# MATH 131 - Spring 2020 Calculus II

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

Class: MWF 1:30-2:30pm in Coxe 7
Lab: Th 10:30am-Noon in Gulick 2000

Office Hours: M: 10:00-11:30am, T: 9:45-11:15am, W: 2:45-3:45pm, Th: 4:00-5:00pm, and by appointment
Math Intern Hours with Sam LeGro at the IC: Su: 4:00-6:00pm; and in Lansing 310: Su: 7:00-10:00pm, M-Th 2:00-5:00pm and 7:30-10:30pm

Course Syllabus for Section 1
Course Homework Guidelines

### WEEK 9: March 23 - March 27

During Spring Break I will be working to determine how best to organize our class for remote learning. I encourage you to read your emails closely, and to contact me with any questions, concerns or suggestions you have. If you have issues with internet accessibility, please let me know what those are. While this will not be ideal, we will work together to make the best learning experience we can. Feel free to start chatting on that chat group you formed at the end of class on March 13th. Make sure everyone in the group is receiving the information I am sending out and posting, just in case it is ending up in someone's spam box!

Look for an email from me no later than Sunday, March 22nd detailing our strategy for proceeding. At this point, you should plan to be available for class at the usual time on Monday, March 23 (1:30pm EST), perhaps via Zoom, but again, I will determine that in the next week.

I may contact you via email in the middle of spring break to ask questions about some options and will appreciate responses as soon as it is possible for you to give them. While it will be helpful for all of us to stay on track with material and assignments, we will need to be a bit more flexible with some deadlines. Be in contact with me about your needs as the semester progresses.

For this next week, you do not need to work on material for this course (although it may be fun and a good distraction for you!); concentrate more on planning for how we will work for the rest of the semester and more importantly on your health (physical and emotional) and your family. Again, I encourage you to come to me with any questions, concerns or suggestions you have. Thank you for your patience with me as I learn new tools like Canvas and Zoom. Also thank you for being a great class; that gives me hope that we can still have a good rest of the semester in whatever form(s) it takes!

### WEEK 8: March 9 - March 13

Our second exam, covering Sections 6.1-6.7, will be on Thursday, March 12th in Gulick 2000, our normal lab space. Make yourself a review sheet for these sections and then compare it to the one I post early in week 8!

Homework due Monday, March 9:

• Review Friday's class lecture notes on work pumping fluids. Check that you agree with the final answer of the first example that we did and work on the second example. Write down any questions you have and bring them to class.
• Review the groupwork that we were doing in class. Recall that we worked on Section 6.7: 25, 27, 28 and 29. 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 work pumping fluids on WeBWorK with the Section67Part2 assignment. This is due Monday at 1:00pm 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!

Due to our exam on Thursday, there will be NO Main Exercises assignment due on Wednesday!

On Wednesday, March 11th at 5:00pm in Napier 201, there will be a colloquium given by Catalina Garcia Tomas, Kaitlyn Geraghty, Connor Parrow, and Yifei Tao about their trip to the Nebraska Conference for Undergraduate Women in Mathematics. Refreshments will be served at 4:45pm. I hope you can make it!

Check out this answer key for the Week 6 Lab! Make sure your answers were correct and that these ideas make sense to you! Look for what makes a solution complete.

Homework due Wednesday, March 11:

• Review the groupwork that we were doing in Monday's class. Recall that in groups we worked on Section 6.7: 37 and 42, as well as two problems from the handout. Be sure that you have completed all of them and that they make sense.
• 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 surface area on WeBWorK with the Section6.7Part3 assignment. This is due Wednesday at 1:00pm online. Just two questions!
• Read Section 8.3 (pages 532-536). 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 1:30pm. Copies of the handout can be found outside my office.
• Carefully read this Review Sheet. Work on the suggested problems on that sheet and/or use odd problems from any of the sections we have done to practice (note that I have posted suggested problems for most sections). Make sure you have worked through all the lab problems and reviewed the answer keys to check your work and solutions. Remember that you can go back to redo WeBWorK problems too! Bring questions to class on Wednesday!
• Note due to our exam on Thursday, there will be NO Main Exercises assignment due on Wednesday!

Check out this answer key for the Week 7 Lab! Make sure your answers were correct and that these ideas make sense to you! Look for what makes a solution complete.

Homework due Thursday, March 12:

• Finish preparing for Exam 2! Have confidence in your abilities!!!
• Arrive on time to lab in Gulick 2000. Spread out to take advantage of the space to think!

Homework due Friday, March 13:

• Reread Sections 8.1 and 8.2 (pages 520-529). See if the examples make more sense after the examples we did on Wednesday. Do the examples in Section 8.2 follow "Hey u! Look I Ate The Egg"?
• Work practice exercises on integration by parts on WeBWorK with the Section82Part1 assignment. This is due Friday at 1:00pm 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 integration by parts practice exercises on WeBWorK with the Section82Part2 assignment. This is due Friday at 1:00pm online. Keep experimenting!
• Note that there is NO reading assignment due on Friday!

### WEEK 7: March 2 - March 6

Homework due Monday, March 2:

• My office hours are rather lonely! It would be great to see more of you there!
• Review Friday's class lecture notes on arc length. Write down any questions you have and bring them to class or office hours!
• Review the groupwork that we were doing in class. Recall that we worked on 16, 17, 41, 43 and 51 from Section 6.4. We used the shell method for all of these (and also disk for 51). Be sure that you have completed all of them and that they make sense. Remember you can check your answers to the odd problems in the text.
• 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: 21, 23, 37, 39, 42, 45 and 47 (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 Section 6.4 and 6.5 on WeBWorK with the Section64Part2and65 assignment. 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 Monday at 1:00pm online.
• Work more practice exercises on arc length on WeBWorK with the Section65Part2 assignment. Note that the first two questions only ask you to set up the integral, but not evaluate the integral. This is due Monday at 1:00pm online.
• Read Section 6.7 (pages 465-473). 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 Monday at 1:30pm. Copies of the handout can be found outside my office.
• We still have a week and a half 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.

Homework due Wednesday, March 4:

• Review the groupwork that we were doing in class as well as Monday's class lecture notes on surface area. Recall that in groups we worked on Section 6.5: 10, 13, 14 and 15. Be sure that you have completed all of them and that they make sense.
• Want more practice with arc length questions? Work on these questions from Section 6.5 and check your answers for most in the back of the text: 11, 16, 17, 31, 33 and 35 (page 456).
• Work practice exercises on surface area on WeBWorK with the Section66 assignment. This is due Wednesday at 1:00pm online.
• Complete the Main Exercises Assignment for Week 7 on this handout. Be sure to write your solution on the handout. Copies of the handout can be found outside my office. This is due Wednesday at 1:30pm.
• Note that there is NO reading assignment due on Wednesday! (Whew! We had many days of one day per section!)
• Remember to 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!

Homework due Friday, March 6:

• Review the groupwork on surface area that we were doing in class as well as Wednesday's class lecture notes on spring compression and stretching. Recall that in group work we worked on Section 6.6: 17, 18, 31 and 33. 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 through the second example about stretching a spring on the handout. We will discuss this in lab on Thursday.
• Want more practice with surface area questions? Work on these questions from Section 6.6 and check your answers in the back of the text: 7, 9, 21 and 23 (page 463).
• Work practice exercises on work problems on WeBWorK with the Section67Part1 assignment. 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 1:00pm online.
• Note that Chapter 7 is a review, particularly the material in Section 7.1. I encourage you to read it if you feel rusty on logarithmic and exponential functions.
• Read Sections 8.1 and 8.2 (pages 520-529). Then complete the Reading Assignment for those sections on this handout. Now we plunge into Chapter 8 to learn a new set of integration techniques to add to our tool box! First, in Section 8.1, think about ways we can use old tools (like completing the square and long division!) to help us rewrite integrands into something we know how to deal with. Then in Section 8.2 learn a new technique that is especially helpful in expanding the kinds of functions for which we can calculate volumes and find other values for different kinds of applications. Remember that each method is undoing something we did with differentiation. There is not a one-to-one correspondence between differentiation and integration techniques, but you should look for connections between the processes. 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 1:30pm. Copies of the handout can be found outside my office.
• 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 Sam, the Math Intern, and send me emails whenever you find something you are unsure about, especially if we have already discussed it in class.

### WEEK 6: February 24 - February 28

Homework due Monday, February 24:

• Remember to bring in your picture if you forgot to bring it to your appointment! Last chance for full credit on that first assignment on Wednesday!
• Review Friday's class lecture notes on the General Slicing Method and Disk Method. Make sure the examples make sense, and finish integrating the integrals we set up and check your final answers. Bring any questions you have with you to class on Monday.
• Work practice exercises on Section 6.3 on WeBWorK with the Section63Part1 assignment. The first two problems are finding volumes using the General Slicing Method, and the last one is working with areas between curves. This is due Monday at 1:00pm online.
• Then work two more practice exercises on WeBWorK with the Section63Part1b assignment. This is due Monday at 1:00pm online.
• Read Section 6.4 (pages 439-447). 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 (flat cylinders) but by using tall cylinders (with prominent holes!). 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 Monday at 1:30pm. Copies of the handout can be found outside my office.

Homework due Wednesday, February 26:

• Remember to bring in your picture if you forgot to bring it to your appointment! Last chance for full credit on that first assignment is today!
• These exercises were supposed to be due on Monday. If you didn't do them yet, do them now: practice exercises on WeBWorK with the Section63Part1b assignment. This is due Wednesday at 1:00pm online.
• Review Monday's class lecture examples and notes about the washer method and rotating around other axes besides the x and y-axes.
• Review the groupwork that we were doing in class on Monday. Recall that we worked on the questions as shown on the Disk Method worksheet. Be sure that you have completed all of them and that they make sense. Bring questions to class or office hours.
• Want more practice with volume questions? Work on these questions from Section 6.3 and check your answers in the back of the text: 11, 13, 17, 25, 37, 53, 57, 61 and 65 (pages 435-438).
• Complete the Main Exercises Assignment for Week 6 on this handout. Be sure to write your solution on the handout. Copies of the handout can be found outside my office. This is due Wednesday at 1:30pm.
• Read Section 6.5 (pages 451-455). 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 roommates should almost be able to say them in their 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 Wednesday at 1:30pm. Copies of the handout can be found outside my office.
• Work practice exercises on Section 6.3 on WeBWorK with the Section63Part2 assignment. This is due Wednesday at 1:00pm online.

On Thursday, February 27th at 4:30pm in Napier 201, there will be a colloquium given by William Smith alum Avery Wickersham '19. She will be telling us about her experience studying abroad in the Budapest Semesters in Mathematics Education program. Refreshments will be served at 4:15pm. I hope you can make it!

Because of the colloquium, my office hours on Thursday will be as soon as I get back to my office (likely before the usual 3:45pm start time) from my other class until about 4:20pm. If you cannot make that time and have questions, please be sure to contact me to make alternate arrangements.

Homework due Friday, February 28:

• Redo any problems you missed on the exam and come ask questions if anything is unclear. We will go over some of these in lab, but I encourage you to come to office hours!
• Review your notes from Wednesday'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 lab, in office hours, or via email. Do not wait to clear things up!
• Review the groupwork that we were doing at the end of class on Wednesday. Recall that we worked on setting up the integrals for finding 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) y=4 and (d) x=-3. Try setting up the integrals for finding the volumes of these using the disk method. Can you integrate these either with shell or disk methods?
• Work practice exercises on Section 6.4 on WeBWorK with the Section64Part1 assignment. 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. This is due Friday at 1:00pm online.

### WEEK 5: February 17 - February 21

Remember our first exam, covering sections 5.1-5.5, will be during lab on Thursday, February 20th in Gulick 2000, our normal lab space. Make yourself a review sheet for these sections and then compare it to the one I post early in week 5!

Homework due Monday, February 17:

• Review Friday's class lecture notes on position, displacement and distance traveled. Evaluate whether or not the material all makes sense and let me know if you still have questions. Review the group work we did as well. Recall that we worked on Section 6.1: 14, 15, 25, 32 and 45 as well as an extra u-substitution question. 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 6.1 and Review on WeBWorK with the Section61andReview assignment. Questions 1-5 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 Monday at 1:00pm online.
• Extra u-substitution Review!!! Work practice exercises on u-substition on WeBWorK with the Section55Part2 assignment. This is due Wednesday at 1:00pm 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! Note that this is not due until WEDNESDAY, but you should at least start it now for extra practice for the exam!
• Note that there is NO Reading Assignment due Monday.

Due to our exam on Thursday, there will be NO Main Exercises assignment due on Wednesday!

Remember that the Section61andReview assignment that was due on Monday has an extension until 10:00am on Tuesday! Make sure you have it finished.

Please double-check that you have your textbook. There was a textbook left in our classroom after class on Friday and I am pretty sure it belongs to one of you!

Homework due Wednesday, February 19:

• Review Monday's class lecture notes. Integrate the integrals we set up in the area example and see if you get the correct answer. Make sure the set up both with respect to x and with respect to y make sense. The set up for the integrals is going to be the most challenging part of the questions in chapter six.
• Solve just two practice exercises on Section 6.2 on WeBWorK with the Section62Part1 assignment. This is due Wednesday at 1:00pm online.
• Read Section 6.3 (pages 425-434). Then complete the Reading Assignment for that section on this handout. We have worked on finding the area under a curve between two curves, but what if we are interested in three dimensions? How can we find the volume of an object that isn't just a cube, a sphere, a cylinder or another common solid for which we already have a straightforward formula? Amazingly, our process for building a formula is very similar to the process we have used for finding other kinds of formulas in previous sections. 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 1:30pm. Copies of the handout can be found outside my office.
• Note due to our exam on Thursday, there will be NO Main Exercises assignment due on Wednesday!
• 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 that you have completed all the labs AND that you have checked your solutions with the lab keys! Remember that you can go back to redo WeBWorK problems too! Bring questions to class on Wednesday! Part of our class will be review.

Check out this answer key for the Week 3 Lab! Make sure your solutions were correct and that these ideas make sense to you! Look for what makes a solution complete.

Check out this answer key for the Week 4 Lab! Make sure your solutions were correct and that these ideas make sense to you! Look for what makes a solution complete.

Homework due Thursday, February 20:

• Finish preparing for Exam 1! (You have actually been preparing for this since week 1!) Have confidence in your abilities!!!
• Arrive on time to lab in Gulick 2000. Spread out to take advantage of the space to think!

Homework due Friday, February 21:

• Review the group work problems on the handout that we worked on in Wednesday's class. Want extra practice? Try odd problems from Section 6.2 such as any of 9-63 odd. You can check the back of the book for answers!
• Work practice exercises on Section 6.2 on WeBWorK with the Section62Part2 assignment. Practice graphing curves by hand! You should be able to graph all of these without a graphing calculator! This is due Friday at 1:00pm online.
• Work two more practice exercises on Section 6.2 on WeBWorK with the Section62Part3 assignment. Practice graphing curves by hand! You should be able to graph all of these without a graphing calculator! This is due Friday at 1:00pm online.
• Note that there is NO reading assignment due on Friday!

### WEEK 4: February 10 - February 14

Homework due Monday, February 10:

• Another great class on Friday! I loved that you were focused and participating even as I accidentally went overtime! In the future, please feel free to clue me in to the time. ;-)
• Review the groupwork that we were doing in class as well as Friday's class lecture notes on even and odd functions, and the introduction to the average value of a function. Recall that we worked on Section 5.3: 40, 41, 42, 45, 47, 48, 61 and 107. Make sure you feel confident with these questions. For Exercise 107, be sure that you can provide a counterexample or a thorough explanation. Evaluate whether or not the material all makes sense and let me know as soon as possible if you still have questions.
• Other questions in Section 5.3 that you could do for practice include: 49, 51, 55, 57, 59 and 62. Most of these are odd so you can check your answers in the back of your book! Other questions in your text would be great to do as well, this is just a starting place!
• Work practice exercises on Section 5.4 and Review on WeBWorK with the Section5.4A assignment. Problem 1 contains questions on the new material in Section 5.4. The other problems require you to apply material in sections previous to 5.4. This is due Monday at 1:00pm online.
• Read Section 6.1 (pages 403-410). Then complete the Reading Assignment for that section on this handout. Although we have a lot more to do to understand how to integrate most 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 Monday at 1:30pm. Copies of the handout can be found outside my office.
• Get started on your Main Exercises assignment posted below!

Homework due Wednesday, February 12:

• Make sure you bring your reading assignment for Section 5.5, which you received graded back on Monday, to class on Wednesday; I will be calling on some of you to share your answers.
• Review the groupwork that we were doing in class as well as Monday's class lecture notes. Recall that we worked on Section 5.4: 16, 17, 23, 24, 32, 33 and 38. Be sure that you have completed all of them and that they make sense. Review how we derived the formula for average value of a function and see if you really believe the formula makes sense! If not, ask questions!
• Other questions in Section 5.4 that you could do for practice include: 20, 21, 27, 37, 45, 49 and 51. Most of these are odd so you can check your answers in the back of your book! Other questions in your text would be great to do as well, this is just a starting place!
• Work practice exercises on Section 5.4 and Review on WeBWorK with the Section5.4B assignment. This is due Wednesday at 1:00pm online.
• Complete the Main Exercises Assignment for Week 4 on this handout. Be sure to write your solution on the handout. Copies of the handout can be found outside my office. This is due Wednesday at 1:30pm.
• Note that there is NO Reading Assignment due Wednesday.

Homework due Friday, February 14 (Happy Valentine's Day!):

• Review your class notes on u-substitution and the groupwork problems on the handout that we worked on in Wednesday's class and Thursday's lab. Be sure that you have worked through each one and that each makes sense. Ask questions if they do not.
• Want extra practice with u-substitution? Exercises in Section 5.5 that you could do for practice include: 45-73 odd. These are odd so you can check your answers in the back of your book!
• Work practice exercises on Section 5.4 AND Section 5.5 on WeBWorK with the Sections54and55 assignment. Some of these questions are just about u-substitution. Other questions combine looking at the average value of a function with u-substitution. This is due Friday at 1:00pm online.
• Read Section 6.2 (pages 416-420). 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 1:30pm. Copies of the handout can be found outside my office.
• Check out this answer key for the Week 2 Lab! Make sure your solutions were correct and that these ideas make sense to you! Look for what makes a solution complete.

### WEEK 3: February 3 - February 7

Due to needing to visit another professor's class, I need to adjust my Monday office hours. They will be 9:30am-10:45am this Monday, February 3rd. If you have a question and cannot make this time, please email me.

Homework due Monday, February 3:

• 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, 46, 61, 62 and 63. 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!
• Other questions in Section 5.2 that you could do for practice include: 29, 37, 44, 45, and 49. Most of these are odd so you can check your answers in the back of your book!
• Work practice exercises on Section 5.2 on WeBWorK with TWO SHORT assignments: Section5.2PartC and Section5.2PartD. As usual, ask me if you have questions. This is due Monday at Noon online.
• Note that there is NO Reading Assignment due Monday.

Homework due Wednesday, February 5:

• Review the groupwork that we were doing in class as well as Monday's class lecture notes. Recall that we worked on Section 5.2: 53, 55, 83 and 87, as well as a question from WeBWorK. Take some time to practice completing the square to make sure you remember how to do that. 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. Be sure to write your solution on the handout. Copies of the handout can be found outside my office. This is due Wednesday at 1:30pm.
• Work practice exercises on Section 5.2 and Section 5.3 on WeBWorK with the Section53Part1 assignments. The first three problems are about the properties of integrals that we worked on in class on Friday and in group work on Monday. The second three are problems about Part 1 of the Fundamental Theorem of Calculus. Here you only have to enter the final answers, but be sure you know how to write out the process as well. This is due Wednesday at 1:00pm online. (Note: I am allowing you until 1pm for this. People must be on time for class for us to continue this due time.)
• Read Section 5.4 (pages 381-385). 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 Wednesday at 1:30pm. Copies of the Reading Assignment can be found in a box outside my office with the Main Exercises.

Homework due Friday, February 7:

• Review the groupwork exercises and notes from Wednesday's class and Thursday's lab. Recall that we worked on Section 5.3: 17, 76, 77, 80, 81 and 86. We also looked at a problem like 86 where both the upper and lower limits of integrations were funcitons. Make sure you feel confident with these questions. Do more practice problems if necessary until you are confident with all the material! Please let me know if you have questions on them. Note that the problems done in class do not necessarily cover all possible types of questions! Other questions in Section 5.3 that you could do for practice include: 73, 75, 79, 80 and 83. Check your answers in the back of your book for the odd ones!
• In lab on Thursday we will prove the Fundamental Theorem of Calculus Part 2. Review the proof. 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 Part 1 of the Fundamental Theorem of Calculus on WeBWorK with the Section53Part1b assignment. This is due Friday at 1:00pm online. There are only three problems in this set!
• (You will probably want to wait until after lab to do these problems!) Also work practice exercises on Part 2 of the Fundamental Theorem of Calculus on WeBWorK with the Section53Part2 assignment. These are mostly working problems applying what we proved in lab on Thursday, 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! This is due Friday at 1:00pm online.
• Read Section 5.5 (pages 388-395). 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 Friday at 1:30pm.
• Check out this answer key for the Week 1 Lab! Make sure your solutions were correct and that these ideas make sense to you! Look for what makes a solution complete.

### WEEK 2: January 27 - January 31

Homework due Monday, January 27:

• Finish working through the example that we were doing at the end of class. Bring any questions on it to class on Monday!
• Finish working through the "Reviewing Calculus I" handout and the Week 1 Lab. Answer keys will be posted for you to check your work by Wednesday. I will not collect these 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 and review on WeBWorK with the Section51Part1 assignment. 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 Monday at Noon.

Homework due Wednesday, January 29:

• Remember to bring in your picture if you forgot to bring it to your appointment!
• Review the groupwork that we were doing in class as well as Monday's class lecture notes. Recall that we worked on Section 5.1: 27, 39 and 42. Be sure that you have completed all of them and that they make sense.
• Work practice exercises on sigma notation and some Riemann Sums from Section 5.1 on WeBWorK with the Section51Part2 assignment. Remember that it is recommended that you print out a hard copy of this before trying to submit the problems online. This is due Wednesday at Noon online.
• Complete the Main Exercises Assignment for Week 2 on this handout. Be sure to write your solution on the handout. Copies of the handout can be found outside my office under Monday's Reading Assignment. This is due Wednesday at 1:30pm.
• Note that there is NO Reading Assignment due Wednesday.

Homework due Friday, January 31:

• Remember to bring in your picture if you forgot to bring it to your appointment!
• Review the groupwork exercises and notes from Wednesday's class. Recall that we worked on Section 5.1: 48 (c) and (d), 49 (g), 50 (e) and 55. We also looked at two sums with indices starting at something other than 1. Make sure you feel confident with these questions. Do more practice problems if necessary until you are confident with all the material! Please let me know if you have questions on them. Note that the problems done in class do not necessarily cover all possible types of questions! Other questions in Section 5.1 that you could do for practice include: 59, 63, 65, 73 and 75. These are all odd so you can check your answers in the back of your book!
• Work practice exercises on Section 5.2 on WeBWorK with TWO SHORT assignments: Section5.2PartA and Section5.2PartB. This is due Friday at Noon online. 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 FIVE!
• Read Section 5.3 (pages 367-377). 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 Wednesday at the beginning of class. Copies of the Reading Assignment can be found in a box outside my office.
• Ready to check your work on the Reviewing Calculus worksheet from the first few days of class? Take a look at this answer key.

### WEEK 1: January 20 - January 24

Welcome to Calculus II!!!

Homework due Thursday, January 23:

Although I will not normally assign homework to be due on lab days, this week we will need to in order to get started and refresh our memories. Please complete the following:
• Be sure to bring the "Reviewing Calculus I" handout you received at the end of the first day of class with you on Thursday and Friday.
• 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.
• Fill out this autobiographical questionnaire. Print it two sided if possible. If not, staple it before submitting. Be sure to leave the top portion on the first side (above where you place your name) blank. This is due Thursday at 10:30am in lab.
• In class we discussed what a hypothesis is. Check out this website for a summary. Still have questions? Be sure to ask in office hours or in class!
• Read Section 5.1 (pages 338-346). 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 Thursday at 10:30am in lab.
• 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 Thursday at 4:30pm.

Homework due Friday, January 24:

• Read the 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 on WeBWorK with the Review assignment. This is due Friday at Noon.
• Be sure to bring the "Reviewing Calculus I" handout you received at the end of the first day of class with you on Friday. We will spend the first half of class working on review problems in groups.
• Note that there is NO Reading Assignment due Friday.

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