about ANY of it: WeBWorK, Main Exercises, Reading Assignments, Labs, Class Notes...you name it! ASK!!! The sooner you start your homework the more time you have to ask me questions!
• Complete the Main Exercises Assignment for Week 10 on this handout. This is due Friday at the beginning of class.
• Work practice exercises on Section 7.5 on WeBWorK. This includes some partial fraction decomposition questions and some L'Hôpital's Rule questions. This is due Friday at 9:00am online.

### WEEK 9: October 26 - October 30

Homework due Monday, October 26:

• Review the integration by parts exercises that we did in Friday's class. Since each group worked a different problem and presented, and not everyone worked through the details of all the problems, be sure that you work through problems that other groups did. Make sure they make sense and you see what was unique about each one!
• After you review the problems we put on the board, work through number 5 from the groupwork handout. Be ready to put it on the board when class begins...in fact, take initiative and put it on the board with your group BEFORE class begins! ;-)
• Go back to problem 1(c) from your Reading Assignment for Section 7.3. Read the hint in the text carefully, then actually show the calculations that show these two solutions are equivalent (this does not have to do with integration or differentiation!!!). Be ready to put your solution for this on the board at the beginning of class.
• THERE IS NO LAB ASSIGNMENT DUE THIS WEEK!!! :)
• Work practice exercises on Sections 7.2 and 7.3 on WeBWorK. This is due Monday at 9:00am online. The first five problems are integration by parts, and the last two are powers of trigonometric functions like we began discussing at the end of class today.

Homework due Wednesday, October 28:

• Finish the problems that we started working on in Monday's class (Section 7.3: 15, 21, 41, 25 and 39 as well as $\int\sec^3x\tan^5x\,dx$.). Be sure that you have completed all of them. Go directly to your groups on Wednesday morning when you arrive in class and compare your answers. I will ask specific groups to put up specific problems before or soon after class begins.
• Work practice exercises on Section 7.3 on WeBWorK. This is due Wednesday at 9:00am online.
• Complete the Reading Assignment for Section 7.5 on this handout. This is due Wednesday at the beginning of class.

Homework due Thursday, October 29:

• Section 3 (the 11:15 class): We did not have an opportunity to talk about other forms we might see and how to choose the substitution. Make a table with the headings: Form, Correlate to..., Restriction, Substitution. The first row you should be able to fill in based on the example we did in class (the form we worked on was $a^2-x^2$ for some constant $a$ [where our $a$ was 5] etc.). There are two other rows to complete. See how much of them you can fill in and we will discuss it at the beginning of lab.
• Work on the problems from the group work sheet you received at the end of Monday's class. Try to complete at least problems 1, 3 and 4 before the beginning of lab - all of them would be great! We will spend some time working on these before we work on the regular lab.

Homework due Friday, October 30:

• Complete the Main Exercises Assignment for Week 9 on this handout. This is due Friday at the beginning of class.
• Work practice exercises on Section 7.4 on WeBWorK. This is due Friday at 9:00am online.
• Don't wait until an exam is imminent to ask questions if you have them! Please come to my office hours, visit the Math Intern, and send me emails whenever you find something you are unsure about. Also do extra practice problems (such as extra fun and odd problems in the text) on material with which you do not feel confident. If you find yourself going to the Math Intern regularly, make sure you are coming to at least one of my office hours as well.

### WEEK 8: October 19 - October 23

Our second exam, covering sections 6.1-6.7, will be on Thursday, October 22nd in Gulick 206A, our normal lab space.

Homework due Monday, October 19:

• Review the pumping fluid exercises that we did in Friday's class. Make sure that the way we set up the integrals make sense to you. Then evaluate the integrals we set up to be sure you agree with the final answers I wrote on the board.
• Read through the handout that I gave you at the end of Friday's class. Try to fill in the blanks. Use your textbook as a reference, for example if you need to remember what the Intermediate Value Theorem says. However, remember that we are looking at the derivation of the formula for surface area in a slightly different way than the text. Be ready to share your ideas of how to fill in the blanks with the class at the beginning of class on Monday.
• Week 7 Lab is due at the beginning of Monday's class! One from each group. Be sure you meet with your group to review each other's final write-ups prior to Monday's class, so that everyone agrees that each group member's set of solutions is a good one. I will roll the die to see which group member will turn in her/hir/his paper. Be sure you send your lab to class with someone else if there is a reason you cannot be there!!!
• Work practice exercises on Section 6.7 on WeBWorK. This is due Monday at 9:00am online. I encourage you to do MORE practice problems from the text!!! Remember that answers to odd problems are in the back!

Homework due Wednesday, October 21:

• Finish the problems on the groupwork sheet that we were working on in Monday's class (surface area and work!). Be sure that you have completed all of them. Go directly to your groups on Wednesday morning when you arrive in class and compare your answers. I will ask specific groups to put up specific problems soon after class begins. The sooner we work through these the more time we will have for general review at the end of class, so please come prepared!
• Work practice exercises on Sections 6.7 and 6.6 on WeBWorK. This is due Wednesday at 9:00am online.
• Complete the Reading Assignment for Section 7.3 on this handout. This is due Wednesday at the beginning of class.
• Carefully read this Review Sheet. Work on the suggested problems on that sheet and/or use any odd problem from any of the sections we have done to practice. Remember that you can go back to redo WeBWorK problems too! I will give you a hard copy of the review sheet in class on Wednesday. Also bring questions to class on Wednesday! We will review the surface area and pumping fluids groupwork we were doing at the end of Monday's class, then discuss Section 7.2, and lastly discuss the review sheet and other questions you have. The more prepared you are with having worked through the problems on the handout from the end of Monday's class, the more time we will have at the end of class. You could even meet with your group ahead of time!
• The Week 6 Lab Key has been taken off line now. If you have questions about it, please send me an email.
• The Week 7 Lab Key has been taken off line now. If you have questions about it, please send me an email.

Homework due Thursday, October 22:

• Prepare for Exam 2! Have confidence in your abilities!!!
• Be sure to review the lab keys for Week 6 and Week 7 posted above.
• Arrive on time to lab in Gulick 206A. Use all the tables and space yourselves out!

Homework due Friday, October 23:

• Work practice exercises on Section 7.2 on WeBWorK. This is due Friday at 9:00am online. There are only two problems here. They ask you to choose $u$ and $dv$ first, so you can be sure whether or not you have chosen correctly. Remember that experimenting is good!
• Complete the Reading Assignment for Section 7.4 on this handout. This is due Friday at the beginning of class.
• THERE IS NO MAIN EXERCISES ASSIGNMENT DUE THIS WEEK!!! :)

### WEEK 7: October 12 - October 16

Have a Great Fall Break!!!

Homework due Wednesday, October 14:

• Week 6 Lab is due at the beginning of Wednesday's class! One from each group. Be sure you meet with your group to review each other's final write-ups prior to Wednesday's class, so that everyone agrees that each group member's set of solutions is a good one. I will roll the die to see which group member will turn in his/her/hir paper. Be sure you send your lab to class with someone else if there is a reason you cannot be there!!!
• Review your notes from Friday's class. Finish the arc length problem we were working on at the end of class. Then think of an alternate way of solving the problem. You should get the same answer both ways! Be sure to do the second arc length problem, Section 6.5 #9 (page 450), as well. Remember that odd answers are in the back of the text. Be ready to share your work in full-class discussion at the beginning of class.
• Try Exercise 31 in Section 6.5 on page 450. It is good to practice the "Explain why or why not" questions. Go back and try others in previous sections!
• Work practice exercises on Section 6.5 on WeBWorK. This is due Wednesday at 9:00am online.
• Complete the Reading Assignment for Section 6.6 on this handout. This is due Wednesday at the beginning of class.

Homework due Friday, October 16:

• Review the spring examples that we did in Wednesday's class (as a class and then in group work). Be sure that you have completed both of them and they make sense.
• Complete the Main Exercises Assignment for Week 7 on this handout. This is due Friday at the beginning of class.
• Complete the Reading Assignment for Sections 7.1 and 7.2 on this handout. This is due Friday at the beginning of class.
• Work practice exercises on Section 6.7 on WeBWorK. The first question is about finding work when you are given a force function. The other four are working with springs. Be sure to read the questions carefully! They are not all asking for the same thing and do not all start by giving you the same information! This is due Friday at 9:00am online.
• Our next exam is next week! Don't wait until next week to ask questions if you have them! Please come to my office hours, visit the Math Intern, and send me emails whenever you find something you are unsure about.

### WEEK 6: October 5 - October 9

Homework due Monday, October 5:

• Finish the groupwork problems that we did in Friday's class (volumes of solids of revolution including around axes other than the $x$-axis and $y$-axis). Be sure that you have completed all of them and they make sense. Go directly to your groups on Monday morning when you arrive in class and compare your answers. I will ask specific groups to put up specific problems soon after class begins.
• THERE IS NO LAB ASSIGNMENT DUE THIS WEEK EITHER!!! You should be working on your Exam Bonus AND reviewing ALL your work on Exam 1! Be sure to read my comments and rework any problems for which you did not receive full credit - even if it isn't the one you are turning in on your bonus assignment. I will not be collecting exam rewrites except for the one you put on your bonus assignment, but you should do it and come see me for any questions you have. ALSO, take note of the things that you did do WELL!!!
• Work practice exercises on Section 6.3 on WeBWorK. This is due Monday at 9:00am online.
• Complete the Reading Assignment for Section 6.5 on this handout. This is due Monday at the beginning of class.

Bonus Assignment due Tuesday, October 6:

• The Exam 1 Bonus is due at 2:00pm in my office. You may turn it in any time before that, either in class on Monday or at my office (sliding it under my door if I am not there).
• Remember that if you would like to discuss this with someone besides yourself, you must talk to me. Be sure to come to office hours or make an appointment well in advance if my office hours do not work for you.

Homework due Wednesday, October 7:

• Review your notes from Monday's class. Set up and solve the integral for the example that we were doing at the end of class (with the region bounded by $y=x$ and $y=x^2$ rotated about the $y$-axis) using the shell method. Then set up the integral using the disk method. Evaluate both integrals. Do you get the same answers? Be ready to share your work in full-class discussion at the beginning of class.
• Work practice exercises on Section 6.4 on WeBWorK. This is due Wednesday at 9:00am online. The first two ask you to use the shell method, the third to use the disk method, and the last two you are able to choose. Sometimes the trickiest part is just setting up the diagram. Remember that disk/washer problems can be calculated by finding the volume of the larger solid, and then subtracting (in a separate integral) the volume of its hole.

Homework due Friday, October 9:

• Review the groupwork problems that we did in Wednesday's class. Evaluate the integrals we set up and make sure you agree with the final answers I put on the board (remember answers to volume problems should always be positive!).
• Complete the Main Exercises Assignment for Week 6 on this handout. This is due Friday at the beginning of class.
• Complete the Reading Assignment for Section 6.7 on this handout. This is due Friday at the beginning of class. ***Note that we are skipping around a little!!! We will get back to Section 6.6 soon!!!***
• Work practice exercises on Sections 6.4 and 6.5 on WeBWorK. The first three problems are practice with volumes (think carefully about whether you want to use shell or disk method for each), the fourth is a matching problem to practice visualizing setting up volumes (note that you only get TWO attempts on this problem!), and the last question is on arc length (although we have not yet discussed these, this is a basic problem to see if you understand how to apply the formula). This is due Friday at 9:00am online.
• We still have two weeks before our next exam, but don't wait to ask questions if you have them! Please come to my office hours, visit the Math Intern, and send me emails whenever you find something you are unsure about. Also make sure you are comfortable graphing functions. Here is a list of functions we have been working with that you should know how to graph.

### WEEK 5: September 28 - October 2

Homework due Monday, September 28:

• Review the groupwork problems that we did in Friday's class (Section 6.1 problems 13, 23, 47 and 39). Be sure that you have completed all of them and they make sense. These are all odd and remember that the answers to odd problems are in the back of the text.
• THERE IS NO LAB ASSIGNMENT DUE THIS WEEK!!! :)
• Work practice exercises on Sections 6.2 on WeBWorK. This is due Monday at 9:00am online.
• Complete the Reading Assignment for Section 6.3 on this handout. This is due Monday at the beginning of class.

Homework due Wednesday, September 30:

• Review your notes from Monday's class. In particular, work through the parts of the examples I skipped over (integrating, finding the points of intersection in the second example, etc.). Make sure you agree with my results and that you understand the process for the problems.
• Work practice exercises on Section 6.2 on WeBWorK. This is due Wednesday at 9:00am online.
• Review Lab 3 and the key to Lab 3 (see last Wednesday's assignments), and let me know if you have any questions on it.

Homework due Friday, October 2:

• Review the groupwork problems that we did in Wednesday's class. Evaluate the integrals we set up. Make sure your answers are positive! Check to see if you get the same answer when setting up with respect to $x$ as with respect to $y$ in the second question. You should!
• Work practice exercises on Sections 6.3 and 6.2 on WeBWorK. The first two problems are finding volumes using the General Slicing Method, and the last three are working with areas between curves. This is due Friday at 9:00am online.
• Complete the Main Exercises Assignment for Week 5 on this handout. This is due Friday at the beginning of class.
• Complete the Reading Assignment for Section 6.4 on this handout. This is due Friday at the beginning of class.

### WEEK 4: September 21 - September 25

Remember our first exam, covering sections 5.1-5.5, will be during lab on Thursday, September 24th in Gulick 206A, our normal lab space.

Homework due Monday, September 21:

• Review the groupwork problems that we did in Friday's class (Section 5.4 problems 11, 13, 25, 30 and 34). Be sure that you have completed all of them and they make sense. Feel like you need extra practice on this topic or previous ones? Remember that the answers to odd problems are in the back of the text. Tackle an odd problem and check your work! We do have our first exam this week!
• Week 3 Lab is due at the beginning of Monday's class! One from each group. I will roll the die to see which group member will turn in her/hir/his paper. Be sure you send your lab to class with someone else if there is a reason you cannot be there!!!
• Work practice exercises on Sections 5.4 and 5.5 on WeBWorK. This is due Monday at 9:00am online.
• Since we were running over in Section 2 (the 10 o'clock class), I did not get a chance to give you the $u$-substitution Guidelines Handout at the end of class. I will hand it out in Monday's class, but you should read through it here first. BOTH sections should study this handout and we will discuss questions and ideas from it on Monday.
• The Week 2 Lab Key has been taken off line now. If you have questions about it, please send me an email.

Homework due Wednesday, September 23:

• Review the groupwork problems that we did in Monday's class on the handout. Be sure that you have completed all of them and they make sense. We will start class with each group putting one of the questions on the board.
• Work practice exercises on Section 5.5 on WeBWorK. This is due Wednesday at 9:00am online. This assignment has a few more problems than usual, but I am hoping that there are a bunch that are relatively straightforward and quick for you.
• Complete the Reading Assignment for Section 6.2 on this handout. This is due Wednesday at the beginning of class.
• Carefully read this Review Sheet. Work on the suggested problems on that sheet and/or use any odd problem from any of the sections we have done to practice. Remember that you can go back to redo WeBWorK problems too! I will give you a hard copy of the review sheet in class on Wednesday. Also bring questions to class on Wednesday! We will review the $u$-substitution groupwork we were doing at the end of Monday's class, then discuss Section 6.1, and lastly discuss the review sheet and other questions you have.
• The Week 3 Lab Key has been taken off line now. If you have questions about it, please send me an email.

Homework due Thursday, September 24:

• Prepare for Exam 1! Have confidence in your abilities!!!
• Note that some of the WeBWorK problems due Friday are about Section 6.1 but many are Review questions. You may want to do the review questions before the exam on Thursday for extra practice!
• Arrive on time to lab in Gulick 206A. Use all the tables and space yourselves out!

Homework due Friday, September 25:

### WEEK 3: September 14 - September 18

Homework due Monday, September 14:

• Review the groupwork problems that we did in Friday's class (Section 5.2 problems 41, 43, 45, 67 and 71). Be sure that you have completed all of them and that they make sense.
• Work practice exercises on Section 5.2 and Section 5.3 on WeBWorK. The first three problems are about the properties of integrals that we worked on in lab on Thursday and class on Friday. The second set is working problems like we did at the end of class on Friday. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online. This is due Monday at 9:00am online. I am hoping that you all find this WeBWorK goes faster than some of the previous ones!
• Week 2 Lab is due at the beginning of class! One from each group. I will roll the die to see which group member will turn in hir/his/her paper. Be sure you send your lab to class with someone else if there is a reason you cannot be there!!!
• Complete the Reading Assignment for Section 5.4 on this handout. This is due Monday at the beginning of class.
• The Week 1 Lab Key has been taken off line now. If you have questions about it, please send me an email.
• Feel a need to review L'Hopital some more? Try problems 31, 33, 33, 49 and 67 from Section 4.7 (pages 307-308). Feel a need to review antidifferentiation? Try problems 27, 41, 61, 69, 109 and 111 from Section 4.9 (pages 328-329). Remember that odd problems have answers in the back of the book.

Homework due Wednesday, September 16:

• Review the groupwork problems that we did at the beginning of Monday's class. Be sure that you have completed all of them and they make sense.
• Review the proof of the Fundamental Theorem of Calculus that we did in class. Isn't it cool! Let me know if you have questions. Make sure you understand how the Mean Value Theorem was valuable to the proof.
• Work practice exercises on Section 5.3 on WeBWorK. This is due Wednesday at 9:00am online. These are mostly working problems applying what we proved in class on Monday, the Fundamental Theorem of Calculus Part 2! Recall that the theorem said that to evaluate a definite integral we could just find an antiderivative of the integrand and then plug in the limits of integration. Wow!
• Complete the Reading Assignment for Section 5.5 on this handout. This is due Wednesday at the beginning of class.

Homework due Friday, September 18:

• Review the groupwork problems that we did in Wednesday's class (Section 5.3 problems 38, 39, 53, 85 and 93). Be sure that you have completed all of them and that they make sense. In particular, be sure you have good explanations for your answers in 85.
• Work practice exercises on Section 5.4 and Review on WeBWorK. Problems 1-3 contain questions on the new material in Section 5.4. We will discuss the formula for the average value of a function at the beginning of lab, so you may want to wait to do these basic problems until after lab. Problems 1, 4 and 5 contain questions that require you to apply material in sections previous to 5.4. This is due Friday at 9:00am online.
• Complete the Main Exercises Assignment for Week 3 on this handout. This is due Friday at the beginning of class.
• Complete the Reading Assignment for Section 6.1 on this handout. This is due Friday at the beginning of class.
• If you did not turn in a picture of yourself with Homework 0 or at your appointment, bring it on Friday!

### WEEK 2: September 7 - September 11

Homework due Monday, September 7:

• Work practice exercises on Section 5.1 on WeBWorK. This is on sigma notation. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online. This is due Monday at 9:00am online.
• Week 1 Lab is due at the beginning of class! One from each group. I will roll the die to see which group member will turn in hir/his/her paper. Be sure you send your lab to class with someone else if there is a reason you cannot be there.
• Complete the Main Exercises Assignment for Week 1 on this handout. This is due Monday at the beginning of class.

Note that due to introductory appointments with you all, some of my open office hours are shortened this week. The revised hours for Tuesday are 1:05-2:00 and for Wednesday are: 1:30-2:30 (or 3:00...I am offering a few slots to the first section). If you cannot make these times and need to see me, please make an appointment.

Homework due Wednesday, September 9:

• Review the groupwork problems that we did at the beginning of Monday's class. Be sure that you have completed all of them and they make sense. Please let me know if you have questions on them.
• Have you finished working through the "Reviewing Calculus I" handout? Then check your answers here. Remember: I will not collect this but you are responsible for knowing all the material covered on it (hopefully just from previous experience). Please let me know if you have questions.
• Work practice exercises on Section 5.2 on WeBWorK. This is due Wednesday at 9:00am online. Hint: Recall our work on page one of the "Reviewing Calculus" handout. There is a theorem there that will help you with your limits at infinity! Beware: One of the problems has ONLY ONE attempt allowed and another has ONLY FOUR!
• Complete the Reading Assignment for Section 5.3 on this handout. This is due Wednesday at the beginning of class.
• The following WeBWorK practice is more review of Calculus I. This assignment is all on limits and using L'Hopital's Rule: L'Hopital Review assignment. This material is covered in Section 4.7 in the text. You may want to review when you can actually apply L'Hopital's Rule. This assignment is not due until Friday at 9:00am, but I wanted to give you extra time to fit it into your schedules.

Homework due Friday, September 11:

• Review the groupwork that we were doing in class as well as class lecture notes. Make sure it all makes sense and let me know as soon as possible if you still have questions. Also remember that you can go back and redo WeBWorK problems that have already been submitted. It will not change your grade, but you can check your answers. If you check the box "Show correct answers" when you are redoing past assignments, it will not only check your answer, but also show you what the correct answer is supposed to be. Cool!
• Finish the following WeBWorK review on limits and using L'Hopital's Rule: L'Hopital Review assignment. This material is covered in Section 4.7 in the text. You may want to review when you can actually apply L'Hopital's Rule. This assignment is due Friday at 9:00am.
• Complete the Main Exercises Assignment for Week 2 on this handout. This is due Friday at the beginning of class.
• Work practice exercises on Section 5.2 on WeBWorK. These problems are very similar to the assignment that was due on Wednesday morning or that we worked on together in class on Wednesday. Hopefully going through this again will help solidify things. As usual, ask me if you have questions. This is due Friday at 9:00am online.

### WEEK 1: August 31 - September 4

Welcome to Calculus II!!!

Homework due Tuesday, September 1:

Although I will not normally assign homework to be due on non-class days, this week we will need to in order to get started and refresh our memories. Please complete the following:
• Orient yourself to WeBWorK, where you will be completing assignments roughly three times a week. Read these pages for instructions about syntax and an introduction to how the system works: WeBWorK Instructions and FAQs, WeBWorK Syntax and List of Functions.
• Practice using WeBWorK with the WeBWorKIntro assignment which can be accessed on the WeBWorK Home Page for Our Class. This is due Tuesday at 2:15pm.
• Read the yellow (Section 2) Syllabus or the green (Section 3) Syllabus and the salmon Homework Guidelines. We went through much of this in class, but you should read all the details and make sure you don't have any questions about either document. Also be sure to record the exam dates in your personal calendar/planner. Remember there are no make-ups.
• Familarize yourself with this website. Note that there is a link at the top of the page to our syllabus and to the homework guidelines, should you lose the ones I handed out in class. The syllabus has a lot of vital information on it and you will likely want to refer back to it regularly. Also at the top of the page is a link to my grade scale. This will let you know what percentage you need to earn in order to obtain specific grades. In addition, there are links to our WeBWorK homepage and the websites with instructions and tips for WeBWorK.
• Write an autobiographical essay as assigned at the end of the syllabus ("Homework 0"). This is due Tuesday at 2:15pm in my office.
• Complete the Reading Assignment for Section 5.1 on this handout. This is due Tuesday at 2:15pm in my office.

Homework due Wednesday, September 2:

• Review Calculus I material with the WeBWorK Review assignment. This is due Wednesday at 9:00am. (Note that you can see all assigned WeBWorK Homework Sets by logging into the general site and clicking on Homework Sets in the lefthand tool bar. Clicking the above link takes you directly to the Review assignment.)
• Remember to bring the "Reviewing Calculus I" handout you received the first day of class with you on Wednesday. We will spend the first half of class working on these problems in groups. You are welcome to work on them before Wednesday's class, but it is not required.

Homework due Friday, September 4:

• Finish working through the "Reviewing Calculus I" handout. An answer key will be posted for you to check your work in a few days. I will not collect this but you are responsible for knowing all the material covered on it (hopefully just from previous experience in Calculus I!).
• Work practice exercises on Section 5.1 on WeBWorK. The first four problems are about Section 5.1 and the last three are review exercises (i.e. Calculus I material). Be sure to read carefully. There are two problems for which you only have ONE attempt. Some problems have hints. Especially take heed for those for which you only have one attempt! This is due Friday at 9:00am online. You may want to wait until after lab on Thursday before you try these as we will be finishing our example from the end of class on Wednesday in lab.
• Complete the Reading Assignment for Section 5.2 on this handout. This is due Friday at the beginning of class.
• Note that normally you will have a Main Exercises Assignment due on Friday. This week because we are just getting started and I want you to have a little more practice first, I will make the Main Exercises assignment (which I will post tomorrow), due on Monday.

Hobart and William Smith Colleges: Department of Mathematics and Computer Science
Erika L.C. King