# MATH 131 - Fall 2018 Calculus II

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

Class: MWF 10:10-11:05am in Eaton 110
Lab: Th 11:55am-1:20pm in Gulick 2000

Office Hours: M: 11:15am-12:15pm, W: 3:00-4:30pm, Th: 2:15-3:45pm, F: 3:00-4:00pm, and by appointment
Math Intern Hours with Drew Scammell in Lansing 310: Su: 4:00-6:00pm and 7:00-10:00pm; M-Th 3:00-6:00pm and 7:00-10:00pm

Course Syllabus
Course Homework Guidelines

### READING/EXAM WEEK: December 12 - December 18

Review Session: Thursday, December 13th 1:30pm-2:30pm in Eaton 110. Bring questions!

Office Hours:

• Wednesday, December 12: 11:30am-1:30pm
• Friday, December 14: 1:30pm-3:30pm
• Monday, December 17: 11:00am-12:30pm
• Tuesday, December 18: 11:00am-12:00pm (Noon)
• By appointment

Final Exam: Tuesday, December 18th 1:30PM-4:30PM in GULICK 2000 (our lab room).

Last Lab Key:

• Here is the Lab Key for the Week 15 Lab. Note that this only has final answers (and a few hints), not full solutions.

### WEEK 15: December 10 - December 14

Homework due Monday, December 10:

• Review your notes from class on Friday on power series leading into Taylor polynomials. Also review the group work that we discussed at the beginning of class from the first question from lab on Thursday.
• Work through the Taylor polynomial example I passed out at the end of class on Friday. At the very least you should have all the derivatives and the evaluation of the derivatives at zero filled out on your handout. Try to also get a general expression for the $k$th derivative evaluated at zero...and as much else as you can!
• 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 Monday at 9:00am online.
• 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 towards your homework grade: Read Section 9.3 (pages 684-694). Then complete the Reading Assignment for that section on this handout. In this section we use our work in Section 9.1 with finite Taylor polynomials to create Taylor series, in other words, infinite polynomials of a particular form. It turns out that we can use these to represent functions, which is especially helpful when we are trying to evaluate an integral of a hard function to which our known techniques do not apply like $\int e^{x^2} dx$ or $\int \sin(x^2) dx$. Why is it helpful? Isn't it easy to integrate a polynomial?! (See Section 9.4 page 699.) Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) This is due Monday at the beginning of class. COPIES OF THE READING ASSIGNMENT ARE AVAILABLE IN THE BOX OUTSIDE MY OFFICE. To earn all five bonus points your assignment must be VERY thorough and contain complete sentences.
• What would you like to see an example of or discuss when we have our review session? 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 for the review session. Let me know by email by Wednesday at 9:00am if you would like to do this.

### WEEK 14: December 3 - December 7

There will be a 20-30 minute quiz at the beginning of class on Monday, December 3rd covering sections 8.1-8.5 (Remember just the Ratio and Root Tests from Section 8.5 not the Comparison Tests). 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, December 3:

• Review your notes from class on Friday on the Ratio and Root Tests. Also review the groupwork. Recall that we worked on Section 8.5: 11, 15, 17, 19, 21, 22 and 23. Practice writing a complete sentence as part of your solution to each exercise. Be sure that you have completed all of the exercises and that they make sense.
• Prepare for your quiz! The quiz will be roughly the first 20-30 minutes of class and will cover Sections 8.1-8.5.
• Work practice exercises on Section 8.5 on WeBWorK. This is a short one! This is due Monday at 9:00am online.
• Read Section 8.6 (pages 649-656). Then complete the Reading Assignment for that section on this handout. In previous sections of this chapter, we have been dealing with series all of whose terms are positive. Note that this meant that the sequence of partial sums was always increasing (think for a minute to make sure you believe that). What happens if some of our terms are positive and some of our terms are negative? Now what happens with the sequence of partial sums? In particular, in this section we will study what happens when the terms of a series alternate between positive and negative terms. Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) This is due Monday at the beginning of class. COPIES OF THE READING ASSIGNMENT ARE AVAILABLE IN THE BOX OUTSIDE MY OFFICE.
• Due to the quiz on Monday, the Main Exercises Assignment will be due on Wednesday! Note that doing it may help you prepare for the quiz, so you should feel free to have it done by Monday even though it is not due that day!

Lab Key: Would you like to check your answers and work on the Week 13 Lab? Would you like to see if you are skipping any steps when working through a question? Check out the key below! Note how solutions include full sentences!

Homework due Wednesday, December 5:

• Remember to think about what you might like to bring to the lab party on Thursday, and with whom you might like to share the responsibility. I will have a sign up sheet in class on Wednesday!
• Review your notes from Monday's lecture on the Direct and Limit Comparison Tests.
• 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 $p=2$.
• 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 Wednesday at 9:00am online.
• Complete the Main Exercises Assignment for Week 14 on this handout. This is due Wednesday at the beginning of class, 10:10am.
• Read Section 9.1 (pages 661-671). Then complete the Reading Assignment for that section on this handout. The moment for which you have all been waiting! Now we can start figuring out how we can represent functions (especially functions that are difficult to integrate) by series! Our series will start having variables in them, not just constants. In particular, we will be interested in using polynomials (nice functions!), indeed infinite polynomials, to represent hard functions. Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) This is due Monday at the beginning of class. COPIES OF THE READING ASSIGNMENT ARE AVAILABLE IN THE BOX OUTSIDE MY OFFICE.
• Want more practice with questions involving the Ratio Test and the Root Test? Work on these questions from Section 8.5 and check your answers in the back of the text: 10, 13, 19, 24, 25, 41, 43 and 45 (pages 647-648).

Homework due Thursday, December 6:

• Bring your book, notes (if you have more than one notebook, bring them all!!!) and snacks to lab! We will do evaluations, discuss the absolute convergence test, and we will review for the final and share tasty treats.
• Bring a laptop or other devise, if you have one, on which you can complete the course evaluations.

Homework due Friday, December 7:

• Review Wednesday's and Thursday's class lecture notes on the alternating series test and the absolute convergence test. Also review the group work from the group worksheet that we did in class.
• Read about the Ratio Extension Test on the handout I gave you in lab. This will be especially helpful as we discuss absolute and conditional convergence.
• 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? (Remember the question Olivia V. asked in class on Wednesday?) 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 Friday at 9:00am online.
• Read Section 9.2 (pages 675-682). Then complete the Reading Assignment for that section on this handout. In this section we extend the ideas of the previous section where we looked at finite Taylor polynomials. Now we will look at infinite polynomials, i.e. power series! We look at when they are convergent, how we can use them to represent functions, and more! Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) This is due Monday at the beginning of class. COPIES OF THE READING ASSIGNMENT ARE AVAILABLE IN THE BOX OUTSIDE MY OFFICE.

### WEEK 13: November 26 - November 30

Have a great Thanksgiving Break!!!

Due to needing to visit another professor's class, I must cancel my Monday office hours on November 26th. If you would like to meet with me before my Wednesday office hours, please email me and we will find another time to meet!

Homework due Monday, November 26:

• Review the groupwork that we were doing in class on Friday the 16th. Recall that we worked on the group work exercises on the handout. Practice writing a complete sentence as part of your solution to each exercise. Be sure that you have completed all of the exercises and that they make sense.
• Also review the class lecture notes from Friday the 16th on Telescoping Series and The Divergence Test. Review your work on the bonus questions and practice writing complete sentences as part of your solution to each of these questions as well.
• 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.
• Reread Section 8.4 (pages 627-638). Review ideas about the Test for Divergence and get ready for our discussion about the Integral Test.
• Want more practice with questions involving sequences? Work on these questions from Section 8.2 and check your answers in the back of the text: 13, 15, 17, 21, 23, 53, 57 and 59 (page 616).
• Make a flow chart or list for the methods you know to decide the convergence or divergence of sequences.
• Note that there is NO Main Exercises Assignment due Monday!
• Note that there is NO reading assignment due on Monday!

Homework due Wednesday, November 28:

• Review your notes from Monday's lecture on the Harmonic Series, the $p$-series and the Integral Test.
• Finish evaluating the series we were working on at the end of class. Recall you were trying to determine whether or not the series $\sum_{n=1}^ {\infty}\frac{1}{2n+3}$ is convergent or divergent. Be ready to share your results in class.
• 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. These questions involve 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 Wednesday at 9:00am online.
• Read Section 8.5 (pages 641-647). Then complete the Reading Assignment for that section on this handout. In this section, we continue to learn different techniques to help us determine whether or not different series converge or diverge. Two of these new techniques involve looking at the general term of the series and manipulating it in some way to a form that is easier to deal with. The other two let us compare the series we are interested in with a series for which determining convergence or divergence is easier. Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) This is due Wednesday at the beginning of class. COPIES OF THE READING ASSIGNMENT ARE AVAILABLE IN THE BOX OUTSIDE MY OFFICE.
• Want more practice with questions involving geometric and telescoping series? Work on these questions from Section 8.3 and check your answers in the back of the text: 25, 27, 29, 31, 33, 37, 53, 57, 59, 65 and 69 (pages 623-624).
• Review Exam 3, reworking any problems on which you missed points. Make sure you feel comfortable with these questions and come to office hours with questions if you do not feel confident with any of the material.

Homework due Friday, November 30:

• Review Wednesday's class lecture notes finishing up the Integral Test example and proving that the Harmonic Series is divergent! Also review the group work from the group worksheet that we did in class. Remember that we now have two Key Limits! You may use these results whenever it is helpful, but you must show that you are using them as we discussed in class! If you would rather reprove them, that is ok as well, but time consuming! ;-) You all did a great job with the presentation of your problems on the board! Good work!
• If you would like another look at the cool proof we did showing that the Harmonic Series is divergent using the idea of looking at a subsequence of the sequence of partial sums of the series, check out this article. Specifically read the intro on page one and Proof 1 on page 2. There are FOURTEEN additional proofs for the same result if you are interested in other approaches!
• Work practice exercises on Section 8.4 on WeBWorK. Remember that finding a way to express a rational number as a fraction can be done using geometric series! Cool! This is due Friday at 9:00am online.
• Want more practice with questions involving $p$-series, the Divergence Test and the Integral Test? Work on these questions from Section 8.4 and check your answers in the back of the text: 11, 17, 21, 25, 30, 33, 47, 51 and 53 (pages 638-639).
• Review past WeBWorK questions and do extra exercises from the textbook to practice for Monday's quiz!
• Note that there is NO reading assignment due on Friday!

### WEEK 12: November 12 - November 16

Our third exam, covering sections 7.1-7.6 and 7.8, will be on Thursday, November 15th in Gulick 2000, our normal lab space.

Homework due Monday, November 12:

• Review the groupwork that we were doing in class as well as Friday's class lecture notes. Recall that we worked on Section 8.1: 24, 29, 35, 63, 64, 65 and 81. Be sure that you have completed all of them and that they make sense.
• 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 Monday at 9:00am online.
• Complete the Main Exercises Assignment for Week 12 on this handout. This is due Monday at the beginning of class, 10:10am.
• Note that there is NO reading assignment due on Monday!
• Practice, practice, practice for the exam! Make sure you are practicing without the book, notes, friends or other resources -- just you and your awesome brain!

Lab Key: Would you like to check your answers and work on the Week 10 Lab? Would you like to see if you are skipping any steps when working through a question? Check out the key below!

Homework due Wednesday, November 14:

• Review Monday's lecture notes on the Squeeze Theorem as well as the group work that we were doing in class. Recall that we worked on Section 8.2: 19, 25, 29, 31, 33, 47, 49, 51, 55, 61 and 75. Be sure that you have completed all of them and that they make sense.
• 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 Wednesday at 9:00am online.
• Read Section 8.4 (pages 627-638). Then complete the Reading Assignment for that section on this handout. The Geometric Series and the Telescoping Series are cool and nice (because we can determine whether or not they converge and what they converge to relatively quickly). But many series are not of these forms. For the rest of this chapter we will be learning different techniques to help us determine whether or not different series converge or diverge. Interestingly enough, though we will be able to determine whether other types of series converge or diverge, we will not necessarily be able to determine what they converge to if they converge! In this section we look at two new tests, one of which uses integration! Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) This is due Wednesday at the beginning of class. COPIES OF THE READING ASSIGNMENT ARE AVAILABLE IN THE BOX OUTSIDE MY OFFICE.
• 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, and then discuss the review sheet and other questions you have.

Lab Key: Would you like to check your answers and work on the Week 11 Lab? Would you like to see if you are skipping any steps when working through a question? Check out the key below!

Homework due Thursday, November 15:

• Finish preparing for Exam 3! Have confidence in your abilities!!!
• Arrive on time to lab in Gulick 2000. Remember that seating is assigned randomly, so wait until name sheets are distributed before you take your seat.

Homework due Friday, November 16:

• Review Wednesday's class lecture notes on geometric series. Get ready to talk about telescoping series on Friday!
• Work practice exercises on Section 8.3 on WeBWorK. This is due Friday at 9:00am online.
• Note that there is NO reading assignment due on Friday!

### WEEK 11: November 5 - November 9

Homework due Monday, November 5:

• Review Friday's class lecture notes. Read over the handout on improper integrals and write down any questions you have about Type 1 Improper Integrals.
• Continue solving the groupwork exercises on the handout that we 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. We will put those as well as some others on the board at the beginning of class.
• Work practice exercises on Section 7.8 on WeBWorK. This is due Monday at 9:00am online.
• Complete the Main Exercises Assignment for Week 11 on this handout. This is due Monday at the beginning of class, 10:10am.
• Read Section 8.1 (pages 596-604). Then complete the Reading Assignment for that section on this handout. This section gives a brief introduction to the topics of this chapter that will be our focus for the rest of the semester: sequences and series. Sequences and series are closely linked, but it is important to understand their differences. Why do we study these? One reason is that even with all the cool techniques we have learned, there are STILL functions that we do not know how to integrate! (Can you think of one?) Series will give us a way to attack these! Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) This is due Monday at the beginning of class. COPIES OF THE READING ASSIGNMENT ARE AVAILABLE IN THE BOX OUTSIDE MY OFFICE.
• Talk to your friends and family about infinity! How would they compare the set of natural numbers with the set of integers? Find out something new!

Homework due Wednesday, November 7:

• 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. Recall that we worked on the four problems from the group worksheet as well as Section 7.8: 17, 23 and 33.
• 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.

Lab Key: Would you like to check your answers and work on the Week 9 Lab? Would you like to see if you are skipping any steps when working through a question? Check out the key below!

Homework due Friday, November 9:

• Review the groupwork that we were doing in class as well as Wednesday's class lecture notes. Recall that we worked on Section 7.8: 41, 49, 61 and 67, as well as three other integrals on the group worksheet. Be sure that you have completed all of them and that they make sense. Please ask me questions, no matter how small you think they are, if you have them!
• 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.
• Want more practice with improper integral questions? Work on these questions from Section 7.8 and check your answers in the back of the text: 15, 19, 25, 31, 39, 43 and 68 (page 578-579).
• Read Section 8.3 (pages 619-623). Then complete the Reading Assignment for that section on this handout. In this section we delve deeper into what a series is, focusing on two very important and interesting kinds of series: geometric and telescoping. We will discover that these two types of series are very nice! What is nice about them? Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) This is due Friday at the beginning of class. COPIES OF THE READING ASSIGNMENT ARE AVAILABLE IN THE BOX OUTSIDE MY OFFICE.

### WEEK 10: October 29 - November 2

Homework due Monday, October 29:

• Review the groupwork exercises on the handout that we were working on in Friday's class. Make sure you finish problems 5 and 6 and come to class prepared to discuss them.
• Complete the Main Exercises Assignment for Week 10 on this handout. This is due Monday at the beginning of class.
• 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.
• Read Section 4.7 (pages 297-307). Then complete the Reading Assignment for that section on this handout. Yes, we are going back to limits! Why? Do you remember when we said that certain integrals are called improper and do not exist as definite integrals like $\int_{-1}^1\frac{1}{x^4}dx$? It would be interesting to have an idea whether the area under these curves actually approaches a fixed number or not as an improper integral even if not as a definite integral. How can we tell? Using limits! But the limits we deal with are usually indeterminate. There are some little tricks for some indeterminate forms, but they don't always work. In this section we remind ourselves how and when we can apply the technique known as l'H\^opital's Rule. Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) This is due Monday at the beginning of class. COPIES OF THE READING ASSIGNMENT ARE AVAILABLE IN THE BOX OUTSIDE MY OFFICE.

Homework due Wednesday, October 31: Happy Halloween!!!:

• Review the groupwork that we were doing in class as well as Monday's class lecture notes. Recall that we worked on two questions from Friday's group work, as well as the integrals from these exercises: Section 7.2: 20 and 30, and Section 7.3: 22, 40 and 42. (I did not originally tell you which sections they were from because I wanted you to figure out which techniques to use!)
• 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.
• Read Section 7.8 (pages 570-578). Then complete the Reading Assignment for that section on this handout. Now we will figure out how to think about integrals that do not exist as definite integrals like $\int_{-1}^1\frac{1}{x^4}dx$. We will use limits to evaluate integrals over intervals containing infinite discontinuities, like this example, and also integrals over infinite intervals of integration. Since we learned about surface area, we can even look at something really odd: Gabriel's Horn, which is an object that has finite volume but infinite surface area! WHAT??!!! This is neat stuff! Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) This is due Wednesday at the beginning of class. COPIES OF THE READING ASSIGNMENT ARE AVAILABLE IN THE BOX OUTSIDE MY OFFICE.
• Work through the problems on Exam 2 making sure you understand any mistakes you made. Come to my office hours after you have finished reworking the exam with any questions you have.

Homework due Friday, November 2:

• Review the groupwork that we were doing in class as well as Wednesday's class lecture notes. Recall that we worked on Section 7.5: 21, 23, 27, 29, 51, 57, 61 and 62. Be sure that you have completed all of them and that they make sense.
• 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.
• Want more practice with partial fraction decomposition questions? Work on these questions from Section 7.5 and check your answers in the back of the text: 19, 25, 31, 37, 59 and 79 (page 549-550).
• If you feel rusty on L'Hôpital's Rule, reread Section 4.7 and work odd exercises from that section, which you can then check in the back of the book!
• Note that there is NO reading assignment due on Friday!

### WEEK 9: October 22 - October 26

Homework due Monday, October 22:

• Review the integration by parts exercises that we did in Friday's class. 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!
• Go back to problem 3 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!!!). A few of you got this, but I want the rest of you to take a second look!
• Note that there is NO Main Exercises Assignment due Monday!
• Work practice exercises on Sections 7.2 and 7.3 on WeBWorK. This is due Monday at 9:00am online. The first three problems are integration by parts, and the last two are powers of trigonometric functions like we began discussing during the second half of class Friday.
• Read Section 7.4 (pages 531-537). Then complete the Reading Assignment for that section on this handout. This is REALLY COOL STUFF!!! Again, don't be shy of the trigonometric functions! Here we take an algebraic function and change the variable to make it into a trigonometric function. Sound crazy? Maybe, but it works beautifully! As you learn this cool approach, still remember your basic tools in your toolbox. For example, even though trigonometric substitution is really cool, you don't need it to solve $\int_0^6\sqrt{36-x^2} dx$! (How DO you solve that one?) Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) This is due Monday at the beginning of class. COPIES OF THE READING ASSIGNMENT ARE AVAILABLE IN THE BOX OUTSIDE MY OFFICE.

Homework due Wednesday, October 24:

• Review the groupwork that we were doing in class as well as Monday's class lecture notes. Recall that we worked on Section 7.3: 12, 15, 19, 21, 24, 50 and 59. Be sure that you have completed all of them and that they make sense.
• Check out the integration of secant at the top of page 528. Do you see how they multiplied secant by a fancy one? Neat! This is an integral you need to know; I would rather you remembered where it came from rather than just memorized it!
• Work practice exercises on Section 7.3 on WeBWorK. This is due Wednesday at 9:00am online.
• Read Section 7.5 (pages 541-548). Then complete the Reading Assignment for that section on this handout. Like in the previous sections with other techniques, the technique of partial fractions can only be used on functions of certain forms (what forms are those???). It turns out that to apply this technique, we do quite a bit of algebra and not so much calculus! So get ready to do some algebra! Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) This is due Wednesday at the beginning of class. COPIES OF THE READING ASSIGNMENT ARE AVAILABLE IN THE BOX OUTSIDE MY OFFICE.
• Want more practice with integration by parts questions? Work on these questions from Section 7.2 and check your answers in the back of the text: 11, 13, 17, 21, 25, 29, 33 and 37 (page 520).

Homework due Friday, October 26:

• Review the groupwork that we were doing in class as well as Wednesday's class lecture notes. Recall that we worked on Section 7.3: 34, 36, 37, 39, 41, 43 and 51. We also worked on $\int\sec^3x\tan^5x\,dx$, $\int\sec x\,dx$ and $\int\sec^3 x\,dx$. Be sure that you have completed all of them and that they make sense.
• Work practice exercises on Section 7.4 on WeBWorK. This is due Friday at 9:00am online.
• Want more practice with powers of trigonometric functions questions? Work on these questions from Section 7.3 and check your answers in the back of the text: 11, 13, 17, 23, 27, 35, 47, 49, 55, 57 and 61 (page 529-530).
• Note that there is NO reading assignment due on Friday!

### WEEK 8: October 15 - October 19

Our second exam, covering sections 6.1-6.7, will be on Thursday, October 18th in Gulick 2000, our normal lab space.

Homework due Monday, October 15:

• Review the groupwork that we were doing in class as well as Friday's class lecture notes. Recall that we worked on Section 6.7: 23a, 23b, 25a, 25b as well as three questions from Thursday's lab. Be sure that you have completed all of them and that they make sense.
• Set up the example we started at the very end of class on Friday. Come to class ready to ask questions and/or share your work.
• In Friday's class, you received a homework that had your overall homework average (WeBWork, Reading Assignments and Main Exercises) on it. If you are not satisfied with what this average currently is, come to office hours so that we can discuss how you can improve it! You have plenty of time to make it happen!
• Complete the Main Exercises Assignment for Week 8 on this handout. This is due Monday at the beginning of class.
• ***Since we didn't finish our pumping example in class on Friday, I am giving until Tuesday at 9am to finish these three (only!) questions. There will be a few more for Wednesday; you will want them for practice! *** Work practice exercises on Section 6.7 on WeBWorK. This is due TUESDAY 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!
• Note that there is NO reading assignment due on Monday!

Lab Keys: Would you like to check your work on the Labs? Would you like to see if you are skipping any steps when working through a question? Check out these keys below!

Homework due Wednesday, October 17:

• Review the pumping fluid exercises that we did in Monday'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.
• Review Monday's lecture notes on integration by parts. Come to class ready to focus on a couple of examples and ideas before reviewing for the exam. Remember the better focused we are at the beginning the more quickly we can move on to review!
• Work practice exercises on Section 6.7 on WeBWorK. This is due Wednesday at 9:00am online. Just two questions!
• Read Section 7.3 (pages 523-529). Then complete the Reading Assignment for that section on this handout. How do we integrate functions that are products of powers of trigonometric functions? In this section you will find tools for how to solve such integrals! Don't be shy of the trigonometric functions! We find ways to use some old formula friends to rewrite these integrals to look like easier algebraic functions! Great puzzles! Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) This is due Wednesday at the beginning of class. COPIES OF THE READING ASSIGNMENT ARE AVAILABLE IN THE BOX OUTSIDE MY OFFICE.
• 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. Make sure you have worked through all the lab problems and reviewed those answer keys. 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. Bring questions to class on Wednesday!

Homework due Thursday, October 18:

• Finish preparing for Exam 2! Have confidence in your abilities!!!
• Arrive on time to lab in Gulick 2000. Remember that seating is assigned randomly, so wait until name sheets are distributed before you take your seat.

Homework due Friday, October 19:

• Review the groupwork that we were doing in class as well as Wednesday's class lecture notes. The group work was all on the handout.
• Reread Sections 7.1 and 7.2 (pages 511-520). See if the examples make more sense after the example we did on Wednesday. Do the examples in Section 7.2 follow "Hey u! Look I Ate The Egg"?
• 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!
• Then try two more practice exercises on Section 7.2 on WeBWorK. This is due Friday at 9:00am online. Keep experimenting!
• Note that there is NO reading assignment due on Friday!

### WEEK 7: October 10 - October 12

Have a Great Fall Break!!!

Homework due Wednesday, October 10:

• Review the groupwork that we were doing in class as well as Friday's class lecture notes. Recall that we worked on Section 6.5: 10, 11, 13, 14, 15, 16 and 31. Be sure that you have completed all of them and that they make sense.
• Work more practice exercises on arc length with this Section 6.5 on WeBWorK. This is due Wednesday at 9:00am online.
• Work practice exercises on surface area with this Section 6.6 on WeBWorK. This is due Wednesday at 9:00am online.
• Complete the Main Exercises Assignment for Week 7 on this handout. This is due Wednesday at the beginning of class.
• Note that there is NO reading assignment due on Wednesday!

Homework due Friday, October 12:

• Review the groupwork that we were doing in class as well as Wednesday's class lecture notes. Recall that we worked on Section 6.6: 5, 7, 9, 11, 13, 14 and 15. Be sure that you have completed all of them and that they make sense. Check your final answer with the back of the text.
• 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 1 - October 5

Homework due Monday, October 1:

• Review the groupwork that we were doing in class as well as Friday's class lecture notes. Recall that we worked on finding the volumes of the solids of revolution formed by rotating the region bounded by the curves $y=-x$, $y=x+4$ and $y=0$ about (a) the $x$-axis, (b) the $y$-axis, (c) $y=4$ and (d) $x=3$, as well as the volumes of the solids of revolution formed by rotating the region bounded by the curves $x=1-y^2$ and $x=0$ about (a) the $y$-axis, (b) $y=-2$, and (c) $x=2$. Be sure that you have completed all of them and that they make sense.
• Want more practice with volume questions? Work on these questions from Section 6.3 and check your answers in the back of the text: 7, 9, 17, 29, 37, 45, 49, 53 and 63 (pages 430-433).
• Work practice exercises on Section 6.3 on WeBWorK. This is due Monday at 9:00am online.
• Read Section 6.5 (pages 445-449). Then complete the Reading Assignment for that section on this handout. How do you determine the distance between two points? What if you could not go "as the crow flies", but rather your path between the points was curved? In other words, how can we find the length of a curve, or the arc length of a segment of a function? Again, we still approach deriving a formula for Arc Length with essentially the same initial steps! Now your roommate should almost be able to say them in her/his/hir sleep! Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) This is due Monday at the beginning of class. COPIES OF THE READING ASSIGNMENT ARE AVAILABLE IN THE BOX OUTSIDE MY OFFICE.
• Note that a slight revision was made to the Main Exercises on Wednesday! If you had a question about the first problem, it might be resolved now!
• Complete the Main Exercises Assignment for Week 6 on this handout. This is due Monday at the beginning of class.

Homework due Wednesday, October 3:

• Review your notes from Monday's class. In particular, make sure you see the difference between setting up an example in terms of the disk method and setting up in terms of the shell method. Make sure you agree with my results (actually do the integration and check the final answer I posted on the board) and that you understand the process for the problems. Let me know as soon as possible if you still have questions, either in class, in office hours, or via email.
• 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 5:

• Review the groupwork that we were doing in class as well as Wednesday's class lecture notes. Recall that we worked on finding the volumes of the solids of revolution formed by rotating the region bounded by the curves $y=x^3$, $y=8$ and $x=0$ about (a) the $x$-axis, (b) the $y$-axis, (c) $x=4$ and (d) $y=-2$, as well as the volumes of the solids of revolution formed by rotating the region bounded by the curves $y=\ln x$, $x=1$ and $y=3$ about (a) the $x$-axis, (b) the $y$-axis, (c) $x=4$ and (d) $y=-2$. We used the shell method for all of these. Be sure that you have completed all of them and that they make sense. Remember you can actually find the volumes for the first four (do this!), but not for the last four (yet!). Try setting up the integrals for finding the volumes of the last four using the disk method. Can you integrate these?
• Want more practice with volume questions? Work on these questions from Section 6.4 and check your answers to most of these in the back of the text: 13, 18, 19, 21, 33, 35 and 37 (pages 442-443).
• As we work through the applications in this chapter, remember to think about whether your final answer makes sense. Answers to volume problems (and area problems AND arc length problems) should always be positive! Thus if you obtain a negative answer, you know there is something incorrect. If you are working a problem on an exam and figure this out but do not have time to go back and fix it, be sure to note that you know there is an issue!
• 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. This is due Friday at 9:00am online.
• Read Section 6.7 (pages 459-467). Then complete the Reading Assignment for that section on this handout. In this section we investigate some physics related applications. Mainly we will investigate how we determine work when the force applied is variable. Guess what? We still start the derivation of the formulas for these applications by partitioning our interval into subintervals and by looking at smaller pieces that we sum together to estimate the whole! Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) This is due Friday at the beginning of class. COPIES OF THE READING ASSIGNMENT ARE AVAILABLE IN THE BOX OUTSIDE MY OFFICE.
• Review 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 you only missed one point! I will not be collecting exam rewrites, 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!!! You ALL have things you did well in your exams!
• 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 24 - September 28

Homework due Monday, September 24:

• Review the groupwork that we were doing in class as well as Friday's class lecture notes. Recall that we worked on Section 6.1: 19, 23, 30, 39 and 47 as well as two $u$-substitution questions. Be sure that you have completed all of them and that they make sense. Check the answers to odd questions in the back of the text.
• Work practice exercises on Section 6.2 on WeBWorK. This is due Monday at 9:00am online.
• Note that there is NO Main Exercises Assignment due Monday.

Homework due Wednesday, September 26:

• 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. Let me know as soon as possible if you still have questions.
• At the end of class we started setting up the integrals needed when finding the area bound between $y=x^3$, $y=x+6$ and $y=-\frac{1}{2}x$. Work on this question and set up the integrals both (a) with respect to $x$ and (b) with respect to $y$. Be ready to share your results at the beginning of class on Wednesday.
• Work practice exercises on Section 6.2 on WeBWorK. This is due Wednesday at 9:00am online.
• Note that there is NO reading assignment due on Wednesday!

Homework due Friday, September 28:

• Rework the first groupwork problem from Wednesday's class until you can get (a) and (b) to match! The problem was: find the area bound between $y=x^3$, $y=x+6$ and $y=-\frac{1}{2}x$ (a) with respect to $x$ and (b) with respect to $y$. Be ready to share your results at the beginning of class on Friday.
• Review the groupwork that we were doing in class as well as Wednesday's and Thursday's class lecture notes. Be sure to work through integrals we only set up to be sure you agree with the results I listed. Recall that in group work we worked on the question above as well as finding the area of the region bounded by $y=x^3-3x+3$ and $y=x+3$, Section 6.2: 10 and 11, and evaluating the integral $\int\frac {36x^{11}+9x^5} {\sqrt{1-81x^{12}}} dx$. Make sure you feel confident with these questions.
• 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.
• Want more practice with area questions? Work on these questions from Section 6.2 and check your answers in the back of the text: 13, 17, 21, 25, 35 and 39 (pages 417-418).
• Read Section 6.4 (pages 434-441). Then complete the Reading Assignment for that section on this handout. In this section we will look at finding the volumes of objects not by using disks but by using cylinders. Sometimes, especially if our solid has a hole, using the Shell Method will be easier than using the Disk Method. Again, we still approach deriving a formula for the Shell Method with the same initial steps! You should almost be able to say them in your sleep! Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) This is due Friday at the beginning of class. COPIES OF THE READING ASSIGNMENT ARE AVAILABLE IN THE BOX OUTSIDE MY OFFICE.

### WEEK 4: September 17 - September 21

Remember our first exam, covering sections 5.1-5.5, will be during lab on Thursday, September 2oth in Gulick 2000, our normal lab space.

Homework due Monday, September 17:

• Review the groupwork that we were doing in class as well as Friday's class lecture notes. Recall that we worked on Section 5.4: 11, 13, 16, 25, 30, 31 and 34. Be sure that you have completed all of them and that they make sense.
• Work practice exercises on Sections 5.4 and 5.5 on WeBWorK. This is due Monday at 9:00am online.
• NOTE THAT THE MAIN EXERCISES ASSIGNMENT WAS REVISED ON FRIDAY AT 3:30PM!!! BE SURE YOU GET THE NEW VERSION!!!
• Complete the Main Exercises Assignment for Week 4 on this handout. This is due Monday at the beginning of class.
• Note that there is NO Reading Assignment due Monday.

Lab and Review Keys: Would you like to check your work on the Calculus I Review Handout and on the Labs? Would you like to see if you are skipping any steps when working through a question? Check out these keys below!

Homework due Wednesday, September 19:

• Review the groupwork problems on the handout that we worked on in Monday's class. Try to complete all of them including the problems other groups worked on and the extra problems. Let me know if there is a particular question you would like to review in Wednesday's class. Feel free to put one on the board as soon as you come to class if there is one you would like to discuss. You do not have to have the solution to get it started!
• 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 some that are relatively straightforward and quick for you. This is good practice with $u$-substitution!
• Read Section 6.2 (pages 412-416). Then complete the Reading Assignment for that section on this handout. What if we are interested in finding the area of a region that is not bound in part by the $x$-axis? What if the region is bound between two curves? In this section we learn how to find the area of regions that are bound in different ways. We will have to consider integrating with respect to $y$ instead of $x$ too! However, keep in mind that all the ideas in this section build off of what we started at the beginning of Chapter 5. Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) This is due Friday at the beginning of class.
• Briefly review Section 6.1. We will spend about half of Wednesday's class discussing that section.
• 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! Bring questions to class on Wednesday! Part of our class will be review.

Homework due Thursday, September 20:

• 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! In particular, questions 1-6 are good review questions about when we need to break up the interval of integration, when we need to brake up the integrand, and about $u$-substitution.
• Arrive on time to lab in Gulick 2000. Remember that seating is assigned randomly, so wait until you are told where to sit.

Homework due Friday, September 21:

• Review Wednesday's class lecture notes on position, displacement and distance traveled. Evaluate whether or not the material all makes sense and let me know as soon as possible if you still have questions.
• Work practice exercises on Sections 6.1 and Review on WeBWorK. Questions 1-6 are good review questions about when we need to break up the interval of integration, when we need to brake up the integrand, and about $u$-substitution. This is due Friday at 9:00am online.
• Note that there is NO Reading Assignment due Friday.

### WEEK 3: September 10 - September 14

Due to needing to visit another professor's class, I must cancel my Monday office hours. If you would like to meet with me before my Wednesday office hours, please email me and we will find another time to meet!

Homework due Monday, September 10:

• Review the groupwork that we were doing in class as well as Friday's class lecture notes. Recall that we worked on Section 5.2: 41, 43, 44, 45, 51, 67, 71 and 75). Be sure that you have completed all of them and that they make sense.
• Complete the Main Exercises Assignment for Week 3 on this handout. This is due Monday at the beginning of class.
• 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 three are problems like we did at the end of class on Friday. Here you only have to enter the final answers, but be sure you know how to write out the process as well. 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!
• Read Section 5.4 (pages 377-381). Then complete the Reading Assignment for that section on this handout. In this section we will learn that if a function has the property that it is even or odd we can use it to our advantage when evaluating definite integrals. We will also learn how to determine the average value of a function and what that means. Lastly, we will look back at some old friends - the Mean Value Theorem and the Extreme Value Theorem - and see what they can tell us about integrals. Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) This is due Monday 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 Wednesday at 9:00am, but I wanted to give you extra time to fit it into your schedules. This review assignment is in addition to the usual WeBWorK assignment due on current material.

Homework due Wednesday, September 12:

• 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.
• Note that there are two WeBWorK assignments on Section 5.3 listed below. However, together they make up the size of one! ;-)
• Work practice exercises on Part 1 of the Fundamental Theorem of Calculus on WeBWorK. This is due Wednesday at 9:00am online. There are only three problems in this set!
• Work practice exercises on Part 2 of the Fundamental Theorem of Calculus 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!
• Read Section 5.5 (pages 384-390). Then complete the Reading Assignment for that section on this handout. Now that we have the Fundamental Theorem of Calculus in our tool box and know that we can use antidifferentiation to solve definite integrals, it is even more important for us to expand our ability to find antiderivatives. Up to this point, our ability to find antiderivatives has been limited to a small number of functions that fit into certain formulas. What happens if we have a composition of functions? This section teaches a strategy for integrating some functions that are really compositions of functions. Note that this will NOT help us with all compositions, but it will help us with many and we will use this technique A LOT. Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) 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 due Wednesday at 9:00am.

Homework due Friday, September 14:

• Review the groupwork that we were doing in class as well as Wednesday's and Thursday's class lecture notes. Recall that we worked on Section 5.3: 11, 38, 39, 40, 43, 45, 46, 49, 63, 64, 67, 68, 101, and 103. Make sure you feel confident with these questions.
• Here are a few more good practice problems from Section 5.3: 53, 85 and 93. For Exercise 85, be sure that you can provide a counterexample or a thorough explanation.
• 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.
• Read Section 6.1 (pages 398-406). Then complete the Reading Assignment for that section on this handout. Although we have a lot more to do to understand how to integrate functions, we can still do a lot with the techniques we have so far. So in Chapter Six we take a break from learning techniques and look at applications of integration. In this first section we look at why we would want to integrate the absolute value of a function, as well as show how we can use integration to find out cell population or production costs (among a myriad of other things) at a future time. Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) This is due Friday at the beginning of class.

Homework due Monday, September 17:

• More will be added on Friday!
• NOTE THAT THE MAIN EXERCISES ASSIGNMENT WAS REVISED ON FRIDAY AT 3:30PM!!! BE SURE YOU GET THE NEW VERSION!!!
• Complete the Main Exercises Assignment for Week 4 on this handout. This is due Monday at the beginning of class.

### WEEK 2: September 3 - September 7

Homework due Monday, September 3:

• 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.
• Complete the Main Exercises Assignment for Week 2 on this handout. This is due Monday at the beginning of class.
• Note that there is NO Reading Assignment due Monday.

Homework due Wednesday, September 5:

• Remember to bring in your picture if you forgot to bring it to your appointment!
• Check your schedule to make sure that you can make the Final Exam as it is listed in our syllabus. Remember that this is during the time slot allotted for our Lab instead of the slot allotted for our class. Let me know ASAP if the revised time does not work for you.
• Review the groupwork exercises and notes from Monday's class. Recall that we worked on Section 5.1: 40 (c) and (d), 41 (g), 42 (e), 42 (f), 56, 64 and 66. Make sure you feel confident with these questions. Do more practice problems if necessary until you are confident with all the material! Note that the problems done in class do not necessarily cover all possible types of questions! Please let me know if you have questions on them.
• Work practice exercises on Section 5.1 and 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! Several of these problems are asking you to practice your Riemann sums and definition of the definite integral, either by setting them up or by thinking about what function would give such a sum. Beware: One of the problems has ONLY ONE attempt allowed and another has ONLY FOUR!
• Read Section 5.3 (pages 362-372). Then complete the Reading Assignment for that section on this handout. In this section we will learn about the area function. This builds up to the moment we all have been waiting for since the beginning of Calculus I: The Fundamental Theorem of Calculus!!! Be sure to work through the ideas of Example 2 very carefully. That example gives a good basis for why the Fundamental Theorem might make sense. Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) This is due Friday at the beginning of class.

Homework due Friday, September 7:

• Last chance to bring in your picture if you forgot to bring it to your appointment! You must do this if you want to earn 100% on your first assignment!
• Check your schedule to make sure that you can make the Final Exam as it is listed in our syllabus. Remember that this is during the time slot allotted for our Lab instead of the slot allotted for our class. Let me know ASAP if the revised time does not work for you. If I don't hear from you by Friday, September 7th, I will assume that the time is good for you and you will be expected to be present during that time!
• Review the groupwork that we were doing in class as well as Wednesday's class lecture notes. Recall that we worked on Section 5.2: 22, 23, 26, 27, 29, 32, 37, 38, 39 and 40. Make sure you feel confident with these questions. Evaluate whether or not the material 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!
• 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.
• 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 Wednesday at 9:00am, but I wanted to give you extra time to fit it into your schedules. This review assignment is in addition to the usual WeBWorK assignments due on current material.
• Note that there is NO Reading Assignment due Friday.

Homework due Monday, September 10:

• More will be added on Friday!
• Complete the Main Exercises Assignment for Week 3 on this handout. This is due Monday 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 Wednesday at 9:00am, but I wanted to give you extra time to fit it into your schedules. This review assignment is in addition to the usual WeBWorK assignment due on current material.

### WEEK 1: August 27 - August 31

Welcome to Calculus II!!!

Homework due Tuesday, August 28:

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. Details about logging into WeBWorK are in the WeBWorK Instructions and FAQs website as well as my greeting email. This is due Tuesday at 3:00pm.
• Fill out this autobiographical questionnaire. Print it two sided if possible. If not, be sure to staple it. Be sure to leave the top portion on the first side (above where you place your name) blank. This is due Tuesday at 3:00pm in my office.
• Read Section 5.1 (pages 333-342). Then complete the Reading Assignment for that section on this handout (this is the same as what I handed out in class). The geometric idea behind integration is area. The area beneath a constant function is just the area of a rectangle. But what if we want the area under a function that is not constant? What if the function is a curve? How do we find the area under that? In this section we will look at estimating the area under a curve using geometric shapes whose areas are easy to find. Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) This is due Tuesday at 3:00pm in my office.

Homework due Wednesday, August 29:

• Read the green Syllabus and the salmon Homework Guidelines. We went through some 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.
• 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 and started working on 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 encouraged to continue working on them before Wednesday's class.

Homework due Friday, August 31:

• 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.
• Read Section 5.2 (pages 348-358). Then complete the Reading Assignment for that section on this handout. We talked about how to estimate the area under the curve of $f(x)$ when $f$ is a positive function. What happens if we use the same procedure (looking at the region between the $x$-axis and the function) but $f$ is a negative function? How do we interpret our results? How do we get better estimations? Can we actually find the exact area under the curve? Answer these questions and more in the reading! Figure 5.21 is a nice accompaniment to the description of the notation on pages 351-352. Be sure to complete the Quick Check Questions while you are reading and check your answers at the end of the section. (You need not write down the Quick Check Questions, but they are helpful to do. Answers to the Quick Check questions are at the end of the exercise set for each section.) This is due Friday at the beginning of class.

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