Math 16A, Fall 2008

Math 16A - Analytic geometry and calculus - Fall 2008

Professor: T.Y. Lam.

Office Hours: Monday 11:10 - 12:30, Friday 1:10 - 2:30, 871 Evans.

E-mail: lam at math dot berkeley dot edu.

Lectures: MWF 10-11am in 1 Pimentel.

Course Webpage: http://math.berkeley.edu/~doker/16A

Homework Assignments:

Week 1 (due Aug 28): 6 Problems assigned in lecture [solutions].
Week 2 (due Sept 4): Section 0.1: 20, 56. Section 0.2: 12, 30. Section 0.3: 20, 24, 26, 28, 32, 33. Section 0.4: 11, 20, 27, 34. Section 0.5: 68, 88. Section 0.6: 10, 15. [solutions]
Week 3 (due Sept 11): Section 1.1: 14, 18, 23, 25, 32, 46. Section 1.2: 24, 28, 32, 36, 37, 38. Section 1.3: 8, 14, 32, 39, 42, 45, 70, 80. [solutions]
Week 4 (due Sept 18): Section 1.4: 14, 20, 23, 34, 41, 46, 53, plus worksheet problems A,B,C,D and E. Section 1.5: 16, 20, 22, 26. Section 1.6: 15,20,28,33,37,38. [solutions]
Week 5 (due Sept 25): Section 1.6: 43, 45, 47, 50, 53. Section 1.7: 20, 25, 30, 39, 40. Section 1.8: 2, 4, 8, 11, 14, 20, 22. Extra Problems (A),(B),(C), and (D) from worksheet [solutions]
First Midterm given on Sept 29. [Midterm 1][solutions]
Note! We are going to be grading midterms all day Tuesday 9/30, so GSI office hours may be postponed on that day (in particular, Jeff will have office hours Wednesday by appointment only this week).
Week 6 (due Oct 2): Section 2.1: 8, 9, 10, 11, 12. Section 2.2: 1, 2, 3, 4, 6, 8, 12, 42. Section 2.3: 4, 12, 22, 24, 28, 30, 31, 32, 43. [solutions]
Week 7 (due Oct 9): Section 2.4: 7, 8, 14, 17, 19, 20, 22, 26, 28, 34. (For curve sketching, follow the instructions on p. 177. The best approach is to include a "FDR chart" and a "SDR chart" to summarize the information on increasing/decreasing, CU/CD, etc.) Section 2.5: 3, 6, 10, 12, 15, 17. [solutions]
Week 8 (due Oct 16): Section 2.5: 19, 23, 26, 28, 29, 31. Section 2.6: 3, 4, 11, 16, 21, 27. Section 2.7: 1, 5, 9, 12.[solutions] And problems A and B on a worksheet. [solutions].
Week 9 (due Oct 23): Section 3.1 3, 8, 10, 19, 26, 27, 31, 36, 39, 44, 46, 56. Section 3.2 3, 10, 16, 20, 25, 27, 30, 35, 38, 40, 42, 59. [solutions]
Week 10 (due Oct 30): Section 3.1: 47. Section 3.3: 15, 18, 25, 27, 36, 38, 40, 46, 47. Section 4.1: 8, 9. 24, 30, 34. Section 4.2: 2, 4, 9, 18, 27, 32, 36, 37, 42. [solutions] And problems A and B on a worksheet. [solutions] The book lacks exercises in applying the Quotient Rule toward implicit differentiations. The extra Problems (A) and (B) on the worksheet provide some practice in this direction.
Week 11 (due Nov 6): Section 4.3: 10, 13, 14, 20, 22, 23, 26, 31, 39, 48. Section 4.4: 18, 21, 32, 38, 39, 40, 43. Section 4.5: 5, 12, 15, 18, 20, 23, 25, 27, 32. [solutions]
Second Midterm given on Nov 10. [Midterm 2][solutions]
Week 12 (due Nov 13): Section 4.5: 35, 36. Section 4.6: 12, 18, 20, 30, 35, 38, 40, 44, 45, 46, 52. Section 5.1: 2, 6, 9, 10, 11, 13, 15, 19, 22, 24. [solutions]
Week 13 (due Nov 20): Section 5.1 25, 29, 30, 31. Section 5.2 2, 5, 8, 10, 14, 15, 20, 22, 23. Section 5.3 5, 6, 8, 9, 10, 17, 20, 21, 22. [solutions] And the three problems on a worksheet. [solutions]
Pre-Thanksgiving Lecture, Nov. 26
Week 14 (due Dec 1): Section 5.4 2, 5, 6, 7, 11 (parts (a) to (d)), 12. Section 6.1 12, 14, 16, 17, 18, 19, 23, 29, 36, 46, 47, 49, 50, 55, 57. [solutions]
Week 15 (due Dec 4): Section 6.2 7, 9, 10, 16, 17, 21. Section 6.3 10, 11, 12, 18, 22, 23, 24, 26, 27, 28, 33, 34, 40, 41, 46. Enrichment Problem. (This is a nice problem to test your skill in playing with minus signs. If you take Statistics, for instance, your Stat professor will assume that you can handle a problem like this.) In class, we have computed an antiderivative of xe^{x}. Use the same method to compute an antiderivative of f(x) = x/e^{x}. (Check your answer before you proceed!) Using this, show that the area bounded by y=f(x) and the x-axis between x=0 and x=3 is 1 - 4/e^{3} (which is about 0.8). Does this answer look "reasonable"? How would you "double-check" it by using a Riemann sum (say, with n=3 and using right endpoints)? [solutions]
HW 16: (Not to be turned in, but be sure to do this assignment, as it will be tested on the Final) Section 6.4: 7, 8, 10, 13, 17, 19, 20, 22, 23, 24 6.5: 3, 6, 7, 8, 10, 31, 33, 34, 35, 36, 44

Exams and Practice Exams:

Practice Midterm 1, version A (actual old exam) [solutions]

Practice Midterm 1, version B (another actual old exam) [solutions]

Practice Midterm 1, version C (some challenging practice problems) [solutions]

Jeff will be holding a review session Friday from 2-4pm in 3 Leconte. He will be going over problems from the practice midterms and other similar problems.

Alan is having a review in Evans on Saturday from 3-5pm. Meet at the vending machines on the ground floor to find out which room he will commandeer.

Sevak is also giving a review, on Sunday at 6pm in Evans. Meet at the vending machines for this review as well.

A student named Rubal is organizing an "informal math party" at Cafe Milano (next to Jamba Juice on Bancroft near Telegraph) on Saturday 9/27 from 12-2pm before Alan's review session. Feel free to email her at rubal@berkeley for details or to arrange other meet-ups. This is a great idea!

[Midterm 1][solutions]

Practice for Second Midterm

Practice Midterm 2, version A [solutions]

Practice Midterm 2, version B [solutions]

Practice Midterm 2, version C [solutions]

Jeff will be holding a review session Friday from 2-4pm in 3 Leconte. He will be going over problems from the practice midterms and other similar problems.

Alan is having a review in 9 Evans on Saturday from 1-3pm.

Sevak is also giving a review, on Sunday at 6pm in Evans. Meet at the vending machines on the ground floor to find out which room he will commandeer.

[Midterm 2][solutions]

Practice for Final Exam

Sample Final [solutions]

Jeff will have a review Thursday from 1-3 in 60 Evans. Please feel free to bring snacks.

Sevak will have a review on Friday at 2. Meet by the vending machines on the ground floor of Evans to see which room he shall use. Please feel free to brings snacks to this one too.

A student named Kasondra is having a last minute study get-together Friday morning at 11am. Send her an email (kasondracarleen@yahoo.com) if you're interested. This is a great idea!

Final Exam

The Final Exam for this course will take place on December 13 (Saturday), 8 a.m. to 11 a.m., in 220 Hearst Gym. The rules for the Final (closed-book test, no external aids, etc.) will be the same as those used for the two midterms. NOTE THAT THERE WILL BE NO MAKE-UP FINALS.

Enrollment information: The course control number is 54337. General enrollment information.

Head GSI: There is no longer a head GSI. If you cannot resolve your enrollment issues on Telebears, then see Barbara Peavy in 967 Evans.

GSIs:
Shuchao Bi [shuchao@math] OH Tu 11-12, Th 5-6, 941 Evans.
Jeffrey Doker [doker@math] OH Tu 3-5, 1015 Evans. (Jeff's office is 787 Evans.)
Richard Dore [rdore@math] OH W 11-noon, 2-3, 1044 Evans.
Sevak Mkrtchyan [sevak@math] OH Th 9:40-11, 2:10-3:30, 1010 Evans.
Alan Tarr [alant@math] OH M 11:30-12:30, Tu 2-3, 935 Evans.

Any Math 16A student is welcome at any GSI's office hours.

Prerequisites: Math 32 or three years of high school mathematics including trigonometry. If you are not sure whether this course is at the right level for you, this diagnostic exam might help you decide. Math 16A and 16B are intended for students who do not intend to take further mathematics courses. If your intended major lies in the sciences, or if you have some previous experience with calculus, you might consider taking 1A and 1B instead, even if your department does not require it.

Required Text: At the math department's request, the publisher has provided a softcover edition of the text split into two volumes, one for Math 16A, and one for Math 16B. For 16A, you need Calculus and its applications, Volume One.
It consists of Chapters 0 through 6 of Goldstein, Lay, Schneider, Asmar, Calculus and its applications, 11th edition, Pearson Prentice Hall, 2007. If you know you will take both 16A and 16B, you could alternatively buy the whole hardcover text containing all Chapters 0 through 12.
An older edition of the text may cover the same subjects, but you will need access to one of the editions above, since homework problems will be assigned from there.

Syllabus:

Functions
The derivative
Applications of the derivative
Exponential and logarithmic functions
The Definite Integral

Grading: 1/6 section grade (80 points), 1/6 midterm 1 (80 points), 1/6 midterm 2 (80 points), 1/2 final exam (240 points). The following list is a guide of what percentages will earn what grades:

85% or higher will result in at least an A- .
70% or higher will result in at least a B-.
55% or higher will result in at least a C-.
45% or higher will result in at least a D.

Quizzes: Quizzes will be administered on a regular basis by your GSI during sections.

Exams: There will be in-class midterms on Monday September 29 and Monday November 10, and a 3-hour final exam Saturday December 13 (location TBA). Notes, books, ipods, cellphones and calculators will not be permitted for exams. Bring your student ID, and pencils or pens to all exams.

Homework: There will be weekly assignments posted on this website, and due at the beginning of section each Thursday. You are encouraged to discuss questions with each other or to come to office hours for help. After discussion with others, write-ups must be done separately. In practice, this means that you should not be looking at other students' solutions as you write your own. Use examples in the book as a model for the level of details expected.

Academic Dishonesty:We treat all incidents of academic dishonesty seriously and will not hesitate to initiate disciplinary procedures should such a case arise. Academic dishonesty includes but is not limited to: copying other students' homework or looking at other students' exams and quizzes, or bringing any kind of unauthorized aids or materials to the exams.

Resources: Student Learning Center, Counseling for academic or other difficulties

Other important things: Please note that enrolling in this course means that you have agreed to take all exams (midterms and final) at the pre-announced times. In fairness to all students in the class, there will be NO MAKE-UP EXAMS for any individual student. If you cannot be absolutely sure that you can take all the exams on the pre-announced dates and times, you should register in Professor Demmel's class (Math 16A, Lecture 1), which has a different exam schedule.

Advice from Professor: You should take this course only if you have had three years of solid high school mathematics, especially high school algebra/geometry. Grade statistics has shown that students with poor algebra background end up with grades below C minus in this course. Therefore, it is essential that you take the (computer-graded) Calculus Placement/Diagnostic Exam on the Math. Department's Webpage to find out where you stand in your preparedness for Math 16A. If you find yourself under-prepared, DO NOT take this course, for otherwise you might end up with a very undesirable grade. Instead, you should take Math 32. Also, if you find yourself struggling with Math 16A early on for any reason, you should drop the course before the College's deadline for dropping, which is September 26, 2008 (before our first Midterm Exam!).

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