- Contact Info
- Office Hours
- Tutoring at SLC
- Textbook
- Brief Grading Policy
- Detailed Grading Police
- Homework Calendar
- Handouts, Quizzes, and Exams
- Related Readings

Theo Johnson-Freyd

Office: 844 Evans

E-mail: theojf@math.berkeley.edu

The class will meet 8-10 am every morning Monday through Friday, with a mix of lecture and discussion. **You must enroll in both the lecture and the corresponding discussion section.**

Monday/Wednesday 10-11

Tuesday/Thursday 11-12

in 844 Evans unless otherwise announced that day in class

The Student Learning Center offers free tutoring. They write:

Math/Stat Drop-In Tutoring

Math/Stat Drop-In provides individual assistance to most lower division math courses and all summer stat courses: Math 1AB, 16AB, 32, 53, 54; Stat 2, 20, 21, 134. Our services are free to all registered Summer Session students. Drop-In is scheduled to start on Wed 6/25. Tutors are available during these hours: Math M-Th 11-4, Stat M-Th 12-4. To get help, students type in their Student ID at the computer located in the west corner of the Cesar-Chavez Atrium, and tutors will provide assistance on a first-come, first-served basis. The Cesar Chavez Student Center is located on lower Sproul. For more information, email mleong at thisuniversity dot edu or mjwong at thisuniversity dot edu.

J. Stewart, *Single Variable Essential Calculus: Early Transcendentals* Student Edition, University of California, Berkeley (2008).

- 10%: Homework and in-class participation
- 10%: Quizzes, 20 minutes, in class, (most) Tuesdays and Thursdays. There will be twelve quizzes total, and I will count only the top ten.
- 40%: Midterm, 2 hours, in class, Tuesday, July 22
- 40%: Final Exam, 2 hours, in class, Friday, August 15

The expected cut-offs for letter grades based on overall percentages are the standard ones: A+ = 98-up, A = 92-97, A- = 90-91, B+ = 88-89, B = 82-87, B- = 80-81, C+ = 78-79, C = 72-77, C- = 70-71, D+ = 68-69, D = 60-67, F = down-59. Depending on how the course goes, these cut-offs might lower — perhaps an 88% will be an A- — but they will not rise (i.e. there will not be a "negative curve").

Learning mathematics requires doing mathematics. Homework will be assigned daily, corresponding to that day's lecture (the calendar is below). Each day I will select eight (often challenging) homework problems. The five odd-numbered problems are suggested for practice, and you should consult the back of the book. The three even-numbered problems are generally harder, and the grader will grade some, but not all, of them. You are expected to complete all of the assigned homework, but whether or not you turn in the first 5/8 each day will not affect your grade. You should expect to budget an hour or three **per day** on homework.

Homework will be collected each week on Friday: please turn in the homeworks assigned on the previous Thursday through Wednesday. **Late work will not be accepted** — turning in work late is rude to the grader. ("Late" is defined as "before the grader has picked up the assignment"; he will collect the homeworks from my mailbox on the 9th floor of Evans sometime Friday, roughly at noon.) The course will move fast enough that it is extremely important that you keep up with the homework. If you do not understand some of the homework, my office hours are your best recourse: I promise to explain any and all homework questions brought to office hours.

Also important is attending (including being attentive in) lecture/discussion. I will not take roll, but I will pay attention to which students chronically sleep through class or chronically participate, and extra credit will be awarded to those students who participate in class. The class structure will be a mix of lecture and in-class discussion, with daily handouts: each handout will include in-class group-work exercises on the day's topic.

**A note on group work:** I highly encourage collaborative work in mathematics, and in-class problem-solving will always be in groups. As such, you are welcome — nay, encouraged — to find study-buddies in the class and do homework together. However, keep in mind that you will take quizzes and tests alone, and when you use this material in the future, you will not have these study friends. Thus, make sure that you understand how to solve each problem: do not just copy homework answers.

Quizzes will be every Tuesday and Thursday, usually on the material from the previous day or two. These are meant primarily as a diagnostic, both for me and for you. Most quizzes will have two or three questions, and most quiz problems will be similar to homework problems, but there might be some variation.

There will be twelve quizzes, and I will count the top ten, so don't worry if you do badly or miss one or two. If you miss quizzes for medical emergency or family emergency reasons, I may drop more than two quizzes on a case-by-case basis, but you should be sure to let me know immediately if something comes up. For non-emergency medical, etc., absences, you may be able to take quizzes **early** during my office hours the day before, but you'll need to let me know a day or two ahead. **Make up quizzes will not be available.** Quiz answers will be available online shortly after each quiz.

One two-hour in-class midterm, on Tuesday, July 22, will contribute 40% of your grade. It will cover all the material from class on techniques of integration and of solving differential equations. **Do not miss the midterm,** as make-up midterms are generally not available, except in extremely special circumstances.

One two-hour in-class final exam, on Friday, August 15, will contribute 40% of your grade. It will include some material from the first half of class, but will be geared towards the material of the second half (sequences and series). **Do not miss the final.** Make-up exams are not available without involving administrators from the math department and from the larger university.

Please at least glance at (better is to actually read) the chapter from Stewart **before** that day's class. Homework problems are from the marked chapters. Occasional chapters are not included in the Berkeley edition of the textbook, but are from StewartCalculus.com; these open as pdfs.

- Week 1:
- Monday, June 23:
**6.1**3, 7, 11, 17, 21, 26, 30, 32 - Tuesday, June 24:
**6.2**1, 3, 5, 9, 15, 20, 32, 36 - Wednesday, June 25:
**6.2**41, 43, 45, 49, 59, 60, 62, 66 - Thursday, June 26: Quiz on 6.1-2
**6.3**5, 7, 9, 15, 25, 36, 40, 42 - Friday, June 27: Strategies 5, 7, 19, 31, 41, 52, 58, 72

- Monday, June 23:
- Week 2:
- Monday, June 30:
**6.6**5, 17, 22, 23, 33, 43, 44, 46, - Tuesday, July 1: Quiz on 6.1-3
**6.6**47, 48, 49,**7.4**3, 5, 7, 8, 14 - Wednesday, July 2:
**7.4**25, 31, Area of a surface of revolution 5, 6, 9, 12, 14, 15, - Thursday, July 3: Quiz on 6.6 Complex numbers 3, 7, 19, 23, 25, 34, 38, 46
- Friday, July 4: No School (National Holiday)

- Monday, June 30:
- Week 3: Theo will be out of town this week. Rob Bayer will lead class.
- Monday, July 7:
**7.6**21-31 (exercises 21-24 are really one exercise) - Tuesday, July 8: Quiz on 7.4
**7.6**1, 7, 9, 12, 13, 14, 15, 16 - Wednesday, July 9:
**7.6**35, 36, 38, 39, 41, 43, 46, 47 - Thursday, July 10: Quiz on 7.6 (separable equations) Linear Differential Equations 1, 3, 11, 13, 16, 20, 23, 24,
- Friday, July 11:
**17.1**1, 3, 5, 7, 9, 12, 14, 16

- Monday, July 7:
- Week 4:
- Monday, July 14:
**17.1**17, 19, 20, 21, 25, 26, 28, 29 - Tuesday, July 15: Quiz on 17.1
**17.2**1, 3, 5-10 - Wednesday, July 16:
**17.2**19, 21, 23-28 - Thursday, July 17: Quiz on 17.2
**17.3**1, 2, 3, 5, 9, 10, 11 - Friday, July 18:
**17.3**12, 13, 15, 17, 18,**Chapter 17 Review**17

- Monday, July 14:
- Week 5:
- Monday, July 21: Review
- Tuesday, July 22: Midterm
- Wednesday, July 23:
**8.1**3, 5, 7, 9, 16, 20, 24, 33, - Thursday, July 24:
**8.2**1, 3, 7, 11, 13, 18, 20, 22 - Friday, July 25:
**8.3**2, 3, 5, 6, 7, 9, 10, 11

- Week 6:
- Monday, July 28:
**8.3**13, 14, 15, 17, 19, 20, 23, 24 - Tuesday, July 29: Quiz on 8.1-3
**8.4**1, 3, 4, 5, 7, 9, 10, 18 (and also for which values of*p*is the series in 18 absolutely convergent?) - Wednesday, July 30:
**8.4**19, 21, 25, 28, 35, 36, 38, 39 - Thursday, July 31: Quiz on 8.4
**8.5**3, 5, 9, 13, 14, 17, 18, 20 - Friday, August 1:
**8.5**25, 26, 28,**8.6**3, 5, 9, 11, 12

- Monday, July 28:
- Week 7:
- Monday, August 4:
**8.6**13, 14, 15, 17, 22, 25, 35, 32 (thus, what are the possible functions that f(x) could be? What is f(0)? What is f'(0)? Hence, what is f(x)?) - Tuesday, August 5: Quiz on 8.5
**17.4**1, 3, 5, 7, 8, 9, 10, 11. What is the radius and interval of convergence of each of your answers? - Wednesday, August 6:
**8.7**2, 3, 5, 7, 9, 11, 14, 18 - Thursday, August 7: Quiz on 8.6 and 17.4
**8.7**23, 25, 27, 29, 31, 32, 34, 36 - Friday, August 8:
**8.7**43, 45, 55, 57, 62, 63, 64, 66

- Monday, August 4:
- Week 8:
- Monday, August 11:
**8.7**19, 47, 49,**8.8**19, 20, 21, 22 - Tuesday, August 12: Quiz on 8.7
**6.5**1, 2, 7, 15, 18, 19, 20, 25 - Wednesday, August 13: Review
- Thursday, August 14: Review
- Friday, August 15: Final Exam

- Monday, August 11:

Daily handouts, quizzes (with answers), and exams (with answers), will be posted shortly after each class, all as PDFs. If you are on a Mac, these should open automatically; Windows users may need to download Adobe Reader if it is not already installed.

- Week 1:
- Monday, June 23: Handout 1: Review and Integration By Parts
- Tuesday, June 24: Handout 2: Trigonometry
- Wednesday, June 25: Handout 3: Trigonometric Substitutions
- Thursday, June 26: Quiz on 6.1-2 and answers (
**Errata:**the second problem on the quiz should be an indefinite integral; as a definite integral the answer is Infinity). Handout 4: Partial Fraction Decomposition - Friday, June 27: Handout 5: Integration (should be titled "More Partial Fractions")

- Week 2:
- Monday, June 30: Handout 6: Improper Integrals
- Tuesday, July 1: Quiz on 6.1-3 and answers. Handout 7: Improper Integrals, Arc Length
- Wednesday, July 2: Handout 8: Arc Length and Surface Area
- Thursday, July 3: Quiz on 6.6 and answers. Handout 9: Complex Numbers
- Friday, July 4: No School (National Holiday)

- Week 3: Theo will be out of town this week. Rob Bayer will lead
class.
- Monday, July 7: Handout: Intro to Differential Equations
- Tuesday, July 8: Quiz on 7.4. Handout: Seperable Equations
- Wednesday, July 9: Handout: Modeling with Differential Equations
- Thursday, July 10: Quiz on 7.6. Handout: Linear Differential Equations
- Friday, July 11: Handout: Finishing Up First Order ODEs; Second Order Equations

- Week 4:
- Monday, July 14: Handout: ay'' + by' + cy = 0
- Tuesday, July 15: Quiz on 17.1 and answers. Handout: ay'' + by' + cy = g(t)
- Wednesday, July 16: Handout: ay'' + by' + cy = g(t)
- Thursday, July 17: Quiz on 17.2 and answers
- Friday, July 18: Handout: Springs and circuits

- Week 5:
- Monday, July 21: Handout: Midterm Review
- Tuesday, July 22: Midterm and answers
- Wednesday, July 23: Handout: Sequences
- Thursday, July 24: Handout: Infinite Series
- Friday, July 25: Handout: Integral and Comparison Tests

- Week 6:
- Monday, July 28: No handout. Lecture on Stirling's Formula and
Σ 1/
*n*^2. - Tuesday, July 29: Quiz on 8.1-3 and answers. Handout: Alternating Series and Absolute Convergence
- Wednesday, July 30: Handout: Alternating Series, Absolute Convergence, and the Ratio Test
- Thursday, July 31: Quiz on 8.4 and answers. Handout: Power Series and Radius of Invergence
- Friday, August 1: No new handout; we continued with the exercises from the previous day.

- Monday, July 28: No handout. Lecture on Stirling's Formula and
Σ 1/
- Week 7:
- Monday, August 4: Handout: Power Series
- Tuesday, August 5: Quiz on 8.5 and answers. Handout: Power Series Solutions to Differential Equations
- Wednesday, August 6: Handout: Taylor Series
- Thursday, August 7: Quiz on 8.6 and 17.4 and answers. Handout: More Taylor Series
- Friday, August 8: No new handout; we continued with the exercises from the previous day.

- Week 8:
- Monday, August 11: Handout: Estimating Series. Optional ``Term Paper'' due
- Tuesday, August 12: Quiz on 8.7 and answers. Handout: Estimating Integrals by Sums
- Wednesday, August 13: Handout: Estimating Integrals by Sums
- Thursday, August 14: Handout: Final Exam Review
- Friday, August 15: Final Exam and answers

- Common Errors in Undergraduate Mathematics
- If you would like to read more about approximate integration, you may want to check out the blog entry I wrote about it.
- I've also written a brief discussion about partial fraction decomposition.
- Stirling's Formula says that
*n! ∼ (n/e)*. Here is a proof. The formula can be improved (although you don't need it to be any better for most applications):^{n}√(2πn)*n! ≈ ((n+1)/e)*. The "^{n+1}√(2π/(n+1)) (1 + 1/(12n) + O(1/n^{2}))*O(1/n*" means "something that's smaller than^{2})*C/n^2*for some constant*C*. Bender and Orszag give a complete "asymptotic expansion": a power series for*n!*in*x = 1/n*. The thing is that this power series doesn't converge for any*n*: the radius of convergence is 0. This is basically because the factorials of negative integers are infinite. - On my blog, I've posted a discussion of "the method of undetermined coefficients" in linear differential equations. It uses a fair amount of linear algebra, but nothing more.

(*Note:* My blog entries and the like
are often more advanced than is expected for the class, or otherwise
extend the material in some way. I link to them here just in case you're
curious about "why" questions, rather than the standard calculus-class
"how" questions.)

Last updated 24 June 2008.

Homepage.