Math 1A - Calculus - Fall 2009

Coordinates

Announcements

Text, syllabus, prereqs

GSIs

Problem sets, reading assignments

Problem set solutions

Lectures

Exam info

Handouts

Coordinates

MWF 10:00-11:00, Room 2050 Valley Life Sciences Building

Instructor:

Michael Christ 809 Evans Hall, 642-2143. mchrist@math.berkeley.edu (send email)

Office hours: W 1:30-2:30, Th 9:00-10:00. M 1:30-2:30 for brief administrative matters only; that hour is dedicated primarily to Math 185 students.

Text, syllabus, prerequisites.

See course policies announcement. 

Enrollment Issues:

GSIs: 

• Shuchao Bi. 941 Evans Hall. M 8:00-9:00am, T 7:30-9:30am, W 8:00-9:00am, Th 5:00-6:00pm or by appointment. Web page
  
• Andrew Critch. critch@math.berkeley.edu, 854 Evans Hall. Office hours MW 6-7, Friday by appointment.
  
• Julia Erhard. 830 Evans Hall, erhard@math.berkeley.edu Office hours: M at 11, Th at 4.
  
• Kate Liesenger
• Ben Preskill. preskill@math.berkeley.edu; Evans Hall 820. Office Hours: M 11-12 AM, T 2-4 PM
  
• Zachary Sylvan. zack@math.berkeley.edu, 836 Evans Hall,  Office hours: W 2-3, Th 1:30-2:30
  
• Lawrence Valby. 814 Evans Hall. Office Hours: W 3-4, Th 11-12.  valby@berkeley.edu
  
• Hwajong Yoo. 853 Evans Hall. hwajong@math.berkeley.edu. M 3:00-4:00, Th 11:00-12:00.
  

Homework Assignments and solutions; reading assignments.

• Read, then study, sections 1.1-1.3 of the text. Due Friday 8/28.
• Read, then study, sections 1.5-1.6 of the text. Due Monday 8/31.
• Section 1.1: Problems 1,6,7,14,18,30,57. Due Wednesday 9/2.
• 1.2: 4,13,15. Due Wednesday 9/2.
• 1.3: 3,6,21,29(f-g,f/g only),33(a,b),55. Due W 9/2.
• 1.4: No problems are, or will be, assigned.
• 1.5: 2,9,17,20. Due W 9/2.
• Solutions for problem set 1
  
• 1.6: 5,6,17,21,23,34,35(a),54,63,65. Due: W 9/9.
• 2.1: 1,3((a): only subparts (i)-(iii)),6. Due: W 9/9.
• 2.2: 1,7,9,15,25,28,35((b) optional),40. (Problem 39 optional) Due: W 9/9.
• 2.3: 2,5,11 Due: W 9/9.
• Solutions for problem set 2
  
• 2.3: 15,22,41,61 Date due: 9/16
  
• 2.4: 3,13,19,27,30 Date due: 9/16
  
• 2.5: 3,22,31,43(a),47,65 Date due: 9/16
  
• 2.6: 3(b,c,f),7,15,21,27,28,48,52,65 Date due: 9/16
• Study text Chapter 2 through section 2.7 by 9/16
• Solutions for problem set 3
  
• 2.7: 1,10(a,b),12,17,20,32,41,46,49 Date due: 9/23
• 2.8: 1(parts (a) through (e)),3,5,13,21,28,41,44. Date due: 9/23
• Study text through section 3.1 by 9/23.
  
• Solutions for problem set 4
  
• Study text through section 3.3 by 9/25.
  
• 3.1: 2,17,23,35,50(a,b),51,62. Due Wednesday 9/30.
• 3.2: 15,18,32,47,53. Due Wednesday 9/30.
• 3.3: 7,10,17,24,35,37,51. Due Wednesday 9/30.
• 3.4: 5,13. Due Wednesday 9/30.
• Solutions for problem set 5
  
• 3.4: 29,31,42,65,82(a,b),83,95. Due Wednesday 10/7.
• 3.5: 11,18,27,43,54,67. Due Wednesday 10/7.
• 3.6: 9,13,27,45. Due Wednesday 10/7.
• 3.7: 5,10,18,28,31. Due Wednesday 10/7.
  
• Reading assignments have been announced regularly in lectures, but haven't always been posted here. For Friday 10/2, you should have read Chapter 3 through section 3.7.
• For Monday 10/5, read section 3.8. We will be skipping section 3.11, and will touch only lightly on 3.10.
• For Wednesday 10/7 read section 3.9; for Friday read 3.10; for Monday 10/12 read 4.1.
• Solutions for problem set 6  
• 3.8: 3,8,11,15,19. Due Wednesday 10/14
• 3.9: 13,18,24,36,44. Due W 10/14
• 3.10: No problems assigned.
• 3.11: No problems assigned; I do not plan to discuss this section of the text unless time remains later in the semester. It is not assigned reading.
  
• 4.1: 5,10,33,51,63,73. Due W 10/14
• Read section 4.1 for Monday 10/12, and 4.2 for Wednesday 10/14.
  
• Solutions for problem set 7  
• Read section 4.3 for Friday 10/16.
• Problem set 8: 4.2: 3,5,18,23,27,33,34. Due Wednesday 10/21.
• Problem set 8: 4.3: 1,8,16,19,26,31,64,71,73. Due Wednesday 10/21.
  
• Solutions for problem set 8  
• Problem set 9: 4.4: 1,2,9,14,15,20,49,64,71,72. Due Wednesday 10/28.
  
• Problem set 9: 4.5: 5,15,21,38,52,56,64,68. Due Wednesday 10/28.
  
• Section 4.6 is about combining what we have learned about graphing using calculus, with the powers of graphing calculators. This section will not be covered in lecture or on exams, and you are not required to read it.
  
• Solutions for problem set 9 and accompanying graphs. (These solutions are mistakenly labeled ``Problem Set 5'', and are in need of other minor non-mathematical edits.)   
• There is no problem set due Wednesday 11/4, so that you can concentrate on studying for the midterm exam on that date. There will be a rather long problem set for Wednesday 11/11. Some of those problems will be posted well ahead of time, by the evening of Friday 11/30, so that those who prefer, can work on them this weekend and early next week.
  
• Problem set 10, due Monday 11/9: (Wednesday 11/11 is a holiday.)
  Section 4.7: 4,16(a),19,37,42,46,53,72.
  Section 4.8: 3,4(a,b,c),29,30(a),38. (Problem 29(b) will require a calculator.)
  Section 4.9: 13,29,47,52(assume s(0)=0),64,70. 
• Solutions for problem set 10 
• We will finish section 5.2 on Friday 11/13, and will discuss the super-important section 5.3 on Monday 11/16.
• Problem set 11, due Wednesday 11/18: 5.1: 3a,14,18,20,26
  5.2: 1,5a,9(requires calculator),22,30,34c,48,51,59,65,68
  5.3: 9,16,23,31,44,51
  
• Solutions for problem set 11 
• There is no problem set due Wednesday 11/25; problem set 12 will due on Wednesday December 2, after Thanksgiving. This problem set will be posted in two installments. Here is the first installment:
  5.3: 53,56,63,65,66,68,74
  5.4: 1,11,16,26,36,44,47,51,52,59,64
  5.5: 3,5,11,13,19.29,43,45,64,67
  Because this problem set spans five lectures, it will be significantly longer than a normal problem set. (It will also count double in the computation of final course grades.) Please consider beginning well before it is due.
• Continue reading the text in synchronization with, or ahead of, the lectures. We will finish section 5.5 on Monday 11/23, and will (probably) begin section 6.1 on Monday as well. On Wednesday 11/25 we'll very quickly review Chapter 5, and will finish 6.1. Read section 6.1 this week, and 6.2 and 6.3 by Monday 11/30. We will finish with a brief discussion of sections 6.4 and 6.5 on Friday 12/4, the final lecture of the semester.
  
• The following assignments are still tentative. (I often delete a few problems in the process of finalizing each assignment.)
  

Lecture Notes

Brief summaries of lectures, indicating topics/sections covered/discussed, will be posted here. These summaries will sometimes include little bits of material which were not included in the lectures due to time constraints. Sometimes preliminary versions will later be corrected in order to provide a more accurate lecture of what was said in lecture. Somtimes these will be quite detailed lecture notes; sometimes they will only be outlines.

1. Lecture 1, W 8/26 (revised/corrected 8/27 11:00 AM)
   
2. Lecture 2, F 8/28 (small corrections 8/31 8:45 AM)
3. Lecture 3, M 8/31
   
4. Lecture 4, W 9/2 (outline) and a few slides from the lecture
5. Lecture 5, F 9/4
   
6. Lecture 6, W 9/9  and two slides which I did not have time to display during the lecture. (Example 4 has been slightly revised on Wednesday 9/16; a paragraph had been missing from the discussion.)
7. Lecture 7, F 9/11. (some corrections made after the lecture)
8. Lecture 8, M 9/14  and some administrative announcements 
   
9. Lecture 9, W 9/16 and Some administrative announcements.
10. Lecture 10, F 9/18. No lecture notes currently available.
11. Class meeting 11, M 9/21: Midterm exam 1.
12. Lecture 12, W 9/23  
    
13. Lecture 13, F 9/25  
    
14. Lecture 14, M 9/28: Chain rule, and derivative of natural logarithm function. (Because of the institution of a reading week at the end of the semester, we have lost 2 or 3 lectures from our original schedule. I'll need to go a bit faster in one or two spots to compensate. Chapter 3 is one.)
15. Lecture 15, W 9/30   Implicit differentiation, and derivative of arcsin.
16. Lecture 16, F 10/2 
    
17. Lecture 17, M 10/5 Exponential growth and decay.
18. Lecture 18, W 10/7 Related rates problems (text section 3.9)
    
19. Lecture 19, F 10/9 Linear approximation/tangent line approximation (text section 3.10). 
20. Lecture 20, M 10/12. No lecture notes currently posted.
    
21. Lecture 21, W 10/14 The Mean Value Theorem (text section 4.2)
22. Lecture 22, F 10/16  First derivatives and graphs 
23. Lecture 23, M 10/19 Concavity, second derivatives, inflection points, and graphs
    
24. Lecture 24, W 10/21 Limits of indeterminate forms, and L'Hospital's rule. (Revised 10/22 at 11 AM, incorporating questions asked by students during and immediately after class.)
    
25. Lecture 25, F 10/23 A few more minutes about l'Hospital's rule, and then the main topic of the lecture, curve sketching.
26. Lecture 26, M 10/26 Curve sketching. Three examples. More on slant asymptotes, and the use of L'Hopital's rule to find them.
    
27. Lecture 27, W 10/28 Optimization problems. 
28. Lecture 28, F 10/30 Approximate solution of numerical equations: Newton's method.
    
29. Lecture 29, M 11/2 Antiderivatives. 
30. Class meeting 30, W 11/4: Midterm exam 2.
31. Lecture 31, F 11/6 Area (especially, areas of curvy regions defined by graphs of continuous functions)
    
32. Lecture 32, M 11/9 Riemann sums, and the definition of the definite integral.
    
33. Lecture 33, F 11/13 More about definite integrals. (text section 5.2)
    
34. Lecture 34, M 11/16 The Fundamental Theorem of Calculus (text section 5.3) 
35. Lecture 35, W 11/18 FTC: Review, proof, an application, a problem. Net Change Theorem. (text 5.3 and begin 5.4)
36. Lecture 36, F 11/20 Evaluation of a limit using a definite integral. Notation for indefinite integrals. Meaning. Substitution rule, and its derivation.
37. Lecture 37, M 11/23 Calculation of indefinite and definite integrals using the substitution rule.
38. Lecture 38, M 11/23 Area between curves. (Text section 6.1.) Brief review of Chapter 5.

Handouts

• Course policies announcement includes important dates and grading policies. You are responsible for reading it and adhering to course rules.
• Exam procedures handout
  
• Midterm exam 1 study guide and sample problems
• Solution to sample problems (2a), (2b), and (5). (On the actual first midterm exam, the algebra will generally be less messy than in these problems. I am not trying to test your ability to do algebraic calculations quickly.)
• Solutions for midterm exam 1. (Revised morning of 9/22 to eliminate a few typos.)
• Review Guide and Practice Questions for Midterm Exam 2
  
• Solutions for practice questions for Midterm Exam 2
  
• There is a typo in practice problem 2(a) and/or in its solution; the problem statement has x tending to infinity, while the solution has x tending to zero. If x tends to infinity, then the limit is zero, because sin(x)/x is always between -1/x and +1/x, so the Squeeze Theorem says that the limit exists and equals zero.
  

Announcements

• The Student Learning Center organizes study groups, exam review sessions, and drop-in tutoring for this class. See http://slc.berkeley.edu/math_stat/math1a.htm for further info.
  
• Notetakers needed. The Disabled Students' Program seeks students willing to take notes for this class (and others), for the benefit of classmates needing assistance. This is a paid position. See http://dsp.berkeley.edu/notetakers.html.
  
• The use of calculators on quizzes and exams will not be permitted. Exams will be composed in such a manner that calculators will not be required.

Exam info

• For midterm 1 study guide and sample exam problems, see above under ``Handouts''.
  
• Exam procedures handout
  
• The final exam will be held on Saturday, December 12. For midterm exam dates, see course policies announcement.
• Quiz dates are as follows: W 9/2, M 9/14, M 10/5, M 10/19, M 11/16
• Barring unforeseen circumstances, solutions to exam problems will be posted here promptly after administration of the exam. I try hard to be prompt, so that you can study the solutions while the exam is still fresh in your mind.
• Please arrive ahead of time for exams. You will need pencils/pens and erasers, nothing more.  You will be given an exam booklet in which all work is to be done, and which includes room for scratch work. No calculators are permitted; no books or notes. Cell phones and other electronic devices capable of communication must be turned off and stowed where they cannot be seen. 
• Solutions for midterm exam 1. Please note that there were three nearly identical versions of the exam, with different numbers and sometimes different functions, but essentially identical problems. For each problem, I've give a solution for only one version (at least for now).
  
• The exam was returned to you in discussion section on Wednesday. The median score was approximately 31, with a classic bell-shaped distribution of scores. There were three perfect scores of 50. Rough cutoffs for conversion to letter grades (These are for advisory purposes only. Your raw numerical score will be used in the computation of your final point total for the semester, which will be converted to a letter grade.) A+: 48. A-: 38. B-: 27. C-: 21.
• A score below 21 is cause for concern. (This is of course an arbitrary cutoff; there's little difference between 21 and 19.) If your score is in that range, please consider going over your exam with your GSI, to assess your prospects for passing the course.
• Midterm 2 is graded and will be returned to you on Monday 11/9. Overall, exam scores were very good! Some info on distribution of scores: 7 perfect scores; 18 scores of 48 or 49 (out of 50). 90th percentile: 47. 80th: 44. 60th: 39. Median: 38. 40th: 35. 20th: 28. 10th percentile: 14.
• Solutions for midterm exam 2  
• Typical distribution of letter grades for Math 1AB: A+/A/A- 30%, B+/B/B- 40%, C+/C/C- 20%, D-F 10%. This semester's course will follow this typical distribution, with the exception that there is no fixed number of D-F grades; everyone who completes all required work, and does work of passing quality, will receive at least a C minus. At the end of the semester, each student's point total will be calculated using the weights announced at the outset of the semester. The class will then be ordered according to total points, and letter grades assigned according to the above distribution so that a higher point total corresponds to a higher, or at least equally high, letter grade. Plus/minus A,B,C grades will be used.
  

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