Calculus II

Professor: Erika L.C. King

Email: eking@hws.edu

Office: Lansing 304

Phone: (315) 781-3355

Home Page

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

Course Grade Scale

WeBWorK Home Page for Our Class

WeBWorK Instructions and FAQs

WeBWorK Syntax and List of Functions

**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.
- Read Section 6.3 (pages 420-429). Then complete the Reading Assignment for that section on this handout. We have worked on finding the area under a curve and you have read about finding the area 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 Monday at the beginning of class. COPIES OF THE READING ASSIGNMENT ARE AVAILABLE IN THE BOX OUTSIDE MY OFFICE.
- Note that there is NO Main Exercises Assignment due Monday.

**Looking Ahead...**

**Homework due Wednesday, September 26:**

- More will be added on Monday!
- Note that there is NO reading assignment due on Wednesday!

**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!

- Calculus I Review
- Lab 1
- Lab 2
- Lab 3 Note that the order of the questions on page 2 is different on the key than on your version of the lab!

**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.
- More will be added on Wednesday!
- 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.

**Looking Ahead...**

**Homework due Monday, September 24:**

- More will be added on Friday!
- Note that there is NO Main Exercises Assignment due Monday.

**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.

**Looking Ahead...**

**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.

**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.

**Looking Ahead...**

**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.

**Welcome to Calculus II!!!**

**Homework due Tuesday, August 28:**

- 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.