**************************************************************************************
Important Class Announcements
1. The final exam has been scheduled for May 14, 5:308:30 pm in BH A53.
2. The 21111 and 21112 sequence is being restructured.
If you are planning to take 21112, the natural successor to this
version of the course will be taught for the last time this summer and
next fall. After that, the new version of 21112 will be in
place, and will differ significantly from the current sequence.
Please feel free to talk to me or an undergrad advisor in the math.
sci. dept. if you have any questions.
**************************************************************************************
Spring 2007
MWF 12:301:20
DH 1212
Instructor: David Offner
Email: doffner AT andrew DOT cmu DOT edu
Office hours MW 1:302:20, PPB 342
directions
to PPB 342
Teaching Assistants:
Joe Klobusicky
Recitation A
TR 3:304:20, SSH 220
Email: jklobusi AT andrew DOT cmu DOT edu
Office hours TR 3:304:20, WEH 6215
Sarah Mogin
Recitation B
TR 3:304:20, SH 220
Email: smogin AT andrew DOT cmu DOT edu
Office hours: TR 1:302:20, UC 314
syllabus (pdf)
(ps)
suggestions (pdf) (ps)
skills assessment (pdf)
(ps) solutions (pdf) (ps)
Review for test 1 (pdf)
(ps)
solutions (pdf)
Test 1 solutions (pdf)
Review for test 2 (pdf)
(ps)
solutions
(pdf)
Test 2 solutions (pdf)
makeup solutions (pdf)
Review for test 3 (pdf)
(ps)
solutions
(pdf)
Compound interest formulas
(pdf)
(ps)
Test 3 solutions (pdf)
Homework #1 (pdf)
(ps)
solutions (pdf)
Homework #2 (pdf)
(ps) solutions (pdf)
Homework #3 (pdf)
(ps) solutions (pdf)
Homework #4 (pdf)
(ps) solutions (pdf)
Homework #5 (pdf)
(ps)
solutions (pdf)
Homework #6 (pdf)
(ps) solutions (pdf)
Homework #7 (pdf)
(ps)
solutions (pdf)
Homework #8 (pdf)
(ps)
solutions (pdf)
Homework #9 (pdf)
(ps) solutions (pdf)
Homework #10 (pdf)
(ps) solutions (pdf)
Homework #11 (pdf)
(ps) solutions
(pdf)
Homework #12 (pdf)
(ps)
solutions
(pdf)
The reason hw12 was delayed is here.
useful links:
* Good
advice on how to write solutions to math problems
* CMU Academic
Development (peer tutoring and academic counseling resources)
* Applets
and more applets
illustrating calculus concepts
* Mathematical Sciences at CMU
Date 
Topic 
References 
Monday, 1/15 
MLK Day, no class 
"I
Have a Dream" speech 
Wednesday, 1/17 
Introduction to Calculus Review of algebra: functions 
Textbook, Ch. 0.1 
Friday, 1/19 
Review of algebra: types of
functions Review of algebra: composition of functions Review of algebra: solving quadratic equations 
Textbook, Ch. 0.2 Textbook, Ch. 0.3 Textbook, Ch. 0.4 
Monday, 1/22 
Review of algebra: fractions Review of algebra: exponents 
Textbook, Ch. 0.5 
Wednesday, 1/24 
Lines and slope 
Textbook, Ch. 1.1 
Friday, 1/26 
The derivative 
Textbook, Ch. 1.2, 1.3 Some applets: tangent lines approximating the tangent line: here and here 
Monday, 1/29 
Detour: Limits 
Textbook, Ch. 1.4 
Wednesday, 1/31 
Rules for calculating derivatives 
Textbook, Ch. 1.3, 1.6 
Friday, 2/2 
Applications of the derivative * Finding equations of tangent lines * Physics: Position and velocity * Economics: Marginal cost 
Textbook, Ch. 1.8 Textbook, Ch. 1.7 
Monday, 2/5 
Second (and higher) derivatives * Application: Position, velocity, acceleration 
Textbook, Ch. 1.8 
Wednesday, 2/7 
Curve sketching * Finding x and yintercepts * Critical points, maxima and minima 
Textbook, Ch. 2.1 
Friday, 2/9 
Finding maxima and minima 
Textbook, Ch. 2.2, 2.3 
Monday, 2/12 
Finding concavity and points of
inflection 
Textbook, Ch. 2.2, 2.3 
Wednesday, 2/14 
Summary of curve sketching Review 

Friday, 2/16 
Test 1 

Monday, 2/19 
Sketching rational functions * horizontal and vertical asymptotes 
Textbook, Ch. 2.4 
Wednesday, 2/21 
Sketching rational functions:
examples Summary of curve sketching 
Textbook, Ch. 2.4 
Friday, 2/23 
Optimization problems 
Textbook, Ch. 2.5 
Monday, 2/26 
More optimization problems * Inventory control 
Textbook, Ch. 2.6 
Wednesday, 2/28 
More optimization 
Textbook, Ch. 2.7 
Friday, 3/2 
Product and quotient rules 
Textbook, Ch. 3.1 
Monday, 3/5 
Chain rule 
Textbook, Ch. 3.2 
Wednesday, 3/7 
Implicit differentiation 
Textbook, Ch. 3.3 
Friday, 3/9 
Spring break 
A
cautionary tale 
Monday, 3/19 
Implicit differentiation and
related rate problems 
Textbook, Ch. 3.3 
Wednesday, 3/21 
More implicit differentiation
and related rates * Astroids and superellipses * Chemistry *Area and Volume 
Astroids, Superellipses, Piet Hein 
Friday, 3/23 
Newton's Method 
Newton's Method 
Monday, 3/26 
Exponential Functions 
Textbook, Ch. 4.1 
Wednesday, 3/28 
The exponential function e^x Derivatives of exponential functions 
Textbook, Ch. 4.2, a picture Textbook, Ch. 4.3 
Friday, 3/30 
Test 2 

Monday, 4/2 
The natural logarithm ln(x) 
Textbook, Ch. 4.4 
Wednesday, 4/4 
The derivative of ln Properties of logs 
Textbook, Ch. 4.5 Textbook, Ch. 4.6 
Friday, 4/6 
Using properties of logs Other logarithmic functions 
Textbook, Ch. 4.6 Textbook, Ch. 4.4 
Monday, 4/9 
Applications of exponential
functions * population growth * radioactive decay 
Textbook, Ch. 5.1 
Wednesday, 4/11 
Application of exponential
functions * compound interest 
Textbook, Ch. 0.5, 5.2 
Friday, 4/13  Calculating a loan payment 
a derivation 
Monday, 4/16 
Mo' Money 

Wednesday, 4/18 
Other applications of
exponential functions 
Textbook, Ch. 5.4 
Friday, 4/20 
Carnival 
website 
Monday, 4/23 
Logarithms in the real world * Richter scale * decibel level 
Logarithmic scale Richter scale decibels, dB chart 
Wednesday, 4/25 
More applications of logarithms 
octaves, the slide rule 
Friday, 4/27 
Computer algebra systems 
Mathematica,
MAPLE, MatLab 
Monday, 4/30 
Test 3 

Wednesday, 5/2 
Review for final exam 
Review questions (pdf) (ps) 
Friday, 5/4 
Review for final exam 