MATH 221 Lectures 2 and 3: Calculus and Analytic Geometry

University of Wisconsin-Madison
Mathematics Department

Math 221 Lectures 2 and 3
Calculus and Analytic Geometry
Lecturer: Arun Ram

Fall 2004

The final exam will be at 7:45am on Dec. 20.
If you are in the 9:55am lecture go to B102 for the final.
If you are in the 11:00am lecture go to B130 Van Vleck for the final.

Some review sessions for the final:

Frank Thorne, Tuesday December 14, 7-9pm in B130.
Julie Simons, Thursday, December 16, 2-5pm in B231 Van Vleck.
David Dueber, Thursday, December 16, 2-6pm, meet in 101 Van Vleck, Topic: HW 5-8.
Rohini Kumar, Friday, December 17, 5pm in B139 Van Vleck.
David Dueber, Friday, December 17, 11am-3pm, meet in 101 Van Vleck, Topic: by request.
Sarah Knoop, Saturday, December 18, 9-12 in B115 Van Vleck.
Derek Moffitt and Jodi Supanich, Saturday, December 18, 12-4 in 180 Science Hall.
Frank Thorne, Sunday, December 19, 1:00-2:30pm in ???.
David Dueber, Sunday, December 19, 2:30-6:30pm, meet in 101 Van Vleck, Topic: HW 9-12.

About the course: Math 221 is the first course in our calculus sequence. The sequence is designed to cover sufficient material in enough depth to provide a calculus background for engineers and scientists. Math 221 covers differentiation and integration and their applications. This course is NOT designed for students that have already taken calculus. If you have taken calculus before then some parts will be review and some parts will be new. Very few high school calculus courses have the same depth as Math 221, and Math 221 will probably be quite different from a high school calculus course. The best preparation for this course is a solid background in graphing functions and in high school algebra.

Text: The textbook for the course is

Calculus, by Varberg, Purcell and Rigdon, Eighth Edition

It is not in my blood to follow the book closely in class. What we will cover in class IS covered in the book and the syllabus indicates how the sections in the book correspond to what we are covering in class. I am most able to explain how I think about the material and how I do calculus. There is no "right way". In class I try to teach the way that I think about things. If the book happens to do some particular part of the material differently from the way I have presented it in class and you would like me to explain to you how the book does it, please do not hesitate to ask me in office hours or to make an appointment. I will do my best to explain it in as many different ways as you to need to see it in order to understand it fully.

Course Structure: There are 3 lectures each week:

Lecture 2: MWF 9:55-10:45 in Van Vleck B102,

Lecture 3: MWF 11:00-11:50 in Van Vleck B102.

Given the number of students in the lecture it isn't usually the best place for discussion and interaction. There are two discussion sections each week with your TA during which you can discuss questions and go over homework problems.

Syllabus

Office Hours: I will hold office hours on Sunday afternoons from 1:00-4:00pm in Van Vleck B239. During office hours we will go over homework problems and try to answer any other questions that you may have. If nobody shows up I will not hang around. You should also feel free to come by my office, Van Vleck 711. You can drop in to talk math or to make an appointment. If I am in my office I am available to talk with you or, if I am busy with something else, we can schedule an appointment for a mutually agreeable time. If the door is closed please knock.
Please also take advantage of the TAs office hours. You should feel free to go to the office hours of any of the TAs for the course. The TAs office hours are as follows:

Discussion sections:

Lecture 2

DIS 321 at 7:45 TR in B333 Van Vleck, TA: Derek Moffitt
DIS 323 at 8:50 TR in 6314 Soc Sci, TA: Derek Moffitt
DIS 325 at 9:55 TR in 4314 Soc Sci, TA: Frank Thorne
DIS 327 at 11:00 TR in B325 Van Vleck, TA: Frank Thorne
DIS 328 at 11:00 TR in B341 Van Vleck, TA: Julie Simons
DIS 329 at 12:05 TR in 4314 Soc Sci, TA: Darren Lo
DIS 331 at 1:20pm TR in 6224 Soc Sci, TA: Julie Simons
DIS 332 at 1:20pm TR in 6310 Soc Sci, TA: Darren Lo
DIS 333 at 2:25pm TR in B329 Van Vleck, TA: Sarah Knoop
DIS 334 at 3:30pm TR in B309 Van Vleck, TA: Sarah Knoop

Lecture 3

DIS 341 at 7:45 TR in B317 Van Vleck, TA: Ben Otto
DIS 342 at 8:50 TR in 6224 Soc Sci, TA: Rohini Kumar
DIS 346 at 11:00 TR in B215 Van Vleck, TA: Jodi Supanich
DIS 348 at 12:05pm TR in B115 Van Vleck, TA: Jodi Supanich
DIS 351 at 1:20pm TR in 6322 Soc Sci, TA: Ben Otto
DIS 352 at 2:25pm TR in B333 Van Vleck, TA: Rohini Kumar
DIS 353 at 2:25pm TR in B337 Van Vleck, TA: David Dueber
DIS 354 at 3:30pm TR in B313 Van Vleck, TA: David Dueber

TA Office Hours:

David Dueber , : M 8:55-9:45, Th 9:55-10:45, F 12:00-1:00 in B101 Van Vleck
Sarah Knoop, : T 1-2, W 11-12, Th 1-2 in 101-2 Van Vleck
Rohini Kumar, : M 2:25-3:25, Th 3:30-4:30 in 101-8 Van Vleck
Darren Lo, : T 2:30-3:30, Th 2:30-3:30 in 718 Van Vleck
Derek Moffitt, : M 9:00-9:50, W 2:30-3:20, Th 12:25-13:15 in 722 Van Vleck
Ben Otto, : T 12:20-1:10, Th 12:20-1:10 in 316 Van Vleck
Julie Simons, : T and Th 9:45-10:45 in 101 Van Vleck, W 12:30-2 at Espresso Royale
Jodi Supanich, : M 7:45--8:45, Th 9:45-10:45, F 2-3 in 722 Van Vleck
Frank Thorne, : M 1:00-2:15, W 2-3, F 9-9:45 in 101-23 Van Vleck

Getting Help: If you are having difficulty first talk to your TA and lecturer. You can make appointments to meet with Prof. Ram by coming up before or after class. There are also many other resources for getting help with calculus. These are described in detail at http://www.math.wisc.edu/~tprogram/mathhelp.html In particular, the Mathematics Tutorial program is well informed about our course and runs a fantastic help service. You must sign up to take advantage of this (it is not a drop in service) and it will be an additional (very helpful) time commitment.

Internet resources: More and more help is available through the internet. The following are some sites that other students have found useful.

Tutorials for the Calculus Phobe

Wolfram's mathworld

An AP Calculus help site

Grading: The term grade will be determined as follows: Homework: 8% Midterm 1: 20% Midterm 2: 20% Midterm 3: 20% Final Exam: 32%. Final grades are computed by totalling the points from the homework, the midterms and the final. Grade letters will be assigned with the following curve as a guideline: 20% A's, 30% B's, 30% C's, 20% D's and F's.

Homework: Homework will be due weekly on Monday, in section. Each week your TA will carefully grade 5 randomly chosen problems from your homework. Each of these problems will be worth 1 point and we will give you 2 more points for completeness and 3 more points for general quality of the rest. If you have specific questions include a note to your TA with your homework so that the TA can help. Most of the answers to the homework problems will be given along with the homework problems and so IF YOU DO NOT SHOW YOUR STEPS, AND JUSTIFY YOUR ANSWERS, AND WRITE CLEARLY AND IN COMPLETE SENTENCES AND PUT EQUAL SIGNS WHERE THEY BELONG you will get no credit. Your homework should be turned in in a form which could be given to a typist for typing, i.e. neat, clear, legible, and in complete sentences. Late homework is not accepted. If you make a deal with your TA . . . . . . . I don't know about it. I will make every effort to cover the material on the homework which is due Monday by the end of the Friday lecture the week before.

THE HOMEWORK ASSIGNMENTS SHOULD BE DOWNLOADED FROM THIS WEB PAGE. See the section "Homework Assignments" below.

Exams: There will be three 50 minute in-class midterms: October 6, November 3 and December 1. There will be a 2 hour final exam at 7:45am Monday December 20. The exams will be a random selection of 10 homework problems from the previous month (including the homework assignment which is due the day after the exam). The final exam will be cumulative.

The Final Exam will be 16 questions: one randomly chosen problem from each HW, plus one extra related rate problem, and one additional "theory/regurgitate" problem (the concepts from Math221). The "theory/regurgitate" problems are

HW1A1-5, HW1B1,2,9, HW1C1-16, HW1D1-5, HW2A1-15, HW2B1-13, HW3A1-26, HW3B1-6, HW3C1-13, HW4G1-17, HW6D1-8, HW7D1-3, HW10E1-7, HW12B1-5, HW12D1-5

All problems on the final exam will be taken verbatim from the homework assignments.

The homework and exams are structured to motivate you to learn. This is a 5 credit course and the homework is designed accordingly (2-3 hours of outside class work per hour of class time). The exams are taken verbatim from the homework. The advantage is that there is never a problem on the exam that you have not seen before on the homework. The disadvantage is that there is lots of homework. However, effort spent on the homework problems usually translates to good scores on the exams and students that do most of the homework usually feel that they have learned a lot at the end of the course. It is quite a bit of work and requires discipline but the pay off is significant. Keep in mind that it is more or less impossible to do the average homework assignment for this course (except the first one) in one night. Planning 3-4 hours per day for 3-4 days per week is one possible way to manage your time on this course. I am aware that you also have other classes to study for that will also require 2-3 hours of outside of class study per hour of class time. If you are spending more than 15 hours per week on the homework for this class, please come see me and let's talk about it. If you do not keep me informed I cannot help.

SAMPLE EXAMS ARE DOWNLOADABLE BELOW.

Calculators: Calculators, textbooks and notes are all extremely good tools for learning calculus. Students are strongly encouraged to use these resources fully in order to learn the material. Calculators are not allowed on exams for the same reasons that books and notes are not allowed on exams. Students are encouraged to use calculators while studying and doing the homework problems in the same way that textbooks help with studying and doing homework problems.

Handouts: Handouts will not be distributed in class, they are available on the web at 2004Fmath221/ . If you are looking at this page on the web and handouts are available you will see them below. Your TA may or may not have paper copies of the handouts. Each week there will be some paper copies of the homework assignments and handouts available outside my office door, Van Vleck 711.

Homework assignments:

Homework assignment 1: DUE September 13, 2004 pdf file

Homework assignment 2: DUE September 20, 2004 pdf file

Homework assignment 3: DUE September 27, 2004 pdf file

Homework assignment 4: DUE October 4, 2004 pdf file

Homework assignment 5: DUE October 11, 2004 pdf file

Homework assignment 6: DUE October 18, 2004 pdf file

Homework assignment 7: DUE October 25, 2004 pdf file

Homework assignment 8: DUE November 1, 2004 pdf file

Homework assignment 9: DUE November 8, 2004 pdf file

Homework assignment 10: DUE November 15, 2004 pdf file

Homework assignment 11: DUE November 22, 2004 pdf file

Homework assignment 12: DUE November 29, 2004 pdf file

Homework assignment 13: DUE December 6, 2003 pdf file

Homework assignment 14: DUE December 13, 2003 pdf file

THAT'S ALL FOLKS!

Some answers for homework problems:

Homework 1 answers: pdf file

Homework 2 answers: pdf file

Homework 3 answers: pdf file

Homework 4 answers: pdf file

Homework 5 answers: pdf file

Homework 6 answers: pdf file

Additional answers for HOMEWORKS 6 and 7.

In jpg format: page 1, page 2, page 3, page 4.

In pdf format: page 1, page 2, page 3, page 4.

Homework 7 answers: pdf file

Homework 8 answers: pdf file

Homework 9 answers: pdf file

Homework 10 answers: pdf file

Homework 11 answers: pdf file

Homework 12 answers: pdf file

Homework 13 answers: pdf file

Homework 14 answers: pdf file

Lecture notes: Since I will not be following the book too closely in class I will make my handwritten lecture notes from when I taught Math 221 in Fall 2000 available for downloading on the web. Though I will certainly change some things when I lecture this year, these notes will give a very good indication of the material and how I will present it. Be very patient and they will download. Over a modem line the downloading may take 5-10 minutes. Sometimes the files look blank for the first 5 minutes or so before they start to come up.

Lecture 1: September 6, 2000.

In jpg format: page 1, page 2, page 3, page 4, page 5, page 6, page 7.

Lecture 2: September 8, 2000.

In jpg format: page 1, page 2, page 3, page 4, page 5, page 6.

Lecture 3: September 11, 2000.

In jpg format: page 1, page 2, page 3, page 4, page 5, page 6, page 7.

Lecture 4: September 13, 2000.

In jpg format: page 1, page 2, page 3, page 4, page 5, page 6, page 7.

Lecture 5: September 15, 2000.

In jpg format: page 1, page 2, page 3, page 4, page 5, page 6, page 7, page 8.

Lecture 6: September 18, 2000.

In jpg format: page 1, page 2, page 3, page 4, page 5.