Math 1A Fall 2006

Mathematics 1A, Section 2 - Calculus - Fall 2006

Professor: Mark Haiman

Time and place: MWF 10-11am, 1 Pimentel Hall. Students taking this class are expected to attend lectures, enroll in and attend one of the discussion sections, do weekly homework assignments, and take the two midterms and final exam. Click here for the schedule of discussion sections.

Professor Haiman's office hours: MW 12:30-2:00, 771 Evans Hall

GSI office hours:

Khalilah Beal (Sections 210, 217): MWF 11:20-12, 1065 Evans
David Berlekamp (Sections 204, 219): M 11-12, W 2-4, 840 Evans
June Chung (Section 201): M 2-3, Th 3-4, 864 Evans
Dan Evans (Sections 209, 211): M 12:30-1:30, W 2:30-3:30, 832 Evans
David Farris (Sections 205, 212): M 5-6, Th 11-11:30, 1085 Evans
Mark Howison (Sections 214, 215): M 11-12, 2-3, F 2-3, 1015 Evans
Greg Igusa (Sections 203, 207): M 12:30-1:30, W 3:30-4:30, 842 Evans
Andrew Marks (Sections 202, 213): M 11:30-12:30, W 3:30-4:30, Th 3:40-4:30, 854 Evans
Koushik Pal (Sections 218, 220): TTh 2:30-3:30, 845 Evans
Steven Sam (Section 208): MF 11:30-12:30, 868 Evans
William Slofstra (Section 206): M 8:30-9:30, W 3:30-4:30, 820 Evans
Tony Varilly (Section 216 - PDP) M 1-3, Tu 11-12:30, F 3-4:30, Stephens 240-A

The Student Learning Center also offers drop-in tutoring and exam review for Math 1A.

Section changes/Waitlists: Contact the Math 1A Head TA, Aaron Greicius, email greicius@math (.berkeley.edu), 1070 Evans Hall. His office hours for the first 2 weeks of class are Tu-W 9-11, Th 1-3, and F 2-4.

Catalog Description: Calculus — Mathematics 1A

Course Format: Three hours of lecture and two hours of discussion/workshop per week.

Prerequisites: Three and one-half years of high school math, including trigonometry and analytic geometry, plus a satisfactory grade in one of the following: CEEB MAT test, an AP test, the UC/CSU math diagnostic test, or 32. Consult the mathematics department for details. Students with AP credit should consider choosing a course more advanced than 1A.

There is an online exam you can take to help you decide whether or not you are ready to take this course.

Credit option: Students will receive no credit for 1A after taking 16B and 2 units after taking 16A.

Description: This sequence is intended for majors in engineering and the physical sciences. An introduction to differential and integral calculus of functions of one variable, with applications and an introduction to transcendental functions.

Textbook

James Stewart, Calculus: Early Transcendentals, 5th edition (Brooks/Cole, 2003). We will cover chapters 1-6. A special paperback edition containing only the chapters for Math 1A/1B is available at the ASUC textbook store.
In case you want additional reading to supplement the Stewart book, you also get free online access from the Berkeley campus to Marsden and Weinstein's Calculus I and the accompanying Student Guide. To access these (and other UCB online resources) from an off-campus connection using your Calnet ID, see Library Proxy Server Instructions.

Grading

There will be a short quiz in the discussion sections each Tuesday (except Aug. 29). No make-up quizzes will be given. Only your 12 best quiz scores and 12 best homework scores will count towards your final grade, so it doesn't matter if you miss one or two.

The grading formula will be approximately: homework+quizzes 35%, midterms 15% each, and final 35% of the grade. There is no grading curve fixed in advance. Grades for the course will be based on my judgment of how well the class is doing, and will be higher if everyone is working hard at the homework and doing well on the exams.

Exam questions will be similar to randomly selected homework questions, with minor changes. If you understand how to solve all the homework problems, you should be able to answer all the exam questions.

Exam and quiz questions will be graded on the following scale:

10 points for a complete, correct solution
8-9 for a solution with only minor errors
5 for a partially correct solution showing significant progress
0 for lack of significant progress toward a solution

Requests to change the partial credit given for a solution will not be considered. Grades will be changed only in cases of clear error on the part of the grader, such as adding up scores incorrectly.

Exams

First Midterm: Friday, Sept. 29 during the lecture hour.
Second Midterm: Friday, Nov. 3 during the lecture hour.
Final Exam: Tuesday, Dec. 12, 8-11am (Exam group 1), 100 Haas Pavillion

The second midterm will cover material from after the first midterm. The final exam will cover the whole course, with extra emphasis on material from after the second midterm.

You may bring one (ordinary sized) sheet of notes with writing on both sides to the exams. Apart from this one sheet, you may not bring textbooks, notebooks, calculators, or other aids. No notes on quizzes.

There will be no make-up exams. If you miss the first midterm, the mark for the second midterm will be doubled. If you miss the second midterm, the mark for the final will be increased by 40%. If you miss both midterms or the final then you are in trouble.

Homework

Homework is due by the end of discussion section each Tuesday. Late homework will not be accepted. Collaboration on homework is fine, but if you hand in similar homework to your collaborator you should clearly state so and say who you are working with, in order to avoid unfortunate misunderstandings.

Incomplete grades

Incomplete "I" grades are almost never given. The only justification is a documented serious medical problem or genuine personal/family emergency. Falling behind in this course or problems with workload on other courses are not acceptable reasons.

Special accomodations

Students requiring special accomodations for exams must provide documentation from the Disabled Students' Program (DSP) and contact me at least ten days prior to the exam, so that arrangements can be made.

Syllabus

Introduction/overview
Functions and ways to describe them. Graph, domain, range, increasing and decreasing functions. Toolkit of important functions.
Operations on functions and transformations on their graphs. Inverse functions. Logarithms, log and exponent laws.
Limits (informally), tangent problem as motivation. Limit laws, computation examples, limits from left and right, non-existent and infinite limits. Vertical asymptotes.
Definition of limit; establishing values of limits.
Continuous functions. Examples of discontinuities. Limit laws as continuity theorems.
Intermediate value theorem; existence of roots. Limits at infinity.
Rate of change; tangents revisited; derivative of a function.
Derivatives of powers xⁿ. Linearity. Product rule.
Derivative of exponential function a^x. Base of natural logarithms, e. Quotient rule.
Derivatives of trig functions.
The chain rule.
Implicit differentiation. Derivatives of inverse functions.
Computation and interpretation of higher derivatives.
Derivatives of logs. Logarithmic differentiation. Limit formula for e. Derivatives of hyperbolic trig functions and their inverses.
Application: related rate problems.
Application: linear approximation and differentials.
Maxima and minima. Extreme value theorem. Derivative test; critical points.
Mean value theorem and its consequences.
Proving inequalities.
Convexity and concavity. Second derivative test. Sign of derivatives and shape of the graph.
Application: optimization problems.
L'Hospital's rule for indeterminate ratios.
L'Hospital's rule continued. Indeterminate products and indeterminate powers. Comparing magnitudes.
More qualitative study of graphs of functions, slant asymptotes.
Newton's method for solving equations numerically.
Using computers to study calculus functions (with demo).
Antiderivatives. Simple examples. Particular and general antiderivatives. Simple differential equations. Graphical anti-differentiation.
The area and distance problems. Area as a limit of Riemann sums. The definite integral.
First properties and simple evaluations of integrals. Meaning of negative integrals. Distance versus displacement.
The fundamental theorem of calculus. Computing simple integrals.
Definite and indefinite integrals. Derivative of a function defined by a definite integral. Integral of a derivative (net change theorem).
Substitution rule.
Substitution in definite integrals. Integrals of even and odd functions.
Using integrals to define logs and exponentials.
Application: area of regions bounded by curves.
Application: volume by integrating over slices.
Application: volume by integrating over cylindrical shells.
Application: average value of a function.
Continuation, review or special topic.

Reading and Homework Schedule

Most questions have answers in the back of the book. The ones in red in the book also have hints on one of the CD's.

Lecture Date Reading Exercises (due in discussion section the following Tuesday)

1-3 Aug 28-
Sept 1 Preview, 1.1-1.3, 1.5, 1.6 1.1: 1, 5, 7, 15, 33, 39, 45. 1.2: 3, 7, 11. 1.3: 1, 5, 7, 23, 29, 43, 47 1.5: 11, 17, 20. 1.6: 5, 7, 11, 27, 31, 37, 41, 51, 65, 69, 71. Quiz 1 solutions: Version A, Version B

4-5 Sept 6-8 2.1-2.4 2.1: 3, 7 2.2: 5, 9, 13, 17, 25, 35 2.3: 1, 7, 19, 21, 25, 41, 43 2.4: 3, 9, 15, 31, 41, 43. Quiz 2 solutions: Version A, Version B

6-8 Sept 11-15 2.5-2.9 2.5: 3, 5, 9, 25, 27, 31, 39, 47, 51, 61 2.6: 3, 5, 15, 21, 31, 37 2.7: 1, 5ab, 9. 2.8: 3, 5, 7, 9a, 15, 23. 2.9: 3, 7, 11, 23, 29, 37, 45. Quiz 3 solutions: Version A, Version B

9-11 Sept 18-22 3.1, 3.2, 3.4 3.1: 11, 15, 17, 23, 25, 31, 41, 45, 55, 63. 3.2: 1, 3, 5, 11, 21, 31, 43. 3.4: 3, 9, 15, 23, 29, 35, 37, 45, 47. Quiz 4 solutions: Version A, Version B

12-13 Sept 25-27 3.5, 3.6 3.5: 1, 5, 7, 9, 19, 23, 33, 37, 39, 45, 51, 57, 61. 3.6: 5, 9, 15, 21, 25, 29, 35, 41, 43, 47. Quiz 5 solutions: Version A, Version B

Midterm 1 — Sept. 29 Covering chapters 1, 2 and 3.1-4. Room information above. Here are Practice exam with solutions, and 2004 midterm 1 with solutions. Midterm 1 solutions.

14-16 Oct 2-6 3.7-3.10 3.7: 1, 3, 7, 11, 23, 35, 39, 47. 3.8: 3, 5, 11, 13, 28, 31, 41, 43, 47. 3.9: 29a, 31, 41. 3.10: 5, 13, 29, 31. Quiz 6 solutions: Version A, Version B

17-19 Oct 9-13 3.11, 4.1, 4.2 3.11: 1, 7, 9, 19, 31, 39, 41, 49. 4.1: 3, 5, 9, 13, 17, 21, 23, 25, 27, 35, 43, 49, 55. 4.2: 7, 13, 15, 17, 31. Quiz 7 solutions: Version A, Version B

20-22 Oct 16-20 4.2 (cont'd), 4.3, 4.7 4.2: 23, 27, 29, 33. 4.3: 1, 5, 7, 11, 17, 21, 29, 37, 41, 45, 63, 69. 4.7: 1, 5, 9, 11, 15, 17, 19, 25, 31, 43, 51. Quiz 8 solutions: Only one version

23-25 Oct 23-27 4.4-4.5 4.4: 5, 9, 11, 17, 21, 23, 25, 27, 29, 31, 39, 41, 43, 45, 47, 49, 53, 57, 67. 4.5: 9, 11, 13, 29, 59, 61, 63. Quiz 9 solutions: Version A, Version B

26-27 Oct 30
-Nov 1 4.6, 4.9 4.6: 13, 23. 4.9: 1, 3, 5, 11, 13, 31, 35, 37.

Midterm 2 — Nov 3 Covering chapters 3.5-3.11, 4.1-4.5 and 4.7. Practice exam with solutions, 2004 midterm 2 with solutions. Midterm 2 solutions.

28-29 Nov 6-8 4.10, 5.1, 5.2 4.10: 3, 7, 9, 11, 15, 17, 19, 21, 27, 35, 39, 41, 43, 45, 47, 59, 67, 73, 75, 77. 5.1: 1, 3, 11, 15, 17, 19, 21. 5.2: 1, 5, 7, 9, 19, 23, 33. Quiz 10 solutions: Version A, Version B

30-32 Nov 13-17 5.2 (cont'd)-5.4 5.2: 37, 39, 47, 49, 53, 55, 61. 5.3: 3, 9, 11, 13, 21, 25, 29, 31, 39, 41, 49, 51, 59, 61, 67. 5.4: 1, 3, 19, 27, 37, 39, 43, 47, 53, 55, 57. Quiz 11 solutions: Version A, Version B (corrected 11/17)

33-34 Nov 20-22 5.5 5.5: 1, 3, 5, 7, 9, 13, 17, 21, 27, 31, 37, 41, 51, 57, 65, 71, 75, 79, 83. Quiz 12 solutions: Version A, Version B

Nov 23-24 Thanksgiving holiday

35-37 Nov 27-
Dec 1 5.6, 6.1, 6.2 5.6: 1, 3, 5. 6.1: 1, 3, 9, 11, 19, 25, 43, 45, 49. 6.2: 1, 3, 9, 11, 13, 17, 31, 47, 49, 51, 61, 65. Quiz 13 solutions: Version A, Version B

38-40 Dec 4-8 6.3, 6.5 6.3: 3, 5, 41, 42, 46. 6.5: 1, 3, 9, 18.
This last homework is due Thursday, Dec 7. Quiz 14 solutions: Only one version

Final Exam — Dec 12 Covering all chapters with extra emphasis on 4.6-4.10, 5 and 6. Practice exam with solutions, 2004 final exam with solutions Final Exam solutions.

Final grades

You will be able to find out your grade for the course from TeleBears once we finish computing them. If you want to know your score on the final exam, contact your GSI. If you want to look at your final exam, you have to wait until next semester, when it will be on file at the Math department office, 970 Evans Hall. The grade cutoffs for the final exam were A: 164+, B: 135+, C: 107+, D: 80+, out of a possible 200 points.

Calendar

Links of interest

A collection of Calculus links
Excerpts from How to ace calculus
www site for the textbook (contains some online quizzes)
History of calculus
Archimedes, Barrow, Berkeley, Johann Bernoulli, Jacob Bernoulli, De L'Hopital, Fermat, Leibniz, Newton, Taylor

[ Top of page | Prof. Haiman's home page ]

Lecture	Date	Reading	Exercises (due in discussion section the following Tuesday)
1-3	Aug 28- Sept 1	Preview, 1.1-1.3, 1.5, 1.6	1.1: 1, 5, 7, 15, 33, 39, 45. 1.2: 3, 7, 11. 1.3: 1, 5, 7, 23, 29, 43, 47 1.5: 11, 17, 20. 1.6: 5, 7, 11, 27, 31, 37, 41, 51, 65, 69, 71. Quiz 1 solutions: Version A, Version B
4-5	Sept 6-8	2.1-2.4	2.1: 3, 7 2.2: 5, 9, 13, 17, 25, 35 2.3: 1, 7, 19, 21, 25, 41, 43 2.4: 3, 9, 15, 31, 41, 43. Quiz 2 solutions: Version A, Version B
6-8	Sept 11-15	2.5-2.9	2.5: 3, 5, 9, 25, 27, 31, 39, 47, 51, 61 2.6: 3, 5, 15, 21, 31, 37 2.7: 1, 5ab, 9. 2.8: 3, 5, 7, 9a, 15, 23. 2.9: 3, 7, 11, 23, 29, 37, 45. Quiz 3 solutions: Version A, Version B
9-11	Sept 18-22	3.1, 3.2, 3.4	3.1: 11, 15, 17, 23, 25, 31, 41, 45, 55, 63. 3.2: 1, 3, 5, 11, 21, 31, 43. 3.4: 3, 9, 15, 23, 29, 35, 37, 45, 47. Quiz 4 solutions: Version A, Version B
12-13	Sept 25-27	3.5, 3.6	3.5: 1, 5, 7, 9, 19, 23, 33, 37, 39, 45, 51, 57, 61. 3.6: 5, 9, 15, 21, 25, 29, 35, 41, 43, 47. Quiz 5 solutions: Version A, Version B
Midterm 1 — Sept. 29			Covering chapters 1, 2 and 3.1-4. Room information above. Here are Practice exam with solutions, and 2004 midterm 1 with solutions. Midterm 1 solutions.
14-16	Oct 2-6	3.7-3.10	3.7: 1, 3, 7, 11, 23, 35, 39, 47. 3.8: 3, 5, 11, 13, 28, 31, 41, 43, 47. 3.9: 29a, 31, 41. 3.10: 5, 13, 29, 31. Quiz 6 solutions: Version A, Version B
17-19	Oct 9-13	3.11, 4.1, 4.2	3.11: 1, 7, 9, 19, 31, 39, 41, 49. 4.1: 3, 5, 9, 13, 17, 21, 23, 25, 27, 35, 43, 49, 55. 4.2: 7, 13, 15, 17, 31. Quiz 7 solutions: Version A, Version B
20-22	Oct 16-20	4.2 (cont'd), 4.3, 4.7	4.2: 23, 27, 29, 33. 4.3: 1, 5, 7, 11, 17, 21, 29, 37, 41, 45, 63, 69. 4.7: 1, 5, 9, 11, 15, 17, 19, 25, 31, 43, 51. Quiz 8 solutions: Only one version
23-25	Oct 23-27	4.4-4.5	4.4: 5, 9, 11, 17, 21, 23, 25, 27, 29, 31, 39, 41, 43, 45, 47, 49, 53, 57, 67. 4.5: 9, 11, 13, 29, 59, 61, 63. Quiz 9 solutions: Version A, Version B
26-27	Oct 30 -Nov 1	4.6, 4.9	4.6: 13, 23. 4.9: 1, 3, 5, 11, 13, 31, 35, 37.
Midterm 2 — Nov 3			Covering chapters 3.5-3.11, 4.1-4.5 and 4.7. Practice exam with solutions, 2004 midterm 2 with solutions. Midterm 2 solutions.
28-29	Nov 6-8	4.10, 5.1, 5.2	4.10: 3, 7, 9, 11, 15, 17, 19, 21, 27, 35, 39, 41, 43, 45, 47, 59, 67, 73, 75, 77. 5.1: 1, 3, 11, 15, 17, 19, 21. 5.2: 1, 5, 7, 9, 19, 23, 33. Quiz 10 solutions: Version A, Version B
30-32	Nov 13-17	5.2 (cont'd)-5.4	5.2: 37, 39, 47, 49, 53, 55, 61. 5.3: 3, 9, 11, 13, 21, 25, 29, 31, 39, 41, 49, 51, 59, 61, 67. 5.4: 1, 3, 19, 27, 37, 39, 43, 47, 53, 55, 57. Quiz 11 solutions: Version A, Version B (corrected 11/17)
33-34	Nov 20-22	5.5	5.5: 1, 3, 5, 7, 9, 13, 17, 21, 27, 31, 37, 41, 51, 57, 65, 71, 75, 79, 83. Quiz 12 solutions: Version A, Version B
Nov 23-24			Thanksgiving holiday
35-37	Nov 27- Dec 1	5.6, 6.1, 6.2	5.6: 1, 3, 5. 6.1: 1, 3, 9, 11, 19, 25, 43, 45, 49. 6.2: 1, 3, 9, 11, 13, 17, 31, 47, 49, 51, 61, 65. Quiz 13 solutions: Version A, Version B
38-40	Dec 4-8	6.3, 6.5	6.3: 3, 5, 41, 42, 46. 6.5: 1, 3, 9, 18. This last homework is due Thursday, Dec 7. Quiz 14 solutions: Only one version
Final Exam — Dec 12			Covering all chapters with extra emphasis on 4.6-4.10, 5 and 6. Practice exam with solutions, 2004 final exam with solutions Final Exam solutions.