Fall 2003

*Course
Text*:
Calculus,
Single Variable, third edition, by D. Hughes-Hallett et al.

*Instructor:
*Matthias Aschenbrenner

*E-mail address: *

*Homepage:* http://www.math.uic.edu/~maschenb

*Office:* 616
SEO

*Office Phone:* (312) 413-2163

*Office Hours:* M 2-3pm, W 2-3pm,
F 11-12am

*Central
webpage for this class: *Math
180

*Teaching
assistant: *Xin
Fang, *e-mail address: *xfang1@uic.edu

*Discussion sections: *TuTh
2:00-2:50pm
or 3:00-3:50pm, 312
Taft Hall

*Office hours: *On TuTh 9am-3:50pm
there will be someone in the Math Lab
(300
Taft Hall) who can answer Math 180 questions.

*Calculator:
*Use of a graphing calculator will be an integral part of the
course.
Instructors will be using the TI
83. Any graphing calculator you now own should be adequate.

*Prerequisites*:
An appropriate grade on the Department placement test or a grade of C
or
better in Math
121 or an approved equivalent course. Students who do not
satisfy
these prerequisites will be dropped.

*Emerging
Scholars Program (ESP):* ESP participants spend an additional four
hours
per week (2-hour sessions) working in groups on challenging mathematics
problems, and receive 1 Satisfactory/Unsatisfactory credit. Admissions
to ESP depends on an adequate score on the university placement
examination
or a grade of C or better in the prerequisite for the math taken with
the
Emerging Scholars workshop. Further questions about ESP should be
directed
to Jeanne
Ward (e-mail: jmward@math.uic.edu).

*ESP
section instructor: *Rishi
Nath (e-mail: nath@math.uic.edu)

*ESP
sections:*TuTh 1:00-1:50pm,
312
Taft Hall.

*Downloading
files from this website requires software to display PDF files, such as
Acrobat
Reader
or Ghostview.*

We will cover the following material:

`
Week Sections Brief
description``
`

`
1 1.1 -- 1.2
Linear,
exponential, elementary functions`

` 2 1.3 --
1.6
Trig functions, composition`

` 3 1.7 --
2.1
Continuity, introduce derivative`

` 4 2.2 --
2.4
Limits, derivative at a point and derivative function`

` 5
2.5
Interpretations of the derivative, Review + Exam I``
`

`
6 2.6 -- 2.7
Second
derivative, continuity`

` 7 3.1 --
3.4
Derivative: powers and basic rules`

` 8 3.5 --
3.7
Composition, implicit functions`

` 9 3.8 --
3.10
Parametric equations, linear approximation`

` 10 4.1 --
4.3
Applications, families, max-min`

` 11 4.4 --
4.6
Applications, optimization`

` 12
4.7
Properties of functions; Review + Exam II``
`

`
13 5.1 -- 5.3 The
definite
integral`

` 14 5.3 --
5.4
Interpretations of integral, the Fundamental Theorem`

` 15
5.4
Properties of integrals; general review for final exam`

Click here to download the course information handout.

**Homework problems will be collected
at the beginning of each lecture.**

**No late homework will be accepted.**

Put the following information in the upper right hand corner of the first page:

*Your Name*

Math 180, Homework
for *month/day.*

On each additional page, put your name in the upper right-hand corner. Work single-sided, that is, write on only one side of each sheet of paper. STAPLE any homework that is more than one page long. Remove all perforation before submitting.

The
homework will be returned in the discussion sections. Some of these
problems
will be on material to be discussed that day and some will be on
material
previously discussed. Below you find a list of assignments with date,
text
sections to be read for the lecture on that date, and problems to be
turned
in during that day's lecture.

Date Section(s) Problems/Comments

08/25 1.1 also, read preface page xi.

08/27 1.2 1.1 #4, 23, 24, 27; 1.2 #1 - 3, 5, 7, 21;

08/29 1.2 1.1 #19, 20, 22, 28; 1.2 #22, 23, 29, 30;

09/01 Labor Day holiday. (no classes)

09/03 1.3, 1.4 1.3 # 3, 5, 16-19; 1.4 #3, 5, 19;

09/05 1.5 1.4 #29, 33, 36, 39; 1.5 #1, 6;

09/08 1.6 1.5 #14, 18, 20, 22, 24; 1.6 #2, 4, 5;

09/10 1.7 1.6 #6, 7, 10, 22, 23, 25, 32; 1.7 #3, 4, 5;

09/12 2.1 1.7 #1, 9, 11, 16; 2.1 #3, 4, 11, 15;

09/15 2.2 2.1 #5, 7, 9, 13, 14, 16; 2.2 #7, 8, 9;

09/17 2.3 2.2 #11, 15, 23, 30; 2.3 #2, 8, 9, 23;

09/19 2.4 2.3 #12, 17, 22; 2.4 #1, 2, 11;

09/22 2.5 2.4 #15, 19, 28, 35; 2.5 #2, 3;

09/24 2.5 #7, 17;

1. Rev #1, 3, 6, 7, 18, 19, 26, 34, 42; review

2. Rev #4, 5, 7, 9, 22, 24, 27, 36; review

09/26 Hour Exam 1 (covers 1.1--2.5 on syllabus)

09/29 2.6 2.6 #8, 9, 10, 11;

10/01 2.7 2.6 #13, 15, 18, 19; 2.7#1, 2, 6, 9;

10/03 2.7 2.7 #4, 7, 11, 13, 16;

10/06 3.1 3.1 #3, 9, 11, 16, 21, 35;

10/08 3.2, 3.3 3.1 #10, 22, 27, 40, 41, 49, 56, 59; 3.2 #1, 3, 4; 3.3 #1, 3, 4;

10/10 3.4 3.2 #10, 16, 22, 28, 37, 42;

3.3 #6, 9, 10, 12, 16, 31, 41, 44; 3.4 #1, 3, 4;

10/13 3.5 3.4 #5, 6, 12, 18, 24, 26, 38, 47, 55; 3.5 #2, 3, 5;

10/15 3.6 3.5 #7, 9, 18, 23, 26, 36, 42, 46, 52; 3.6 #1, 2, 5;

10/17 3.7 3.6 #6, 9, 14, 18, 19, 35, 44, 46, 49, 50; 3.7 #1, 2;

10/20 3.8 3.7 #3, 6, 9, 13, 20, 21, 26; 3.8 #1, 3, 6;

10/22 3.9 3.8 #3, 8, 11, 14, 18, 26, 28; 3.9 #3, 5;

10/24 3.10 3.9 #2, 7, 9, 12, 15; 3.10 # 1, 2, 5;

10/27 4.1 3.10 #7, 8, 9, 11, 13, 15, 16; 4.1 #2, 3, 10;

10/29 4.2 4.1 #11, 13, 17, 27, 33, 29, 35, 40, 41; 4.2 #2, 13;

10/31 4.3 4.2 #12, 14, 15, 18, 21, 32; 4.3 #1, 2, 4;

11/03 4.4 4.3 #7, 9, 15, 18, 22, 25; 4.4 #1, 2, 6;

11/05 4.5 4.4 #7, 8, 9, 10, 13, 15; 4.5 #1, 3;

11/07 4.6 4.5 #6, 8, 9, 14, 16, 18; 4.6 #1, 2, 6;

11/10 4.7 4.6 #8--12, 18, 21; 4.7 #2, 3, 4, 5, 6, 9;

11/12 4.7 #13, 14, 16, 26, 27, 29, 30;

3.R #1, 3, 5, 53, 72, 73, 74, 75, 81;

4.R #1, 3-6, 7, 12, 17, 24, 25, 28, 38; review

11/14 Hour Exam 2* (covers 2.6--4.7 on syllabus)

11/17 5.1 5.1 #2, 5, 10, 11;

11/19 5.2 5.1 #3, 6, 7, 8; 5.2 #2, 3;

11/21 5.3 5.2 #6, 9,12, 14, 20, 24, 32; 5.3 #1, 3, 7;

11/24 5.4 5.3 #12, 16, 20, 23, 26, 27; 5.4 #1, 2;

11/26 5.4 5.4 #4, 5, 6, 7, 11, 13, 14, 21;

11/28 Thanksgiving Holiday; (no classes)

12/01 5.R #1, 8, 10, 32, 33; review

12/03 5.R #12, 16, 18, 34, 37; review;

last day for resolving final exam conflicts.

12/05 5.R review.

**No makeup quizzes will be given.**

Two
*hour exams,* given in class, on 09/26
and 11/14.
No quizzes
during weeks of hour exams. Please see here
for sample exams.

Click here for the solutions to the first hour exam.

**Except in the case of emergency,
students
must discuss absences from hour exams with me in advance of the exam.**

*Final
exam:* Thursday, 12/11/03, 1:00-3:00pm,
at a place to be announced.

**Students with final examinations
which
conflict with the Math 180 final examation are responsible for
discussing
a makeup examination with me no later than 12/03.**

Students are expected to be thoroughly familiar with the University's policy on academic integrity. The University has instituted serious penalties for academic dishonesty. We have encouraged you to work with your classmates on homework. Regarding homework, quizzes, hour exams, and the final examination:

**Copying work to be submitted for
grade,
or allowing your work to be submitted for grade to be copied, is
considered
academic dishonesty.**

It is University policy that students with disabilities who require accommodations for access and participation in this course must be registered with the Office of Disability Services.

Some remarks about your solutions to the various problems:

1. OK, for the most part. Some people forgot that constants have derivative 0. Also- read the problems carefully- you were supposed to indicate the rules which you used!

2. Most people found the derivative. Some forgot what "local linearization" means.

3. Here many were assuming that both parts could be done using L'Hopital's Rule- in the second limit this rule didn't apply! "Getting the right answer" (namely 0) is not enough. For example, in computing the limit of (sin x)/(x+1) as x -> 0, if you would apply L'Hopital's Rule (which again is not admissible) you would get 1, and not the correct answer (i.e., 0).

4. Many people forgot to explain why the critical point which they found was a global maximum.

5. In part 2, many did not argue why there is only one y such that (1,y) is on the curve described by the given equation.

6. (Extra credit.) Some people got it!

Click here to access the questions which appeared on the quizzes covering Sections 2.6-4.3.

Also check the main webpage for Math 180 for announcements about this class.

Do
*not* use this form to address personal concerns. All other
matters
specific to your situation (for example, your performance in the class)
should be sent by usual e-mail.

Your submission may remain anonymous, but please provide your name and e-mail address if you would like a personal response. Please indicate whether I may publish your question and my response to it on this webpage.

**Click here
for a brief history of calculus, and below to learn more about some of
our calculus heroes:**

Archimedes
of Syracuse

Jacob
Bernoulli

Johann
Bernoulli

Augstin
Louis Cauchy

René
Descartes

Leonhard
Euler

Pierre
de Fermat

Guillaume
de l'Hopital

Gottfried
Wilhelm von Leibniz

Sir
Isaac Newton

Brook
Taylor

Last modified 11/19/03.