Fall 2005

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

*Instructor:
*Matthias Aschenbrenner
*E-mail address: *
*Homepage:* http://www.math.uic.edu/~maschenb
*Office:* 417
SEO
*Office Phone:* (312) 413-3150
*Office Hours:* M 9-10, T
3-4, W 9-10

*Central
webpage for this class: *Math
181

*Teaching
assistant: *Phil Grizzard, *e-mail address: *grizzard@math.uic.edu
*Discussion section: *TuTh 11-11:50am, 305
Taft Hall
*Math Lab: *On TuTh 9am-2:50pm
there will be someone in the Math Lab
(300
Taft Hall) who can answer Math 181 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*:
Membership in the Honors College. Students who do not satisfy
these prerequisites will be dropped.

*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 6.1 -- 6.3
relations between derivative and integral,
differential
equations

2 6.4 -- 7.1
2nd Fundamental Theorem, motion, integration by
substitution

3 7.1 -- 7.2 integration by parts

4 7.3 -- 7.5
integral tables, trigonometric substitution, approximations

5 7.6 -- 7.7
approximation errors, improper integrals

6 8.1 -- 8.3
applications of the definite integral to geometry

7 8.6 -- 8.8
applications: economics; distributions and
probability

8 9.1 -- 9.2 sequences, geometric series

9 9.3 -- 9.5
convergence, convergence tests, power series

10 App.
B
complex numbers

11 10.1 -- 10.2 Taylor series

12 10.3 -- 10.5
convergence of Taylor series, Fourier series

13 11.1, 11.2, 11.4
differential equations, slope fields, separation of variables

14 11.5
growth and decay

15 11.6
applications and modeling; review for
final exam

` `Click
here
to download the course information handout.

Your responsibilities are as follows: You are expected to complete the assigned reading in the text before each class. Homework problems will be collected at the beginning of each lecture; the homework will be returned in the discussion sections. Some of the assigned problems will be on material you have read, but not yet covered in class. Doing these problems beforehand will prepare you to get more from the lecture.

**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 181, 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.

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. The problems and sections are numbered according to the 4th ed. of the textbook; if the numbering in the 3rd. and 4th ed. differs, the number of the corresponding section or problem in the 3rd ed. follows in parantheses.

Date Section(s) Problems/Comments

08/22 6.108/24 6.2 6.1 #6, 12, 16;08/26 6.3 6.2 #4, 8, 10, 31, 50 [51], 56 [57], 58 [59];

08/29 6.408/31 6.5 6.3 #8, 14, 18;09/02 7.1 6.4 #7 [6], 15 [14], 21 [20], 34 [24];

09/05Labor Day holiday. (no classes)09/07 7.1 7.1 #25 [22], 38 [36], 50 [46], 60 [56]09/09 7.2 7.2 #8 [6], 11 [10], 18

09/12 7.3 7.3 #4, 16 [14], 21 [18], 23 [20]09/14 7.4 7.4 #11 [16], 15 [20], 17 [22], 21 [24]09/16 7.5 7.5 #4, 15 [18], 23 [26], 25 [28]

09/19 7.6 7.6 #4, 5, 609/21 7.709/23First hour exam: Chapters 6 and 7;

Suggested review problems:

Chapter 6, #3-52 [1-50], 60-69 [52-61];

Chapter 7, #1-104 [1-114], 121-132 [115-126], 156 [146].09/26 7.7

09/28 7.8 7.7, #8, 12, 16

09/30 8.1 7.8, #4, 8, 16, 24

10/03 8.2

10/05 8.4 [8.3] 8.1, #1, 3, 6, 8, 10; 8.2, #4, 9 [8]

10/07 8.7 [8.6] 8.2, #16 [14], 20 [18]; 8.4, [8.3] #6, 8, 10, 1410/10 8.8 [8.7] 8.7 [8.6], #20; 8.8 [8.7], #5, 8, 9

10/12 9.1 9.1, #1, 13, 14, 40, 52;

10/14 9.2 [9.1] 9.1, #20, 22, 26, 28; 9.2 [9.1], #19 [16], 20 [17], 31 [26]

(The material in 9.1 of the 4th ed. does not appear in the 3rd. ed.

The problems for 10/12 and 10/14 from 9.1 refer to the 4th ed.

I handed out copies of this chapter on 10/17.)

10/17 9.310/19 9.4 9.3, #10, 12, 16, 18 [9.2, #15, 18, 13, 19]

9.4, #6, 10, 14, 20 [9.3, #5, 12, 15, 17]

10/21 9.5 9.4, #52, 53 [9.3, #27, 28]

9.5, #12, 16, 18, 22 [9.4, #12, 16, 18, 22]

10/24 9.5 9.5, #23, 28, 29, 32 [9.4, #23-26]10/2610/28Second hour exam: 7.7, 7.8, and Chapters 8 & 9;

Suggested review problems:

Chapter 7, #133-146 [#127-140]

Chapter 8, #1-22, 41-42 [#1-11, 17-18]

Chapter 9, #1-53 [#1-15, 24]

(Also, try to do as many problems from 7.7, 7.8, and from the sections

in Chapters 8 & 9 that we covered.)

10/31 App. B [App. C]11/02 10.1 App. B, #2, 4, 6, 8, 10, 12, 14, 29, 38, 42

[App. C, #2, 4, 6, 8, 10, 12, 14, 29, 38, 42]11/04 10.2 10.1, #2, 4, 6, 12, 14, 22, 26 [10.1, #1, 7, 8, 12, 14, 19, 22]

11/07 10.311/09 10.4 10.2, #8, 10, 14, 16, 18, 22, 44 [10.2, #4, 6, 10, 12, 14, 18, 40]

10.3, #2, 4, 6, 26, 27 [10.3, #2, 5, 8, 19, 20]11/11 10.5 10.4, #5, 6, 19 [10.4, #2, 3, 15]

10.5, #6, 8

11/14 11.111/16 11.2 10.5, #11

11.1, #6, 8, 10, 14 [11.1, #4, 5, 10, 13]

11.2, #4, 8, 10 [11.2, #6, 8, 10]11/18 11.3 11.3, #2, 6 [11.3, #3, 6]

11/21 11.4 11.4, #2, 4, 6, 8, 30, 32, 34 [11.4, #1, 3, 4, 8, 29, 31, 34]11/23 11.5 11.5, #6, 8 [11.5, #3, 9]

last day for resolving final exam conflicts.

11/25 Thanksgiving Holiday. (no classes)

11/28 11.611/30 11.6, #7, 8 [11.6, #5, 13]12/02 Review for final

**No makeup quizzes will be given.**

Two
*hour exams,* given in class, on 09/23
and 10/28.
No quizzes
during weeks of hour exams.

*Final
exam:* Thursday, 12/08/05, 8:00-10:00am, in 512 SEO.

**Except in the case of emergency, students
must discuss absences from hour exams with me in advance of the exam. Students with final examinations which
conflict with the Math 180 final examation are responsible for discussing
a makeup examination with me no later than 11/23.**

Students are expected to be thoroughly familiar with the University's policy on academic integrity. The University has instituted serious penalties for academic dishonesty.

**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.

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 11/28/05.