*Math 175 Section 2: Calculus II.*

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**Instructor:** Andres Caicedo.

**Contact Information:** See here.

**Time:** MTuWF 9:40-10:30 am.

**Place:** Multipurpose building, Room 208.

**Office Hours: **MW 10:40-11:30 am.

**Text:** Hass, Weir, Thomas, *University Calculus, *Addison-Wesley (2007). Part I suffices.

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**Contents:** Chapters 6-9. This page is frequently updated with detailed week-to-week descriptions.

Roughly:

- We will begin with a (very quick) review of Calculus I. You are responsible for whatever material should have been covered in Calculus I (including Integration, Chapter 5), even if the course you took did not cover some of these topics; consult the online department course description for a brief outline. It will be particularly useful throughout the term if you review: Definitions of the notions of derivative and definite integral, and the definition of limit, trigonometric identities, and the material on polynomials typically covered in precalculus or algebra courses.
- We will continue with Chapter 6 (Applications of definite integration).
- We will then jump to Chapter 9 (Polar coordinates and conics).
- We will then go back and cover Chapter 7 (Techniques of integration).
- Finally, we will cover at least part of Chapter 8 (Infinite sequences and series).

**Detailed week to week description:**

- August 24-28. Review of Calculus I, Sections 6.1, 6.2.
*Homework problems:***Section 6.1:**1, 3, 8, 12, 13, 25, 26, 31, 35, 36, 46, 47.**Section 6.2:**2, 3, 5, 13, 14, 19, 23, 24, 27, 33, 34, 38. - August 31-September 4. Sections 6.3, 6.4, and half of 6.5.
*Homework problems:***Section 6.3:**1, 6, 7, 12, 16, 18, 29, 30, 34, 36.**Section 6.4:**9, 11, 16, 19, 20, 22, 28, 29.**Section 6.5:**1, 2, 3, 6, 7, 11, 17, 19, 20, 21. First quiz: Friday, September 4. - September 8-11: Remainder of Chapter 6.
*Homework Problems:***Section 6.5:**30-41.**Section 6.6:**1, 2, 7, 8, 19,20,23, 24, 31–34.**Section 6.7:**1-8, 14-24, 29-32. - September 14-18: Finish 6.7. Chapter 9 up to half of 9.3.
*Homework Problems:***Chapter 6, Practice Exercises:**1-4, 13-16, 20-24, 28-30, 33, 37, 40-42, 44-47, 52-54.**Section 9.1:**1, 4, 6, 7, 11, 16, 20, 24, 25, 31, 42, 48, 52, 59, 63, 64.**Section 9.2:**1, 3, 7, 9, 12, 14, 15, 18, 19, 21, 22, 25, 26.**Section 9.3:**1-10. (It may not be possible to solve some of these integrals with the techniques we know so far. If this seems to be the case, simply leave the integrals indicated. We will learn the required techniques once we cover Chapter 7.) Second quiz: Friday, September 18. - September 21-25: 9.3-9.4.
*Homework problems:***Section 9.3:**13-20, 28-30. (It may not be possible to solve some of these integrals with the techniques we know so far. If this seems to be the case, simply leave the integrals indicated. We will learn the required techniques once we cover Chapter 7.)**Section 9.4:**1-4, 5-8, 13, 21, 25, 31, 37, 41, 57, 63, 69, 76. First midterm: Friday, September 25. It covers Chapter 6 and Chapter 9, up to the material covered on Wednesday inclusive. - September 28-October 2: 9.4, 9.5, 7.1.
*Homework problems:*Those problems from**Section 9.4**that require theory beyond what we covered last week. Also:**Section 9.5:**1, 3, 7, 11, 15, 21, 27, 33, 37, 45, 49, 51, 55.**Section 7.1:**1, 4, 5, 8, 9, 12, 13, 18, 20, 23, 28-31, 33, 35, 39-50. Third quiz: Friday, October 2. - October 5-9: 7.1-2.
*Homework problems:*For**Section 7.1**, as indicated for last week.**Section 7.2:**9-14, 19-22, 29-32, 42, 43. - October 12-16: End of 7.2-7.4; including the notes posted online.
*Homework problems:***Section 7.2:**37-39, and the exercises posted online.**Section 7.3:**1, 5, 9, 13, 16, 18, 23, 25, 33-36, 38, 39. Fourth quiz: Friday, October 16. - October 19-23: 7.4, 7.6, including the note “
*Simpson’s rule is exact for quintics*” by Louis A. Talman, published in the American Mathematical Monthly, vol 113 February 2006, pp. 144-155. The American Mathematical Monthly can be found in Albertson Library. You can also find the paper online, either through JSTOR (which Albertsons library gives you access to) or in Dr. Talman’s page.*Homework problems:***Section 7.4:****All odd problems from 1 until 45, inclusive. 49, 50.** - October 26-30: 7.6.
*Homework problems:***Section 7.6:**1-10, 11, 15, 21, 23, 24, 27, 29, 35, 37. Second midterm: Friday, October 30. It covers 9.4, 9.5 and Chapter 7 (up to the material covered on Tuesday, and including the discussion of Dr. Talman’s paper presented in lecture). - November 2-6: End of 7.6, 7.7.
*Homework problems:***Section 7.7:**All odd problems in 1-33. Fifth quiz: Friday, November 6. - November 9-13: End of 7.7, Chapter 8. From Section 8.1: Notion of sequence, convergence and divergence (pages 502-505); from Section 8.2: Notion of series, geometric series (page 515).
*Homework problems:***Section 7.7:**37, 42, 53, 59, 60, 65, 66, 74.**Section 8.1:**1-6. Sixth quiz: Friday, November 13. `Self test’ on Monday and Wednesday. - November 16-20: Section 8.2: Series, geometric series (pages 515-519 (only up to Example 6)); from Section 8.8: Notion of Taylor (and Maclaurin) series, and examples; from Section 8.2: page 519.
*Homework problems:***Section 8.2:**1, 2, 3, 7, 24, 37, 51, 57.**Section 8.8:**9, 10, 12, 15, 19. Seventh quiz: Friday, November 20. - November 30-December 4: Section 8.8 (more examples), 8.2 (pp. 520, 521), 8.5.
*Homework problems:***Section 8.2:**49, 50, 64, 68-71.**Section 8.5:**1-5, 13-19, 29, 36, 45, 46. Eight (and last) quiz: Friday, December 4. - December 7-11: Sections 8.5 (root test), 8.3 and 8.4.
*Homework problems:***Section 8.3:**1, 5, 15, 39, 40.**Section 8.4:**3, 6, 11, 23, 27. - Remember that the final exam is Monday, December 14, 10:30 am – 12:30 pm. This exam is cumulative.

**Prerequisites:** 170 (Calculus I) or equivalent.

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**Exams:** There will be 2 in-class exams and a comprehensive final exam.

- Exam 1: Friday, September 25. Chapters 6 and 9 (until Section 9.3).
- Exam 2: Friday, October 30. Chapters 9 (Sections 9.4, 9.5) and 7 (until Section 7.6).
- Final exam: Monday, December 14, 10:30 am – 12:30 pm. This exam is cumulative.

Dates and times are non-negotiable. Failure to take a exam will be graded as a score of 0. There will be no make up for the final exam. For the in-class exams, a make up can be arranged if I am notified **prior** to the exam date and a **valid** reason is presented; keep in mind that make up exams will be more difficult than regular in-class exams.

You need to provide me during the first week of classes with **3 blue books** with your name on them, and the pages blank. One will be returned to you prior to each exam. You should solve the exams in these blue books, and won’t be allowed to turn in any other paper, even if it is a blue book that you bring to class the day of the exam.

**Quizzes:** There will be bi-weekly quizzes, on the last 20 minutes of Friday’s lecture. Each quiz will evaluate, roughly, the material covered the last two weeks (except for the Friday of the quiz itself). You are * not *allowed to only show up about 20 minutes before the end of the lecture in order to take the quiz; if you show up only for the quiz, your score is 0. If you fail to take a quiz, it will be scored as 0. There are no make-up quizzes. I may increase the frequency, if need be. In that case, I will notify at least a week in advance, both during lecture and in this page. There is a total of eight quizzes; the lowest score is dropped.

For each quiz, I will provide you with a page with the question(s) printed. You may use this page to solve the questions. You need to bring any additional pieces of paper you may require.

*Notes from class, textbooks, and calculators, are allowed during exams and quizzes. Bring your own pen, pencil, eraser, etc.*

**Homework: **I will frequently assign homework. This is not to be graded, or collected, but rather a guide for you to have an idea of what material to focus on, and what kind of skills are required from you. It is a **very good** idea to do **all** of the assigned homework. During office hours, you are welcome to ask about problems from the assigned sets (or any other problems you find interesting). Some (but not all) of the problems from the quizzes will be fairly close, if not outright identical, to homework problems.

**Grading:**

- Quizzes: 35%. (Each quiz will weigh the same towards the final grade.)
- Exam 1: 20%.
- Exam 2: 20%.
- Final exam: 25%.

I will then grade on a linear scale:

- If your final score is 90% or higher, you receive an A.
- If it is between 80 and 89%, you receive a B.
- If it is between 70 and 79%, you receive a C.
- If it is between 60 and 69% you receive a D.
- If it is 59% or lower, you receive an F.
- There may be a small curve up if the distribution of scores warrants this. Plus and minus grades might be used for grades near the top or bottom of a grade range.

**Attendance:** Not required, but encouraged. Any material covered in lecture may be used in quizzes and exams, even if it is not discussed in the textbook. I will use this website to post any additional information, and encourage you to use the comments feature, but (in general) I will not post here standard content covered in the textbook and in class. If you leave a comment, please use your **full name**, which will simplify my life filtering spam out.

**Core outcomes:** In this class you will be assessed on a wide range of skills. Among these, the following make Math 175 a part of the University Core. By the end of the course, you should be able to:

- Identify and appropriately apply different integration techniques.
- Express solutions using (reasonably) correct mathematical language.
- Know that integration is an inverse operation to differentiation, and can be used to measure lengths, areas, and volumes, among others.
- Formally manipulate power series.
- Solve (separable) differential equations using the integration techniques covered throughout the course.

In order, these correspond (among others) to the following University Core Outcomes:

- Apply and evaluate a variety of strategies for solving a problem. / Interpret written materials.
- Write clearly for specific purposes and audiences.
- Demonstrate an understanding of the essential concepts underlying theories in the field. / Apply theories to typical problems in the field.
- Demonstrate an understanding of the basic methods of inquiry used in this field.
- Apply theories to typical problems in the field.

[…] 175- Syllabus […]

You probably noticed that I had a broken arm today I had surgery on it a few hours ago and I’m not sure I will be able to make class tomorrow. Is there any way I could get some kind of notes or something. I can also meet you between 10:30 and twelve on Thursday if that could work for you.

Hi Jordan,

Hope things are ok. Take the time off that you may need. (If necessary, you could take the quiz this coming week rather than this Friday; let me know). It may be a bit tricky to meet Thursday, though. I’ll try to email you some notes; please remind me tomorrow Wed.

If you could email me notes from class today I think I should be fine to take the quiz on friday, at least I hope I will be. Thanks for the help.