Calculus I, 21-111

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)

Review for final (pdf) (ps)

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) (pssolutions (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

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

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
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