*Math 175, Section 2: Calculus II.*

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**Instructor:** Andrés Caicedo.

**Contact Information:** See here.

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

**Place:** Business and Economics building, Room 217.

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

**Text: Calculus. Whitman College (David Guichard and others)**. The text is distributed under a Creative Commons license. The department has a Calculus page, where the book (version of May 10, 2010) can be downloaded; scroll down the page to reach the section on Calculus II, and

**make sure to download the chapter marked 10A as well as the one marked 10**.

The book can also be downloaded at Whitman College, here. But their latest version (August 10, 2010, as of this writing) differs slightly from the one we will be following.

This is the first term we will be using this textbook for Calculus II, and your feedback is greatly appreciated. We will supplement the book with **Schaum’s Outlines Calculus, Frank Ayres Jr and Elliot Mendelson, Fifth Edition, McGraw Hill 2009**.

Please make sure each day you bring to class a copy of the pages that are being covered from the online text, according to the list below; this may be an electronic copy. (To be safe, bring the pages corresponding to the sections for that day, for the previous day, and for the next day, since I may cover a bit more than what is scheduled, and we may need to refer back to recently covered material.)

**Contents:** Chapters 8, 9, 10A, 10. Please bookmark this page, as I will update it frequently with detailed week-to-week descriptions.

Roughly:

- We begin with a (quick) review of Calculus I. You are responsible for whatever material should have been covered in Calculus I (including Integration), 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. The self test you took the first day should give you a good idea of some (but certainly not all!) of the background techniques and results that we will be needing through the term.
- We will continue with Chapter 8 (Techniques of integration; I will supplement the techniques discussed in the text. This is a topic that leads to very interesting current work, in what is called symbolic integration), Chapter 9 (Applications), a
*very brief*tour of Chapter 10A (Polar coordinates, conics, and parametric equations), and close with what will hopefully be a slow paced discussion of Chapter 10 (Infinite sequences and series). In the ideal world, we will have some time left to discuss some additional material, such as infinite products. In reality, I expect we will not get to cover all the material discussed in Chapter 10).

Please refer to the course description provided by the department for a generic syllabus. As you can imagine, the material for this term is much denser than the material for Calculus I; it is a very good idea to make use of office hours.

**Detailed week to week description:**

**January 18-21.**Review of Calculus I. Section 8.1.**January 24.**Sections 8.1, 8.2.*Homework:*Section 8.2: 2, 4, 7; [Suggested exercises from Schaum: Ch. 32: 29-37].- January 25. Section 8.2.
- January 26. Section 8.3.
*Homework:*Schaum Ch. 22: 32, 35, 37, 43, 50, 52, 58; [Suggested exercises from Schaum: Ch. 22: 25-29, 38-40, 44-46, 55-57, 60-62]. Schaum Ch. 24: 16, 18, 24; [Suggested exercises from Schaum: Ch. 24: 12-15, 20-23, 27-30]. - January 28. Section 8.3.
**First quiz. (Solutions)**

The **first homework set** is due **Tuesday, February 1st**, at the beginning of lecture. **See below for the required format.** The homework consists of all the problems listed as Homework in January 24-28. The problems listed in square brackets (such as Exercises 25-29 of Chapter 22 of Schaum) are optional, and do not need to be turned in. All the others are required. Unless otherwise specified, problems come from the Whitman textbook.

**January 31.**Sections 8.3, 8.4.*Homework:*8.3: 2, 4-6, 10, 12; [Suggested exercises from Schaum: Ch. 32: 57-69].- February 1. Section 8.4.
*Homework*: 3, 4, 7-9, 11; [Suggested exercises from Schaum: Ch. 31: 14-24, 27, 28]. - February 2. Section 8.4. Reduction formulas. Handout on integrals of products of powers of secant and tangent and extra credit exercises.
- February 4. Section 8.5.
**Second quiz. (Solutions)**

The **second homework set** (the problems listed January 31, February 1) is due **Tuesday, February 8**, at the beginning of lecture. See below for the required format.

**February 7.**Section 8.5.*Homework:*3, 4, 6-9; [Suggested exercises from Schaum: Ch. 33: 7, 8, 10-12].- February 8. Section 8.5.
*Homework:*8.6: 4, 8, 11, 12, 18, 20, 22, 28; [Suggested exercises from Schaum: Ch. 33: 9, 13-19, 23, 24]. - February 9. Section 8.5. Here is a link to a rather more general (and abstract) discussion of the method of partial fractions than covered in class.
- February 11. Review. The extra credit problems from February 2 are due today.
**Third quiz. (Solutions)**

The **third homework set** (the problems listed February 7th and 8th) is due **Tuesday, February 15**, at the beginning of lecture. See below for the required format.

**February 14.**Review: Section 9.1. [Suggested exercises: Section 9.1: 3-5, 8-11].- February 15. Review: Section 9.2.
*Homework:*3, 4, 6, 8, 10. - February 16. Section 9.3.
*Homework:*3, 5, 6; [Suggested exercises from Schaum: Ch. 30: 18-22]. - February 18. Section 9.3.
*Homework:*11-13; [Suggested exercises from Schaum: Ch. 30: 23-42, 46-49].**Fourth quiz. (Solutions)**

The **fourth homework set** (problems listed February 15-18) is due ** ****Wednesday, February 23** at the beginning of lecture. See below for the required format. Recall that the **first midterm** is also **Wednesday, February 23** during class.

**Monday, February 21**. President’s day. (No class.)- Tuesday, February 22. Review. Please bring questions. I’ll have office hours 11:40-12:30.
- Wednesday, February 23.
**First midterm.**It covers Chapter 8 and Chapter 9 up to (including) section 9.3 of the online text.**Please bring an empty blue book.** - Friday, February 25. Sections 9.3 and 9.4.
*Homework:*Section 9.4: 3, 4, 6. From Schaum’s book: Chapter 24: 33. There is no quiz today.

The **fifth homework set** (problems listed February 25) is due **Tuesday, March 1st** at the beginning of lecture. See below for the required format.

**Monday, February 28.**Section 9.5.*Homework:*2, 4, 6, 8.- Tuesday, March 1. Sections 9.5, 9.6.
- Wednesday, March 2. Section 9.6.
*Homework:*3, 7, 9, 11. - Friday, March 4. Section 9.6.
**Fifth quiz. (Solutions)**

The **sixth homework set** (problems listed February 28 and March 2) is due **Tuesday, March 8** at the beginning of lecture. See below for the required format.

**Monday, March 7.**Sections 9.6, 9.7.- Tuesday, March 8. Section 9.7.
*Homework:*2, 4, 7, 10, 12, 14; [Suggested problem from Schaum's book: Chapter 35: 19]. - Wednesday, March 9. Section 9.7.
- Friday, March 11. Section 9.7.
**Sixth quiz. (Solutions)**

The **seventh homework set** (problems listed March 8 ) is due **Tuesday, March 15** at the beginning of lecture. See below for the required format.

- Monday, March 14. Section 9.9.
*Homework:*4-7; [Suggested problems from Schaum's book: Chapter 29: 13; Chapter 35: 24]. - Tuesday, March 15. Sections 9.9, 9.10.
*Homework:*Section 9.10: 3, 5; [Suggested problems from Schaum's book: Chapter 36: 12-17]. - Wednesday, March 16. Section 9.10.
- Friday, March 18. Section 9.11.
**Seventh quiz. (Solutions)**

The **eight homework set** (problems listed March 14, 15) is due **Tuesday, March 22** at the beginning of lecture. See below for the required format.

**Monday, March 21.**Section 9.11.*Homework:*4,7,12,17, 18. [Suggested problems: Handout on the logistic equation. These are notes originally prepared by Michael Christ for the Calculus II course at UC Berkeley. Exercises here count as extra-credit problems. They are due**April 5**; please turn them in*separately*from the regular homework set.]- Tuesday, March 22. Section 9.11.
- Wednesday, March 23. Review.
- Friday, March 25. Section 10.A.1. (Chapter 10A deals with Parametric equations and polar coordinates.)
**Eight quiz.**

The **ninth homework set** (problems listed Monday, March 21) is due **Tuesday, April 5** at the beginning of lecture. See below for the required format.

**March 28-April 1.**Spring break.**April 4.**Section 10.A.1.*Homework:*4, 6, 10, 12, 14, 16, 19, 22, 23; [Suggested problem from Shaum's book: Chapter 41: 46].- April 5. Review.
- April 6.
**Second midterm.**It includes Chapter 9, from 9.3 to 9.11. Please do not forget to bring calculators and blue books.**(Solutions)** - April 8. Sections 10.A.2 and 10.A.3.
*Homework:*Section 10.A.2: 1-6 (only ). Section 10.A.3: 10, 14, 17, 19; [Suggested problems from Schaum's book: Chapter 41: 30, 40-43]. There is no quiz today.

The **tenth homework set** (problems listed April 4 and 8 ) is due **Tuesday, April 12** at the beginning of lecture. See below for the required format.

**April 11.**Sections 10.A.3, 10.A.4, 10.A.5.*Homework:*Section 10.A.4: 1-6; [Suggested problem from Schaum's book: Chapter 37: 22]; Section 10.A.5: 1, 6, 7; [Suggested problems from Schaum's book: Chapter 37: 7-12, 17-20].- April 12. Sections 10.A.5, 10.1, 10.11 (Chapter 10 deals with sequences and series).
- April 13. Sections 10.1, 10.11.
*Homework:*Section 10.1:~~1, 4, 6.~~

- April 15. Section 10.11.
**Ninth quiz.**

The **eleventh homework set** (problems listed April 11 and 13) is due **Tuesday, April 19** at the beginning of lecture. See below for the required format.

**April 18.**Section 10.11. Homework: 1-3.- April 19. Sections 10.11, 10.10.
- April 20. Section 10.10. Homework: 1-5. (Ignore the part about the “radius of convergence.”)
- April 22. Section 10.9.
**Tenth quiz.**

The **twelfth homework set** (problems listed April 18 and 20) is due **Tuesday, April 26** at the beginning of lecture. See below for the required format.

**April 25.**Applications of power series. The material we covered in lecture is usually called*generating functions*. A very good downloadable reference (with much much more than what we did) is the book generatingfunctionology, by Herbert S. Wilf. [Suggested exercises: Problem 1 (a-g), in page 29 of this book.]- April 26. Applications of power series to differential equations. This pdf (of Stewart‘s
*Calculus*) contains many examples of this technique. [Suggested exercises: Problems 1-4, in page 5 of this pdf file.] Sections 10.7, 10.8. - April 27. Sections 10.7, 10.8.
*Homework:*Section 10.7: 5-8. Section 10.8: 1, 2, 6. Section 10.10: 1-5 (only the radius of convergence). - April 29. Sections 10.7, 10.8.
**Eleventh quiz.**

The **thirteenth homework set** (problems listed April 27) is due **Tuesday, May 3** at the beginning of lecture. See below for the required format. As **extra credit problems,** turn in the suggested exercises mentioned April 25, 26, by **Friday, May 6** at the beginning of lecture.

**May 2.**Review of Chapter 8. Here is a pdf (from Stewart’s Calculus) with some suggestions and many exercises on this topic. The website for Stewart’s Calculus also has a page with many links and resources on techniques of integration.- May 3. Review of Chapter 9. Here are pdfs on areas of surfaces of revolution (from Stewart’s), and on moments of mass (from the “freestudy” website; in the link, the relevant moments are referred to as “first moments of area”, and are discussed in pages 1-5). Here is a page from Stewart’s website with links and resources on applications of integration.
- May 4. Review of Chapters 10A and 10. Here is a page from Stewart’s website with links and resources on polar coordinates and parametric equations.
- May 6. Review of Chapter 10. Here is a page from Stewart’s website with links and resources on series. See also this link. You may want to practice with Exercises 2, 8, 10, 18, 21, 23, 25, 27, 30 of Section 10.12 from our textbook. Also, practice approximating to within using the techniques we covered.
- May 9.
**Final exam.**10:30 am – 12:30 pm. Please bring a blue book.*Good luck!*It has been a pleasure having you as my students this term.

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

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

- Exam 1:
**Wednesday, February 23.**It includes Chapter 8 and Chapter 9 up to (and including) 9.3. - Exam 2:
**Wednesday, April 6.**It includes Chapter 9, from 9.3 to 9.11. - Final exam:
**Monday, May 9**, 10:30 am – 12:30 pm.

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. Please bring **blue books** to the exams.

**Quizzes:** There will be weekly quizzes, on the last 20 minutes of Friday’s lecture. Each quiz will evaluate, roughly, the material covered until Wednesday. 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, unless I am notified in advance and a valid excuse is provided, just as with midterms. I will remove the lowest score when computing your grade.

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. I am MUCH more interested in the process by which you reach your solutions. Correct answers that do not show details and procedure will be marked as if they had been left blank.
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**Homework:** There is weekly homework, due Tuesdays at the beginning of lecture; you are welcome to turn in your homework early, but I will not accept homework past Tuesdays at 9:40 am. The homework consists of the problems assigned during the previous week, as detailed in the week-by week description above. It is a good idea to work daily on the homework problems corresponding to the material covered that day. A **grader (Nicole S. Castro) **will check your homework for completeness, and grade carefully 1 or 2 questions (each homework is graded out of 10 points, completeness is worth 2 points). You should use it as a guide for 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 (it is a better idea to also do the suggested homework, although I tend to suggest many problems). During office hours, you are welcome to ask about problems from the assigned sets or any other problems you find interesting. Frequently, some (but not necessarily all) of the problems from the quizzes will be fairly close, if not outright identical, to homework problems. I will remove your lowest score when computing your grade.

Your homework **must** follow the format developed by the mathematics department at Harvey Mudd College. You will find that format at this link. ** If you do not use this style, your homework will be graded as 0.**

**Grading:**

- Quizzes: 20%. (Each quiz weighs the same towards the final grade.)
- Homework: 20%. (Each homework set weighs the same towards the final grade.)
- Exam 1: 20%.
- Exam 2: 20%.
- Final exam: 20%.

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.

Please also check the Student Code of Conduct. Feel free to ask me if there are any questions.