**************************************************************************************
Important Class Announcements
1. The final exam has been scheduled for May 14, 5:30-8:30 pm in BH A53.
2. The 21-111 and 21-112 sequence is being restructured.
If you are planning to take 21-112, 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 21-112 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 12:30-1:20
DH 1212
Instructor: David Offner
Email: doffner AT andrew DOT cmu DOT edu
Office hours MW 1:30-2:20, PPB 342
directions
to PPB 342
Teaching Assistants:
Joe Klobusicky
Recitation A
TR 3:30-4:20, SSH 220
Email: jklobusi AT andrew DOT cmu DOT edu
Office hours TR 3:30-4:20, WEH 6215
Sarah Mogin
Recitation B
TR 3:30-4:20, SH 220
Email: smogin AT andrew DOT cmu DOT edu
Office hours: TR 1:30-2:20, 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)
make-up 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 y-intercepts * 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 |