MATH 103: CALCULUS I (Announcements,
my schedule)
MWF 10  10:50am and 11
 11:50am, Bronfman Science Center 105
Review
Classes: All in Thompson Biology Lab 202:
Mon, Dec 8 (1011am); Wed, Dec 10 (10amnoon)
Final will be
Thursday, December 11th at 9:30am in Thompson Biology Lab 112
Professor Steven Miller (Steven.J.Miller AT williams.edu)
202
Bronfman Science Center, 4135973293
REVIEW SESSIONS: LAST DAY THURS, DEC 4TH

Class TAs (Alan.B.Arias AT williams.edu, Douglas.O.Onyango AT
williams.edu):
 Monday, Tuesday: 7  8:30pm in Bronfman 104
 Wednesday: 7  8:30pm in Bronfman 107
 Thursday, Friday: 1:30  3pm in Clark 204
 Sunday: 7  8:30pm in Clark 204
 Math & Science Resource Center: Thompson Physics
Laboratory, room 113 or 114
 Sundays: 8pm  10pm (Edgar)
 Mondays: 8pm12am (Laura)
 Tuesdays: 8pm10pm (Nancy)
 Wednesdays: 9pm11pm (Edgar)
 Thursdays: 10pm  midnight (Nancy)
QUICK LINKS
Resources Course Description
HW/Exams/Grading
Syllabus/HW Problems
Handouts Other
QUICK LINKS
RESOURCES FOR HELP: (not
responsible for any errors on any page!)

Free tutoring:
Math &
Science Resource Center Coordination

Webpage with useful explanations, examples and
applets:
http://math.brown.edu/help/
 Summary of calculus formulas and rules: (with thanks to
Lambert Peng): Calc I Summary
 Summary of calculus definitions (by Lauren Z, checked by
Kyle V): calcdefns (note: it doesn't have the
FTC: If f(x) is a continuous, differentiable function and f'(x) is bounded,
then the area under the curve y = f(x) from x=a to x=b, denoted
ʃ_{a}^{b} f(x)dx, is F(b)  F(a),
where F(x) is any antiderivative of f(x) (ie, F'(x) = f(x)).
 Review sessions: Dates and times TBD.
 The
Calculus Lifesaver (by Adrian Banner): a good supplemental book with
numerous worked through examples; this book is not required for the course,
but is an excellent resource. Videos of the review sessions he ran at
Princeton for Calc I are also
available here.
 My lecture notes: for
your convenience and viewing pleasure, I've scanned in my notes and are
posting them here. Remember that these are just meant to remind me what to
say, and thus sometimes have minimal detail. We'll mostly go in order.
COURSE DESCRIPTION:
Calculus permits the computation of velocities and other instantaneous rates of
change by a limiting process called differentiation. The same process also
solves "maxmin" problems: how to maximize profit or minimize pollution. A
second limiting process, called integration, permits the computation of areas
and accumulations of income or medicines. The Fundamental Theorem of Calculus
provides a useful and surprising link between the two processes. Subtopics
include trigonometry, exponential growth, and logarithms. This is an
introductory course for students who have not seen calculus before. Students who
have previously taken a calculus course may not enroll in Mathematics 103
without the permission of instructor.
Format: lecture. Evaluation will be based primarily on homework, quizzes, and/or
exams.
Prerequisites: Mathematics 102 (or demonstrated proficiency on a diagnostic
test; see Mathematics 101). No
enrollment limit (expected: 30).
HOMEWORK / EXAMS / GRADING: I encourage you to work in groups,
but everyone must submit their own HW assignment. HW is to be handed in on time,
stapled and neat  late, sloppy or unstapled HW will not be graded. Please show
your work on the HW and exams (otherwise you risk getting no credit).
Homework problems will mostly be taken from this sheet
(these problems are also in the textbook, but this way you don't have to lug the
book with you everywhere). There will be at least three midterms (with at least
the lowest grade dropped) and a final;
grades are 20% HW, 40% Midterm, 40% Final. All exams are cumulative.
Click here to see an example of how to write up
calculus homework problems.
SYLLABUS / GENERAL:
We will do most of the sections of the textbook through
Chapter 5. The textbook is
Calculus with Early Transcendentals (7th edition, Edwards and Penney). If
you want to see if an earlier edition is close enough, let me know and you can
compare it to my copy. My son found this to be an
interesting, readable book. Also, please feel free to swing by my office or
mention before, in or after class any questions or concerns you have about the
course. If you have any suggestions for improvements, ranging from method of
presentation to choice of examples, just let me know. If you would prefer to
make these suggestions anonymously, you can send email from
mathephs@gmail.com (the password is the
first seven Fibonacci
numbers, 11235813). My lecture notes are
available online here (but remember these are meant to remind me what to
say, and thus sometimes have few details).

Week 1: Friday, September 5th

Read: Chapter 1, review algebra through webpages above

HW: Due Wednesday, September 10th: 1.1: #1, #29, #47;
1.2: #5, #65; #1.4: #14.

Suggested HW: 1.1: #36; 1.2: #79; 1.4: #22, #7, #8.
 Week 2: September 8th to 12th

Read: Chapter 2

Mathematica notebook: Example of the
squeeze theorem

HW: Due Wednesday, September 17th: 2.1: #5, #15;
2.2: #1, #4, #6, #25; 2.3: #1, #7, #25; 2.4: #49

Suggested HW: 2.1: #33; 2.2: #27, #37;
2.3: #2, #32, #70; 2.4: #1, #20, #47, #63 (very important for
applications!), #66.
 Week 3: September 15th to 19th

Read: Chapter 2, Chapter 3: 3.1, 3.2, 3.3, 3.4.

HW: Due Wednesday, September 24: Problem from 3.1: in the HW list (ie, find
the derivative of f(x) = 3x^{2}  4x + 1) from the definition of the
derivative); 3.2: #3, #8, #16, #25; 3.3: #1, #7, #54; 3.4:
#1, #17, #31.

Suggested HW: 3.2: 55, 61, 66, 73; 3.3:
#39, #42, #33; 3.4: #43, #47, #63, #71.
 Week 4: September 22nd to 26th

Read: Chapter 3: 3.4, 3.7, 3.5, 3.6.

Mathematica notebook:
Example of
derivatives and tangent lines,
Drowning swimmer problem.

General Comment: First exam will
be Monday, September 29th

HW: Due Wednesday, October 1st: 3.7: #1, #8,
#45; 3.5: #1, #18; 3.6: #1, #20, #47.

Suggested HW: 3.7: #41, #61, #71,
#77; 3.5: #9, #28, #41, #42; 3.6: #7, #13, #15, #27, #42.

Week 5: September 29th to October 3rd:
In class exam on Monday, Sept 29th

Read: Chapter 3: 3.6, 3.8; Chapter 4: 4.1, 4.2.

HW: Due Wed October 8th: 3.8: #1, #18, #39, #59.

Suggested HW: 3.8: #7, #33, #63, #64, #72.
 Week 6: October 6th to 10th

Read: Chapter 3: 3.9, 3.10; Chapter 4: 4.1, 4.2, 4.3;

Mathematica notebook:
Related Rates problem:
filling a cone with water; chaos and fractal geometry:
executable file
program (sadly, these programs
of mine were written over a decade ago in pascal, and won't run on most
systems, thus see also
http://aleph0.clarku.edu/~djoyce/newton/newtongen.html). You can
download a nice program to study fractal geometry
here (it's called xaos). See also
zooming in on
1dimensional and 2dimensional plots.

General Comment: Second exam will
be Monday, October 20th

HW: Due Wed Oct 15: 3.9: #5, #15, #44; 3.10:
#1. NOTE: Friday is Mountain Day.

Suggested HW: 3.9: #13, #37; 3.10: #21.
 Week 7: October 13th to 17th

Read: Chapter 4: 4.1, 4.2, 4.3.

General Comment: Second exam will
be Monday, October 20th.

General Comment: Third exam will be
in class on Wednesday, October 22nd.

For next week, you are responsible for redoing your
second exam and making sure you understand all problems. As no one got every
problem entirely correct, you must talk with at least one other student
about the exam questions, and make sure you both understand each problem.
You DO NOT need to hand in your second attempt on the exam; you are on the
honor system to write up all problems you got wrong and make sure they are
correct.
 Week 8: October 20th to 24th

Read: Chapter 4: 4.3, 4.4, 4.5.

HW: Due Wed, Oct 29: 4.2: #28, #42; 4.3:
#15, #25, #33, #45; 4.4: #1, #11, #29; 4.6: Sketch f(x) =
(x^3/3) + 5x^2  16x + 2004; #13; #33.

Suggested HW:
4.2: #2, #11; 4.3: #1, #4, #5, #16, #17, #18, #26, #27, #48,
#61; 4.4: #27, #30, #31, #34, #42; 4.6: #4, #35, #77, #80,
#82, #83, #89.
 Week 9: October 27th to 31st
 Week 10: November 3rd to 7th

Read: 5.1, 5.2.

General Comment: Fourth exam is
Friday, November 7th

HW: Due Wed, Nov 12th: 4.8: #1, #9, #42; 5.2:
#1, #3, #16; WRITE AND CHECK REVIEW SHEET.

Suggested HW: 4.8: #2, #62, #68, #70, #73;
5.2: #37, #58, #68.

Week 11: November 10th to 14th

Read: 5.2, 5.3, 5.6

HW: Due Wed, Nov 19th: 5.3: #3, #9, #19 (you may
use the identity listed above), #39.

Suggested HW: 5.3:
Prove the three identities before problem 19, #52, #53.
 Week 12: November 17th to 21st
 Week 13: November 24th to 28th (Thanksgiving recess
on the 26th and 28th)
 Week 14: December 1st to 5th
 Week 15: December 8th to 12th
HANDOUTS:
OTHER:
QUICK LINKS
Resources Course Description
HW/Exams/Grading
Syllabus/HW Problems
Handouts Other
QUICK LINKS
REVIEW SESSIONS: LAST DAY THURS, DEC 4TH

Class TAs (Alan.B.Arias AT williams.edu, Douglas.O.Onyango AT
williams.edu):
 Monday, Tuesday: 7  8:30pm in Bronfman 104
 Wednesday: 7  8:30pm in Bronfman 107
 Thursday, Friday: 1:30  3pm in Clark 204
 Sunday: 7  8:30pm in Clark 204
 Math Science Resource Center:
 Nancy: Sundays and Thursdays: 810pm
Laura: Mondays: 8pm12am
Edgar: Tuesdays and Wednesdays: 911pm