*Math 170 Section 6: Calculus I.*

* *

**Instructor:** Andres Caicedo.

**Contact Information:** See here.

**Time:** MTuWF 1:40-2:30 pm.

**Place:** Interactive Learning Center, Room 204.

**Office Hours: **I’m thinking MF 10:30-11:30 am, but this may change depending on scheduling conflicts that ought to be resolved in two weeks.

**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.

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, 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:** Sections 1.1-8.1, 9.1-9.2. Please bookmark this page. I update it frequently with detailed week-to-week descriptions. See the course description in the department website for a generic syllabus.

**Detailed day to day description**** and homework assignments: **

**August 23**. Section 1.1. Homework: 3, 6, 9, 12.- August 24. Section 1.2. Homework: 1(d,e,f), 2(d,e,f), 5.
- August 25. Section 1.3. Homework: 4, 9, 14, 16.
- August 27. Section 1.4.
**First Quiz,**on sections 1.1-1.3. Homework: 7, 11, 17, 19.

The first homework set is due Tuesday, August 31. It consists of all the problems listed above. See below for the required format.

**August 30.**Sections 1.4 and 2.1.- August 31. Section 2.1. First homework is due today. Homework: 1, 3, 4, 7. [The following problems from the Schaum’s book are strongly suggested, but not required: Chapter 1 (Supplementary problems): 10-16; Ch. 9 (Solved problems): 1-10; (Supplementary problems): 14-17.]
- September 1. Section 2.2. Homework: 2, 3.
- September 3. Section 2.3.
**Second Quiz**, on sections 1.4, 2.1, 2.2. Homework: 2, 5, 11-15, 17, 18. [The following problems from the Schaum’s book are strongly suggested, but not required: Ch. 7 (Solved): 9-12; (Suppl.): 16, 17, 22, 23.]

The second homework set is due Tuesday, September 7. It consists of all the problems from the Whitman book listed on August 31, and September 1, and September 3. See below for the required format.

**September 7.**Section 2.3 (continued). Homework problems as listed last week.- September 8. Section 2.4. Homework: 2, 4, 7 [Suggested problems from Schaum’s: Ch. 9 (Solved): 11; (Suppl.): 18, 19, 22-24.]
- September 10. Section 2.5.
**Third quiz**, on Sections 2.3, 2.4. Homework: 3, 5, 7 [Suggested problems from Schaum’s: Ch. 8 (Solved): 2; (Suppl.): 4-8.]

The third homework set is due Tuesday, September 14. It consists of all the problems from the Whitman book listed on September 3, 8, and 10. See below for the required format.

**September 13.**We will briefly conclude the discussion of Sections 2.4 and 2.5, and then cover 3.1 (and the beginning of 3.2). Homework: Section 3.1, exercises 3, 4, 6.- September 14. Sections 3.2 and 3.3. Homework: Section 3.2, exercises 3-5, 8, 10. [Suggested problems from Schaum’s: Ch. 10 (Solved): 1, 2(4), 5-9; (Suppl.): 27-33.]
- September 15. Sections 3.3 and 3.4. Homework: Section 3.3, exercises 2, 4, 5. [Suggested problems from Schaum’s: Ch. 10 (Solved): 2(6); (Suppl.): 43.]
- September 17. Sections 3.4 and 3.5.
**Fourth quiz**, on sections 3.1-3.4 and graphing of derivatives. Homework: Section 3.4, exercises 2, 4, 6, 9 [Suggested problems from Schaum’s: Ch. 10 (Solved): 2(7); (Suppl.): 35, 44.]

The fourth homework set is due Tuesday, September 21. It consists of all the problems from the Whitman book listed on September 13-17. See below for the required format.

**September 20.**Section 3.5. Homework: 2, 4, 6, 8, 10, 15, 37. [Suggested problems from Schaum’s: Ch. 10 (Solved): 11-16, 18-21; (Suppl.): 32-34, 36-43, 45-50.]- September 21. Review. Please bring questions and doubts.
- September 22.
**Midterm 1.**It covers the material from the first 3 chapters of the book, with emphasis on Chapters 2 and 3.*Remember to bring an empty blue book. No notes, books, or calculators are allowed.* - September 24. Sections 4.1-4.3. There is no quiz this week. Homework: Section 4.1: 3, 9, 11 [Suggested problems from Schaum’s: Ch. 16 (Solved): 1-7, 11-12; (Suppl.): 1-22.] [Suggested problems from Schaum’s: Ch. 17 (Solved): 1; (Suppl.): 21-24, 26.]

The fifth homework set is due Tuesday, September 28. It consists of all the problems from the Whitman book listed on September 20 and 24. See below for the required format.

**September 27**. Sections 4.3, 4.4, 4.5. Homework: Section 4.3: 3, 5, 6. Section 4.4: 2, 3, 4.- September 28. Sections 4.5, 4.6. Homework: Section 4.5: 4, 6, 12, 14, 16, 18 [Suggested problems from Schaum’s: Ch. 17 (Suppl.): 25.]
- September 29. Section 4.6. Homework: 2, 6, 10, 12, 16 [Suggested problems from Schaum’s: Ch. 26 (Solved): 1, 4, 6, 7; (Suppl.): 11, 17, 18.]
- October 1. Section 4.7.
**Fifth quiz**, on Section 4.1-4.5.

The sixth homework set is due Tuesday, October 5. It consists of all the problems from the Whitman book listed on September 27, 28, and 29. See below for the required format.

**October 4.**Section 4.7. Homework: 4, 6, 12, 16, 18, 21. [Suggested problems from Schaum’s: Ch. 25 (Suppl.): 8, 11, 12; Ch. 26 (Solved): 1, 2, 4, 6, 7; (Suppl.): 8, 11, 17-21.]- October 5. Section 4.8. Homework: 2,5,6. [Suggested problems from Schaum’s: Ch. 7 (Solved): 3, 7 (Suppl.): 17, 18; Ch. 27 (Solved): 1-4; (Suppl.): 7, 10.]
- October 6. Sections 4.8, 4.9.
- October 8. Section 4.9. Homework: 2, 5, 7, 14, 20. [Suggested problems from Schaum’s: Ch. 11 (Solved): 1-3; (Suppl.): 6-8, 12; Ch. 17 (Suppl): 31; Ch. 26 (Suppl.): 22, 25.]
**Sixth quiz**, on sections 4.6-4.8.

The seventh homework set is due Tuesday, October 12. It consists of all the problems from the Whitman book listed on October 4, 5, and 8. See below for the required format.

**October 11.**Sections 4.9, 4.10. Homework: Section 4.10: 4, 6, 9, 10, 12. [Suggested problems from Schaum’s: Ch. 18 (Solved): 1-14; (Suppl.) 1-24.]- October 12. Sections 4.10, 5.1. Homework: Section 5.1: 4, 6, 8, 10, 16. [Suggested problems from Schaum’s: Ch. 14 (Solved): 1, 4, 5.]
- October 13. Sections 5.1, 5.2. Homework: Section 5.2: 4, 6, 8, 10, 14. [Suggested problems from Schaum’s: Ch. 14 (Solved): 7, 8; (Suppl.): 23, 26.]
- October 15. Sections 5.2, 5.3.
**Seventh quiz**, on sections 4.9, 4.10, 5.1, 5.2.

The eight homework set is due Tuesday, October 19. It consists of all the problems from the Whitman book listed on October 11-13. See below for the required format.

**October 18.**Sections 5.3, 5.4. Homework: Section 5.3: 2, 4, 6, 8, 9, 12. [Suggested problems from Schaum’s: Ch. 14 (Solved): 2, 3, 6, 9; (Suppl.): 24.]- October 19. Sections 5.4, 5.5. Homework: Section 5.4: 2, 4, 6, 8. [Suggested problems from Schaum’s: Ch. 15 (Solved): 1-8; (Suppl.): 11, 12; Ch. 17 (Solved): 14; (Suppl.): 29.]
- October 20. Sections 5.5, 6.1. Homework: Section 5.5: 2, 7, 10, 15, 19, 23, 30, 32. [Suggested problems from Schaum’s: Ch. 15 (Solved): 9-10; (Suppl.): 13; Ch. 17 (Solved): 15.]
- October 22.
**Eight quiz**, on sections 5.3, 5.4, 5.5.

The ninth homework set is due Tuesday, October 26. It consists of all the problems from the Whitman book listed on October 18-20. See below for the required format.

**October 25.**Section 6.1.- October 26. Review. Please bring questions and doubts.
- October 27.
**Second Midterm.**It covers the material from Chapters 4 and 5 of the book.*Remember to bring an empty blue book. No notes, books, or calculators are allowed.* - October 29. Section 6.1. There is no quiz this week.

There is no homework due Tuesday, November 2.

**November 1.**Section 6.1. Homework: 3, 5, 8, 11, 15. [Suggested problems from Schaum’s: Ch. 14 (Solved): 1, 11, 12, 14, 18; (Suppl.): 26-30.]- November 2. Section 6.2. Homework: 5, 6, 9, 15, 17, 19. [Suggested problems from Schaum’s: Ch. 20: All problems.]
- November 3. Sections 6.2, 6.3. Homework: Section 6.3: 2.
- November 5. Section 6.3.
**Ninth quiz**, on sections 6.1-3.

The tenth homework set is due Tuesday, November 9. It consists of all the problems from the Whitman book listed on November 1-3. See below for the required format.

**November 8**. Section 6.5. Homework: 2, 3, 5, 8, 10. [Suggested problems from Schaum’s: Ch.13 (Solved): 1-4, 6-7; (Suppl.): 16-20, 25; Ch. 22: all problems.]- November 9. Section 6.5.
- November 10. Section 7.1. Homework: Section 7.1: 2, 4, 6, 8. [Suggested problems from Schaum’s: Ch. 23: all problems.]
- November 12. Section 7.1.
**Tenth quiz**, on sections 6.5, 7.1.

The 11-th homework set is due Tuesday, November 16. It consists of all the problems from the Whitman book listed on November 8-10. See below for the required format.

**November 15.**Section 7.1.- November 16. Review. Please bring questions and doubts.
- November 17.
**Third Midterm.**It covers the material from Chapter 6 and Section 7.1 of the book.*Remember to bring an empty blue book. Calculators are allowed (in fact, it is a good idea to bring one), but no notes or books.* - November 19. Section 7.2. Homework: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20. [Suggested problems from Schaum’s: Ch. 24 (Solved): 1-5; (Suppl.): 8-26, 29, 31.]

There is no homework for this week. The exercises from November 19 will be part of the next homework assignment.

(Happy Thanksgiving!)

**November 29.**Sections 7.2, 7.3. Homework: Section 7.3: 2, 3, 5. [Suggested problems from Schaum’s: Ch. 24 (Solved): 6; (Suppl.): 27, 28, 30, 32, 37; Ch. 25 (Solved): 1; (Suppl.): 13, 14, 17.]- November 30. Sections 7.3, 8.1. Homework: Section 8.1: 2, 6, 7, 10, 16, 18. [Suggested problems from Schaum’s: Ch. 24 (Suppl.): 34; Ch. 25 (Solved): 5; (Suppl.): 9; Ch. 26 (Suppl.): 9.] The extra-credit problem is due today.
- December 1. Sections 8.1, 9.1.
*(Class canceled due to weather.)* - December 3. Section 9.1.

The 12-th homework set is due Tuesday, December 7. It consists of all the problems from the Whitman book listed on November 19-~~November 30. See below for the required format.~~

**December 6.**Section 9.1. Homework: 3, 4, 8, 11. Eleventh quiz, on sections 7.2, 7.3, 8.1.- December 7. Section 9.2. Homework: 3, 4, 6, 8, 10.
- December 8. We will conclude whatever is left from section 9.2, and start the review of the course.
- December 10. Review.

Although I will not collect the homework assigned on Monday and Tuesday, it is a good idea to work on it to prepare for the final exam.

- I will be in my office on Monday December 13 from 10 to 12, and then briefly from 4 until sometime between 4:30 and 5. Same on Tuesday. Feel free to email me if you have questions but the office hours do not work for some reason. The final exam is
**Wednesday, Dec. 15, 1-3 pm**. Do not forget to bring a blue book. Calculators are allowed, but no notes or textbooks. Remember that the exam is cumulative. Good luck!

**Exams:** There will be 3 in-class exams and a comprehensive final exam.

** **

- Exam 1: Wednesday, September 22.
- Exam 2: Wednesday, October 27.
- Exam 3: Wednesday, November 17.
- Final exam:
**Wednesday, December 15, 1:00-3:00 pm.**This exam is cumulative. (**Solutions**)

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.

**ALEKS assessment:** Check at ALEKS for the rules concerning the ALEKS assessment, which apply to this class. No late ALEKS assessment will be accepted.

- Students who do not meet the required minimum score by the deadline (
**midnight, August 27, 2010**) are strongly encouraged to drop the course. Anyone who stays without a satisfactory ALEKS score will have their**final grade lowered by one full letter grade**. (This is a departmental rule over which I have no control.) - Minimum score is 70%.

**Quizzes:** There will be weekly quizzes, on the last 20 minutes of Friday’s lecture. Each quiz will evaluate, roughly, the material covered from Friday to 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. 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 and textbooks are not allowed. Calculators will only be allowed on certain occasions; I will let you know at least a week in advance. Bring your own pen, pencil, eraser, etc.*

**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 1:40 pm. The homework consists on the problems assigned during the previous week. It is a good idea to work daily on the homework problems corresponding to the material covered that day. A **grader** (**John Hutchins, hutchinsjh at hotmail dot com**) 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. 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.

Following Otis Kenny‘s suggestion, 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:**

Please pay attention to the * Student Code of Conduct*. Feel free to ask me if there are any questions.

- Quizzes: 10%. (Each quiz will weigh the same towards the final grade.)
- Homework: 10%. (Each homework will weigh the same towards the final grade.)
- Exam 1: 20%.
- Exam 2: 20%.
- Exam 3: 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.
**If your ALEKS score was below 70%, your grade will be lowered one letter grade.**

**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 textbooks. 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 textbooks and in class. If you leave a comment, please use your **full name**, which will simplify my life filtering spam out.

**Learning Objectives:** Upon completion of this course, you should be able t:

- Systematically apply rules of differentiation to find derivatives and the fundamental theorem of calculus to find definite and indefinite integrals.
- Sketch the graph of a function defined by an expression, and conversely recognize what kind of expression is likely to be associated with a given graph. Identify features of special classes of functions (both intrinsically and in relation to other classes, as in considering relative rates of growth.) Recognize and apply symmetries of functions (evenness, oddness, periodicity) where appropriate.
- Given a graph of a function, sketch the graph of its derivative and antiderivative(s).
- Solve optimization and related rates word problems: Identify the variables and given equations from the problem text, draw a picture if appropriate, set up a mathematical problem and apply the methods of calculus to find a mathematical solutionto answer the original question.
- Be familiar with different ways of understanding the derivative(respectively integral) of a function: rate of change, slope, instantaneous velocity, limit of difference quotients (respectively area, distance covered, limit of Riemann sums).
- Apply logical thinking to check calculations and results, e.g. in curve discussions.
- Apply precalculus methods in the calculus context.
- Explain the Intermediate Value Theorem, Extreme Value Theorem, and Mean Value Theorem geometrically. Apply these theorems to deduce other Calculus results.
- Be familiar with linear approximations to functions (viewing the tangent line as the graph of a function) and possibly with the method of differentials. Approximate zeroes of a function using Newton’s method and explain the geometric reasoning behind the method.
- Determine areas under curves and areas between curves using the definite integral (evaluated by means of the Fundamental Theorem of Calculus); solve “distance traveled” and “total change” problems using definite integral calculations.