Prof. Jean-Luc Thiffeault's 221 Home Page: Spring 2008

Lecture Room:	B130 VAN VLECK
Lecture Time:	MWF 8:50-9:40
Lecturer:	Jean-Luc Thiffeault
Office:	503 Van Vleck
Phone:	(608)263-4089
Email:
Office Hours:	11-12 MW, 1-2 W, or by appointment.

Letter Grades

Ranges for the letter grades, based on the three midterms, are very roughly as follows:

average of midterms 1–3	letter grade
80–100	A
69–80	B
52–69	C
42–52	D
0–42	F

Note that there is no guarantee that these boundaries won't move up or down for the final grade. They are provided only as a rough guide, and account for only 45% of the final grade. In particular, I expect both the Discussion Section grade and the final to push up the scores a bit, so it's a bad idea to "aim" too much for a particular score in the final.

Final Exam

Remember that the final exam is Tuesday May 13, 2008 at 7:45-9:45 A.M., Chamberlin 2103
The final will consist of eight questions, each of a style and length similar to the midterms'. Since the final is 120 minutes rather than 50, this means that you will have 15 min per question rather than 10 min in the midterm. Hence, you can work more carefully and slowly for the final.
You are not allowed to have any material with you in the final. A sheet of paper or "cheat sheet" with formulas is not allowed.
Calculators are not allowed.
The final will include material from all the sections of the book that we did in class. The content of the final will not be weighted towards the material after midterm 3, and will for the most part resemble a combination of the first 3 midterms, plus some of the later material. It will probably include a bit more material from the second half of the course over the first, since some of the early stuff was elementary.
No epsilon-delta definition of limits. That's right: I won't ask about proving limits using the rigorous definition, though you should know how to find limits in general.
"Complicated" and seldom-seen formulas will be provided as needed. For example, you are expected to know the formulas for derivatives and integrals of elementary functions, but not the formula for the volume of a cone. However, primary-school and high-school level formulas such as Pythagoras' theorem, or the area of a triangle or a disk, are assumed.
You should know the derivatives of the inverse trigonometric functions and the associated integrals, but you do not need to remember the domain of definition. If this is necessary, it will be provided to you.
Study trick: A great way to do well is to observe that, as before, most of the problems will be from the book. Hence, the best way to prepare, once you've done the basic groundwork of studying the book, lecture notes, and homework, is to team up with somebody in the class. Write up a "trial exam" for each other by selecting questions from the book, maybe changing a number here and there. Enforce on yourself a strict 1 hour or 2 hour time limit (depending on the length of your trial exam), without any notes or book, and practice answering the questions in the order you are most comfortable with, not the order they are presented in. Afterwards you can mark each other's exams. Repeat as necessary. This is best done in an environment that mimics an actual exam (with minor noise and distractions): a library is best, failing that a quiet coffee shop, to get used to "blocking out" distractions.
Don't forget to take advantage of sidewalk math: TAs will answer questions on the plaza of Van Vleck (by the 1st floor entrances) on Monday of finals week from 12–4 (and Tuesday, but that's not so relevant unless you have another math exam after this one). (Free lemonade!)
I will ask for at least one of the definitions and/or proofs below on the final. This might seem like a lot, but note that most of these are needed anyways to be able to solve problems. Hence, you can think of these as a partial "study guide".

name	proof or def?	page in Thomas	comment
Function	def	19
Periodic Function	def	52
Vertical asymptote	def	118
Continuous at a point	def	125
Slope, tangent line	def	137
Derivative function	def	147
Differentiable function, one-sided derivative	def	152
Differentiation rule 5: Product rule	proof	163
Differentiation rule 7: Power rule for negative integers	proof	166	As in Thomas, you can assume the quotient rule
Derivative of other trigonometric function	proof	187	You can assume the derivative of sine and cosine
Chain rule	def	192	I won't ask you to prove the chain rule
Increasing/decreasing function	def	263
Concave up/down	def	268
Point of inflection	def	268
Second derivative test for local extrema	def	270
L'Hopital's rule (weak/strong form)	def	292/293
Antiderivative	def	307
Substitution rule	proof	370
Substitution in definite integrals	proof	376
Volume of an arbitrary solid	def	398
Length of a curve	def	420
One-to-one function	def	466
Inverse function	def	468
Derivative rule for inverses	def/proof	471
Natural logarithm function	def	476
Properties of logarithm	def/proof	479
Natural exponential function	def	486
General exponential function	def	487
Base-a logarithm function	def	497
Law of exponential change	def	503
Identity (4) for inverse trig functions	proof	521	Draw the triangle as in Fig. 7.21 and explain.
Derivative of inverse trig functions	proof	524	I want the "alternate derivation", as done in class.

Homework

Week 1

Exercises 1.1 (page 7) problems 4, 14, 15, 18, 19, 20, 26, 28, 34, 38, 39, 42, 44, 45, 46.

Week 2

Exercises 1.2 (page 16) problems 1, 4, 9, 10, 17, 21, 26, 32, 44, 48, 50.

Exercises 1.3 (page 26) problems 1, 2, 3, 6, 7, 8, 10, 22, 23, 26, 28, 37.

Exercises 1.4 (page 37) problems 5, 19, 20, 22, 24, 26, 28, 29, 30.

Exercises 1.5 (page 45) problems 5, 6, 8, 9, 49, 51, 54, 55, 58, 75, 79.

Week 3

Exercises 1.6 (page 56) problems 7, 8, 10, 31, 32, 33, 34, 43 44, 46, 51.

Exercises 2.1 (page 81) problems 2, 3, 4, 5, 6, 9, 17, 20.

Exercises 2.2 (page 88) problems 1–34, 38, 42, 51, 52.

Week 4

Exercises 2.3 (page 98) problems 1, 2, 3, 4, 37, 38, 39, 40, 41, 42, 43, 44, 45. (Do some exercises in between 4 and 37 if you don't feel comfortable with problems 37–45)

Exercises 2.4 (page 112) problems 11–16, 21–32.

Exercises 2.4 (page 113) problems 37–44, 47–53, 57, 58.

Exercises 2.5 (page 122) problems 1–5, 17–21, 32–35.

Week 5

Exercises 2.6 (page 132) problems 1–3, 13–21, 29–32, 35–37.

Exercises 2.7 (page 140) problems 5, 6, 7, 11–15, 27, 28, 29.

Exercises 3.1 (page 155) problems 1–6, 7–12, 13, 14, 17, 19, 20, 23, 39–44, 45, 46.

Week 6

Exercises 3.2 (page 169) problems 1–12, 13, 14, 17–23, 29, 31–35, 39.

Week 7

Exercises 3.3 (page 179) problems 7, 8, 9, 10, 23, 25.

Exercises 3.4 (page 188) problems 1–9, 13, 14, 15, 21, 22, 23, 27, 28, 31, 32, 50.

Exercises 3.5 (page 201) problems 1–5, 9–15, 21, 23–7, 31–36, 39, 41, 43, 50, 51, 68–72, 88–90, 96, 97.

Week 8

Exercises 3.6 (page 211) problems 1–7, 15–18, 19–27, 33, 35, 37, 38, 39, 45, 63–65.

Exercises 3.7 (page 218) problems 1–5, 8, 9, 10, 13.

Exercises 3.8 (page 231) problems 1–3, 5–9, 11, 12, 13, 15, 17.

Exercises 4.1 (page 252) problems 1–10, 15–19, 24–29, 35–43, 45–51, 53, 55, 56, 59, 61, 62.

Week 9

Spring Break.

Week 10

Exercises 4.3 (page 266) problems 1–6, 9–13, 21–27.

Exercises 4.4 (page 275) problems 1, 2, 3, 7, 9, 10, 13, 14, 17, 10, 20, 21, 23, 24, 25–28, 31, 32, 33, 35, 36, 37, 39, 40, 41, 42, 43, 50, 51, 53.

Week 11

Exercises 4.5 (page 286) problems 1, 3, 5, 7, 10, 12, 13, 14, 31, 33, 37.

Exercises 4.6 (page 298) problems 1, 3, 7–13, 21–25, 27, 28, 29.

Exercises 4.7 (page 305): Not covered.

Exercises 4.8 (page 314) problems 1–7, 10–15, 17–31, 37–43, 49–53, 55–59, 61, 63.

Week 12

Exercises 5.1 (page 333): No problems assigned, but you should still read the chapter.

Exercises 5.2 (page 343): 1–8, 11–15.

Exercises 5.3 (page 352): 9, 11, 12, 13, 14, 15–22, 23, 24.

Exercises 5.4 (page 365): 1–26, 27–36, 37–46. (I know that's a lot of problems, but practice is really important when it comes to integrals.)

Exercises 5.5 (page 374): 1–50.

Exercises 5.6 (page 383): 1–5, 13–23, 25, 27, 28, 30, 33, 35, 39, 41, 43, 45, 51, 53. (Do more if you have time!)

Week 13

Exercises 7.1 (page 473): 9, 10, 13, 14, 19, 20, 21, 23, 27, 28, 30, 31, 32.

Exercises 7.2 (page 484): 1, 3, 5–11, 21–29, 33, 35, 37–45, 51, 52, 53, 55–61, 65, 66, 67.

Exercises 7.3 (page 493): 1, 3, 5, 6, 7, 10, 11, 13, 17–23, 33–37, 41–51, 59, 61, 63, 64, 66.

Exercises 7.4 (page 500): 1, 3, 5, 7, 11–16, 23–31, 35–38, 39–46, 47–53, 57, 59, 61–67, 71, 72, 73.

Week 14

Exercises 7.5 (page 508): 1, 3, 5, 11, 13, 17, 19.

Exercises 7.7 (page 530): 29, 31, 33, 35, 36, 39, 41, 43, 44, 45, 47, 49–57, 67, 69, 71–83, 91, 93, 95–101, 105, 107, 111, 113, 115, 117, 119, 121, 123.

Week 15

Exercises 6.1 (page 405): 1, 3, 4, 5, 7, 8, 9, 13, 15, 21, 27.

Exercises 6.3 (page 423): 1, 3, 5, 6, 7, 9, 13, 14, 15, 30.

Week 16

No new homework assigned.

Syllabus

See the official syllabus and list of topics.

Textbook

The textbook for the class is Thomas' Calculus, 11th edition. We will cover chapter 1 to 7, inclusive.

If you want additional viewpoints, have a look at the excellent notes by Prof. J. W. Robbin and the equally-excellent notes by Prof. S. B. Angenent.

Prerequisites

The official prerequisite is one of

satisfactory placement scores, OR
Math 112 and Math 113, OR
Math 114.

You should be comfortable with basic algebra and trigonometry. If you want to do some revision beforehand, work through Chapter 1 of Thomas and of the lecture notes mentioned above.

If you want to check your basic algebra skills, you can take Prof. Robbin's pre-test, with answers.

Teaching Assistants

Name	Office	Phone	E-Mail
Anne Candioto	101-11 Van Vleck	3-1350	candioto	@	math.wisc.edu
Seth Meyer	520 Van Vleck	2-3601	smeyer	@	math.wisc.edu
Joanna Nelson	822 Van Vleck	2-0537	nelson	@	math.wisc.edu
Chalermpong Worawannotai	101-20 Van Vleck	3-9720	worawann	@	math.wisc.edu

Discussion Sections

Number	Time	Days	Room	TA
301	7:45	TR	B305 VAN VLECK	Candioto
302	8:50	TR	B341 VAN VLECK	Candioto
303	8:50	TR	B325 VAN VLECK	Meyer
305	9:55	TR	B321 VAN VLECK	Nelson
306	11:00	TR	B135 VAN VLECK	Worawannotai
307	12:05	TR	B215 VAN VLECK	Worawannotai
309	13:20	TR	123 INGRAHAM	Nelson
310	14:25	TR	B123 VAN VLECK	Meyer

Homework and Quizzes

Each week I will assign homework from the textbook and post it here. Each following Tuesday (starting in the second week of class), your TA will give a 20 min quiz during your discussion section, consisting of a few questions from the previous homework. This will make up part of your grade, as described below. The TA for your section might decide to collect some homework or have some additional methods of assessment, at their discretion.

Notes, textbooks, or calculators will not be allowed in the quizzes. Your lowest quiz score will be discarded, and there will be no make-up quizzes.

Even if it is not collected, you should do all of the homework if you want a chance to do well in the class.

Course Policy and Grading

There will be three midterm exams. Each of the three midterm exams is worth 15 percent, for a total of 45 percent of the final grade. The final exam will count for 30 percent. The remaining 25 percent will be allocated by your TA who will base it on homework, quizzes, participation, attendance, and effort. (This last portion will be adjusted to account for variations among the TAs.)

Calculators, notes, and textbooks are not allowed in exams or quizzes.

The intelligent use of calculators outside of exam rooms is however encouraged. For example, here is calculator warmup that Prof. Robbin used in the past to help you appreciate that a derivative is a ratio of infinitely small quantities. Graphing calulators can be used to check your reasoning. Here is a link to an online graphing calculator which Prof. Robbin wrote a few years ago specifically for use in this course and which I may occasionally use in the lectures.

Exam Dates

The midterm exams will be given during the regular 50 minute lecture period.

Midterm Exam 1	~~Monday February 25, 2008 at 8:50-9:40 A.M.~~
Midterm Exam 2	~~Wednesday March 26, 2008 at 8:50-9:40 A.M.~~
Midterm Exam 3	~~Monday April 21, 2008 at 8:50-9:40 A.M.~~
Final Exam	Tuesday May 13, 2008 at 7:45-9:45 A.M., Chamberlin 2103

Midterm 1 Results

Midterm 1 solutions (courtesy of Seth)

Updated after drop deadline.

# of scores	135
mean score	64.9
standard deviation	15.4
median score	68

Midterm 2 Results

Updated after drop deadline.

# of nonzero scores	133
mean score	58.7
standard deviation	22.3
median score	61

Midterm 3 Results

Midterm 3 solutions (courtesy of Seth)

# of nonzero scores	128
mean score	57.7
standard deviation	18.9
median score	61

How to do Well in this Course

There are many ways to get help with math. In addition, following these guidelines is a recipe for (but not a guarantee of) success:

During lectures

Taking notes (students who are talking, reading newspapers or magazines, or playing with cellphones, laptops, ipods, etc... will be asked to leave the classroom);
Asking questions if something the instructor says or writes is unclear.

Outside lectures

Reading the textbook;
Working out homework problems as well as additional problems;
Practicing doing problems under timed, exam-like conditions;
Doing problems without looking at the answers or solutions as you go;
Coming to office hours if necessary (TA first, then instructor).
The Math Library is located in B224 Van Vleck. This is a nice quiet place to study and has additional sources you may wish to consult if you are not satisfied with the textbook.