Math 1B: Calculus, Summer 2009

2:10 – 4:00 pm in 6 Evans. CCN: 58465 and 58470
Instructor: Theo Johnson-Freyd. Office Hours: MTTF 1:15 – 2:00 pm, W 4:00 – 4:45 pm, in 1058 Evans

You must be enrolled in both the "lecture" (P005) and "discussion" (S501) components of the course.

The course website is this syllabus:

The course textbook is Single Variable Calculus: Early Transcendentals for UC Berkeley, James Stewart, 2008. We will cover chapters 7, 8, 9, 11, and 17.

If you require special accommodation for the course, because of a documented disability or otherwise, please talk to me immediately, and no later than the end of the first week of classes. (Of course, if something comes up, don't be afraid to talk to me any time.) If you're not sure whether you are elligible for campus-wide disability accommodation, you should consult with the specialists at the Disabled Student Program.

Table of Contents

Contact Info and Office Hours

Instructor: Theo Johnson-Freyd
Office: 1058 Evans
OH Times: Monday, Tuesday, Thursday, Friday 1:15 to 2:00 pm, Wednesday 4:00 to 4:45 pm, and by appointment.
E-mail: theojf at math dot thisuniversity dot edu

For enrollment questions, please talk to Barbara Peavy, at peavy at math dot thisuniversity dot edu.

Return to top.

Course Policies

Welcome to Math 1B. This section documents the policies and expectations for the course. In particular, this course will not be quite like most math classes you have taken. Lecturing will be kept to a minimum, and your participation in the class is required.

Grading Overview

Your grade for the course will be computed as follows:

If you're total percentage score is at least X, you will be guaranteed a grade of at least Y, according to the following chart. It is likely that your final letter grade will be higher than what is on this chart: these are minimum grades, not maximum grades. (I.e. the course will probably be curved, but there will not be a negative curve.) There will be no extra credit.
X 98% 92% 90% 88% 82% 80% 78% 72% 70% 60% 0%
Y A+ A A- B+ B B- C+ C C- / P D F / NP

Attendance and participation

Math should not be learned by listening and reading, but rather by practicing and doing. I hope to lecture very little: most of class will consist of you working in small groups learning the material. I will not take role, but I expect that you will attend class and actively participate. In particular, at the end of class most days I will ask a few students to present solutions to some of the in-class handout exercises. You must present at least one solution during the eight-week course.

The calendar below includes the readings for the course. All readings are from Single Variable Calculus: Early Trancendentals for UC Berkeley, James Stewart, 2008, or are available online. As such, it is a requirement for the course that you have daily access to the textbook. Note: Early Transcendentals for UC Berkeley is almost identical to parts of Stewart's most recent hardbound Calculus: Early Transcendentals (6th edition), and similar to past versions. You may choose to use one of these older books for the readings, but the burden is on you to make sure that your chapters match the assigned readings (so find a friend with the correct book). Moreover, the homework exercise are different from version to version.

I expect that you will have carefully read each day's assignment before class. In this way, we can keep lecturing to a minimum and favor discussion time. Reading mathematics is not like reading a novel: it requires much more activity of the reader. In particular, while reading, you should keep open a pad of paper and a pen, so that you can jot down any notes, ideas, and questions. You should bring your questions to class each day.


Homework will be assigned daily: five odd-numbered exercises and five even-numbered exercises. Solutions to the odd-numbered exercises are in the back of the book; I recommend that you complete them for practice, but they are not required. You are required to submit solutions to all even-numbered exercises, and the grader will choose from each day's assignment one even-numbered exercise to carefully grade and will also assign a score for completion of the other exercises.

I recommend that you complete your homework before the next class session: the course will move very quickly, and it is very easy to fall behind. Homework will be collected in class on Thursdays: you should compile each week's homework and staple it together. All homework from the previous Thursday up through and including the most recent Wednesday is due — for example, the first three days' homework is due Thursday, the 25th. The grader will collect the homeworks from my mailbox some time Thursday afternoon or Friday morning. If you get your homework into the mailbox before the grader collects it, it is not late. After this deadline, late work will not be accepted, no exceptions.


We will have quizzes Mondays and Thursdays on the material from the previous few days. The exact calendar is available below. There will be thirteen quizzes total, but only your top ten scores will count. There will be no make-up quizzes. If you have a medical or family emergency that forces you to miss more than two quizzes, I may drop more than two quizzes from your average. But your two dropped quizzes are for sick days as much as they are for "I forgot to study" days. All quizzes are closed-note but "open-chalkboard": before each quiz, I will give you five minutes to write anything you want on the boards.

Exams and Essays

The bulk of your grade for this course consists of the three exams, on Tuesday, July 7, Friday, July 24, and Friday, August 14. Although you will be given the full class-time to complete each exam, the exams are designed to take roughly 75 minutes to complete. The exams are not cumulative, except in that all mathematics is cumulative: you are not allowed forget previous material, because it will be important for understanding later material. Exams are closed note except that you may bring a one-page (front and back) hand-written cheat sheet. Any missed exam counts as a "0", and makeup exams will not be offered except in extraordinary circumstances. In particular, it is essentially impossible to make up the final exam: I will submit grades that weekend.

You may submit up to three optional essays for the course. Each essay you submit will be worth 15% of your overall grade, and the corresponding exam will be worth 10%. This is not an extra-credit opportunity. Rather, it is a chance for students who do not perform well on tests to nevertheless do well in the class. Writing a good essay takes a lot of time, and I will grade them against a very high standard — it is much easier to do A-level work on an exam than on an essay. As such, I do not recommend that most students submit these essays. Then again, writing a good essay is a wonderful learning opportunity.

Regardless of which exam it replaces, if you submit only one essay, it is due on Monday, August 10. If you plan on submitting two essays, the first is due Monday, August 3, and the second on Monday, August 10. If you submit three essays, please have the first in by Monday, July 27. When you submit an essay, you and I will arrange to meet sometime later that week. At this meeting, you will present a five-to-ten-minute overview of your essay, and I will ask you questions about the material for five to ten minutes.

There are no length requirements on these essays, but I expect that a good essay will be roughly ten pages long, double spaced. Essays should be well-written, well-researched, typed, and copy-editted. Some essays will include detailed calculations: you must include all details, but I recommend that you relegate them to an appendix, and in the text of your essay refer to where in the appendix the calculation is included. Appendices may be hand-written but must be neat and in ink.

You may use any resource or reference at your disposal, but any resource or reference must be correctly cited in your bibliography. I take academic honesty extremely seriously. The following is quoted from "Citing Your Sources". University of California Berkeley Library, 2007. <>:

What is plagiarism?

Plagiarism is defined by the Berkeley Campus Office of Student Life as a form of Academic Dishonesty, violating the Berkeley Campus Code of Student Conduct which defines plagiarism as follows:

Plagiarism is defined as the use of intellectual material produced by another person without acknowledging its source. This includes, but is not limited to:
(a.) Copying from the writings or works of others into one's academic assignment without attribution, or submitting such work as if it were one's own;
(b.) Using the views, opinions, or insights of another without acknowledgment; or
(c.) Paraphrasing the characteristic or original phraseology, metaphor, or other literary device of another without proper attribution.

Plagiarism is a serious violation of academic and student conduct rules and is punishable with a failing grade and possibly more severe action. For more information, consult the following UC Berkeley websites:

Please discuss with me your proposed topic before beginning to write any essay for the class. The "Discovery Projects" on pages 538 and 550 in the textbook would make good starting points for the First Essay, although you will need to go further than just what's outlined in the textbook. (Of course, your submission should be in essay form, not numbered responses to questions in the book.) The First Essay may also consist of a more in-depth exploration than we will provide in class of an application of calculus to any of the topics in Sections 8.3, 8.4, or 8.5. Alternately, you could look into the history of calculus, the "Writing Project" on page 399 being an example.

For the Second Essay, the "Applied Projects" on pages 588, 590, or 601 could begin your paper. Other options include an exploration of how AM radios work, or an in-depth discussion of predator-prey systems. Mathematics exposition could also work — for example, a discussion of a method of solving differential equations not discussed in this course.

For the Third Essay, the computer-savy may begin with the "Laboratory Project" on page 687 and proceed to study other discrete dynamical systems. The "Writing Project" on page 748 would be appropriate, or the "Applied Project" on page 757. You could write about the contributions made by Leonard Euler to the theory of infinite series. An introduction to Fourier Series (similar in many respects to Taylor Series) would also be very nice. Possibly the most interesting topic for the third essay would be a development of "discrete calculus".

Return to top.

Calendar and daily handouts

Overview and jump-to

Homework is due on Thursdays. Quiz days are marked with a "Q".
Monday Tuesday Wednesday Thursday Friday
22: Review 23: 7.1 24: 7.2 25: Q. 7.3 26: 7.4
29: Q. 7.7 30: 7.8
1: 8.1 2: Q. 8.2 3: No School
6: Review 7: 1st Exam 8: 8.3 9: Q. 8.4 10: 8.5
13: Q. 8.5 14: 9.1, 9.2 15: 9.3 16: Q. 9.4 17: 9.5
20: Q. Complex #s 21: 17.1, 17.3 22: 17.2 23: Review. Q 24: 2nd Exam
27: 11.1 28: 11.1, 11.2 29: 11.2 30: Q. 11.3 31: 11.4
3: Q. 11.5 4: 11.5, 11.6 5: 11.6 6: Q. 11.8 7: 11.9
10: Q. 11.10 11: 11.11 12: 17.4 13: Review. Q 14: Final Exam

Detailed calendar

Most links open as PDFs. On a Mac these should open automatically. Windows users may need to download Adobe Reader if it is not already installed.

Day Reading (before class) Homework (after class) Handouts (in class)
Week 1
June 22 Chapters 1 – 6 Chapter 5 Review: 33–38, 45–48
June 23 Section 7.1 7.1: 3, 4, 11, 12, 15, 18, 33, 34, 49, 50
  • Discussion Exercises: Integration by Parts
  • June 24 Section 7.2 7.2: 19–26, 61, 62
  • Discussion Exercises: Trigonometric Integrals
  • June 25 Section 7.3 7.3: 4, 5, 7, 11, 16, 22–26
  • Quiz on 7.1, 7.2 and answers.
  • Discussion Exercises: Trigonometric Substitutions
  • June 26 Section 7.4 7.4: 1, 6–10, 17, 18, 27, 28
  • Discussion Exercises: Partial Fraction Decomposition (in #2d, the 1 should be a 2).
  • Here is a short proof that partial fraction decompositions always exist.
  • Week 2
    June 29 Sections 7.5 and 7.7 7.7: 5–10, 19, 20, 31, 32
  • Quiz on 7.3, 7.4 and answers.
  • Discussion Exercises: Approximate Integration (various errors; see Tuesday's version)
  • June 30 Section 7.8 7.8: 1, 2, 5–10, 29–30
  • Discussion Exercises: Approximate Integration — Corrected
  • Discussion Exercises: Improper Integrals
  • July 1 Section 8.1 8.1: 7–10, 23–26 (Simpson's rule only), 38, 39
  • Discussion Exercises: Improper Integrals
  • July 2 Section 8.2 8.2: 5–8, 13–18
  • Quiz on 7.7 and answers
  • Optional Quiz on 7.8 (errata: should say "3x - x^2") and answers
  • Discussion Exercises: Arc Length and Surface Area
  • July 3 No School: National Holiday
    Week 3
    July 6 Section 7.5 7.5: 20–29
  • Review TRUE/FALSE quiz
  • July 7 First Exam: Sections 7.1 through 8.2 and answers
    July 8 Section 8.3 8.3: 2–5, 16, 19, 21, 22, 25, 26
  • Discussion Exercises: Physical Geometry
  • July 9 Section 8.4 8.4: 4, 5, 7, 9, 10, 12, 17, 18
  • Quiz on 8.1–8.3 (errata: should include "x > 0") and answers.
  • Discussion Exercises: even more applications of integration
  • July 10 Section 8.5 8.5: 1–10 Theo was out of town. Prof. N. Reshetikhin led class.
    Week 4
    July 13 8.5: 11–19 Quiz on 8.4 or 8.5 canceled.
    July 14 Sections 9.1 and 9.2 9.1: 1, 2, 6, 8, 11; 9.2: 3–6 (really one exercise), 7–10
  • Discussion Exercises: Intro to Differential Equations
  • July 15 Section 9.3 9.3: 7–14, 36, 39
  • Discussion Exercises: Separable Differential Equations
  • July 16 Sections 9.4 and 9.6 9.4: 1, 2, 4, 5, 10, 15, 18, 21
  • Quiz on 9.1–9.3 and answers.
  • Discussion Exercises: Word Problems
  • July 17 Section 9.5 9.5: 1–4 (easy), 5–8, 15–17, 34
  • Discussion Exercises: Linear Differential Equations of First Order
  • Week 5
    July 20 Complex Numbers Complex Numbers: 2, 4, 9–11, 19–21, 45, 46
  • Quiz on 9.4, 9.5 and answers.
  • Discussion Exercises: Complex Numbers
  • July 21 Sections 17.1 and 17.3 17.1: 8, 9, 17–20, 25–28
  • Discussion Exercises: ay'' + by' + cy = 0
  • July 22 Section 17.2 17.2: 1–4, 7, 8, 11–14
  • Discussion Exercises: ay'' + by' + cy = g(t)
  • July 23 17.3: 1–6, 13–16
  • Quiz on 17.1–17.3 and answers. An error in the answer key has been corrected.
  • July 24 Second Exam: Sections 8.3 through 17.3 and answers
    Week 6
    July 27 Section 11.1 11.1: 5–10, 15–18
  • Discussion Exercises: Sequences
  • July 28 Section 11.2 11.1: 43–46, 60, 61; 11.2: 5–8
  • Discussion Exercises: Infinite Series
  • July 29 11.2: 13–16, 21–24, 35, 36;
  • Discussion Exercises: The Harmonic Series
  • July 30 Section 11.3 11.3: 3–6, 9–14
  • Quiz on 11.1, 11.2 and answers
  • Discussion Exercises: The Integral Test
  • July 31 Section 11.4 11.4: 27–36
  • Discussion Exercises: The Comparison Tests
  • Week 7
    August 3 Section 11.5 11.5:11–16, 21–24
  • Quiz on 11.3, 11.4 and answers.
  • Discussion Exercises: Alternating Series
  • August 4 Section 11.6 11.5: 27–30; 11.6: 2–7
  • Discussion Exercises: Absolute and Conditional Convergence
  • August 5 11.6: 15, 16, 25–30, 35, 36
  • Discussion Exercises: Ratio and Root Tests
  • August 6 Section 11.8 11.8: 29, 30, 3–6, 25–28
  • Quiz on 11.5, 11.6 and answers.
  • Discussion Exercises: Power Series and Intervals of Convergence
  • August 7 Section 11.9 11.9: 7–10, 15–18, 27, 28
  • Discussion Exercises: Power Series
  • Week 8
    August 10 Section 11.10 11.10: 13–16, 29, 32, 35, 38, 47, 48
  • Quiz on 11.8, 11.9 and answers.
  • Discussion Exercises: Taylor Series
  • August 11 Section 11.11 11.11: 3–5, 13–16, 20, 32, 35
  • Discussion Exercises: Taylor Series
  • August 12 Section 17.4 17.4: 3–9 (what is the interval of convergence of your answer?), 12
  • Discussion Exercises: Power Series Solutions to Differential Equations
  • August 13 Section 11.7 11.7: 1–10
  • Quiz on 11.10, 11.11, 17.4 and answers.
  • August 14 Final Exam: Chapter 11 and answers
    Return to top.

    Last updated Friday, 14-Aug-2009 15:08:39 PDT.