Calculus I Spring 2005

First Day Handout Homework Homework hints

Class List

Maple Labs

In Class Demos

Notebook Posted Grades Help Sessions


5/11/05 Final letter grades have been posted.  Good work everyone!  (PS--if you checked before 12:45 pm on Thursday, please check again now--they have been corrected.)
5/9/05 We went over the old final during the review session--here are the smartboard notes from the review session:  calcsamplefinal.xbk, calcsamplefinal.pdf
5/9/05 Grades to date have been posted, and here is a copy of last semester's final exam, plus solutions.  Happy to cover any of this during the review session.  Finalf04.pdf finalf04 solutions.pdf.

Your exam will have different questions of course, with some kinds of questions replaced by other kinds, but this gives a good idea.

5/9/05 Review session-- Tonight at 6:30 to about 7:30, in JEM 366 (just up the hall from our usual classroom).  Will mostly be covering related rates, optimization, and graphing.
5/6/05 Overheads from Alice Dean's talk:  AliceDeanUBVGs.pdf

Extra Credit Talk

Date: Thursday, 05/05/05

Time:  3:30 � 4:30 p.m.

Location: SMC Campus, Jeanmarie 362

 Title:  Characterizations of Unit-Bar Visibility Graphs

 Speaker:  Alice Dean, Department of Mathematics and Computer Science, Skidmore College


Representations of graphs using horizontal bars for vertices and vertical visibilities for edges have been studied since the mid 1980s, motivated by applications to circuit design and display of data. Graphs that can be represented in this way have been fully characterized, but the bar lengths may differ by impractical amounts. I consider graphs that can be represented using bars all of equal length. These graphs, called unit-bar visibility graphs (or UBVGs), have not been fully characterized. I will discuss results for several classes of graphs, including trees and outerplanar graphs. The final result is a characterization of the triangulated polygons (TPs) that are UBVGs. The characterization uses a character string associated with each TP to determine if a UBV layout exists and if so, to produce such a layout.

4/28/05 STUDY TIPS for the final exam.  The final exam will emphasize chapter 5.  You can find a practice test at:  Chapter tests.   In fact, this is probably one of the best places to study for all the chapters, since some multiple choice questions on the final will be very similar to these. Additional problems may be taken from (or similar to) these drills:  Drills.

It is too scary (and probably not even possible) to do every problem from every drill--just do one from each drill, and note which you are uncertain about, then go back and do a couple more of that type.  Do this as many times as you have time for.

There will also be a "delta-epsilon" problem, of much the same flavor as # 15 - 18 in section 2.4, a related rate problem, an optimization problem, a graphing problem (factored derivatives will be given), and a proof of the derivative of some like a quotient/product rule or trig function or its inverse.  These 5 questions will be worth more than the multiple choice questions.

Note:  You may have FOUR sheets of notes, front and back, as usual.  However, in addition, you may bring photocopies of the flyleaves of your text (two pages from the front of the book, four from the back) to use during the test.




Math Awareness Month!

Wednesday April 27

Jeanmarie 281-- 2:30 � 4:15 p.m.

2:30 Screening of �The Proof�

In 1992 Andrew Wiles announced a proof of Fermat�s Last Theorem, a conjecture that had fascinated mathematicians for more than 300 years. This video tells the story of Andrew Wiles and his proof. (This video should be of particular interest to those of you attending the Hudson River Conference on 4/30 since the invited address will be about this theorem - and the HRUMC speaker, Ken Ribet, also appears in this video.)

3:30 Refreshments

3:40 Screening of �The Right Spin

Math Awareness Month 2005 special video:

the story of a dramatic rescue in space and the mathematics behind it told by Astronaut Michael Foale and narrated by Robert Osserman. Guaranteed to make you appreciate Calc.III (35 minutes)

If you can�t come to all of the celebration

you are welcome to �drop in� for part of it!

Sponsored by Math Department and Pi Mu Epsilon.


4/22/05 Reminder on the population lab-- It says you must research population literature, including IntelPop.  The site for IntelPop is in the references (section 5.2, second listing), but here is a direct link for your convenience: .  The java applet is pretty easy to use.
4/22/05 Due dates have been posted for Chapter 5 Challenge problems and the last Maple lab.  Do the Maple lab as soon as possible, since it will help with homework as well.
4/14/05 In order to provide out-of-class time for the populations project, class will not meet on 4/22, and the due date for Part III (section 3.3.1) has been moved to 4/25.
4/13/05 Challenge problems for chapter 4 are due Wednesday, 4/20.
4/7/05 Maple Lab 6 is due Friday, April 15.  This is a good warm-up for section 4.6, and will help reinforce important concepts for the test on the 12th.
4/7/05 About section 4.3 no 47, which is:

limit( sqrt(x^2+1)-x, x = infinity).

I figured it out right after class and boy do I feel stupid...

How many times have I said that if you see square root-y things, it is always a good idea to try multiplying by the conjugate?  Be good if I followed my own advice, hmm?

Just mult top and bottom of this by the conjugate, and then it is easy to see the limit is 0.

4/6/05 The third hour test will be on Tuesday, April 12.  The test will cover sections 3.3-3.8, 3.10, 4.1-4.5.    You should study from the tutorial quizzes at: Chapter tests.  There will be questions (proofs) for the derivatives of the trig and inverse trig functions.

Also helpful are the derivatives, differentiation methods, curve analysis, and mean value theorem tutors under the tools menu in Maple.

Here are a some drills:

VC Lhopital drill

VC Lhopital drill inf limits,

quiz 1, (Note--include  endpoints for inc/dec and questions about f' or f'' pos/neg, and global extremes.  Do not include endpoints for local extremes.  Also, on #7 there are asymptotes at C and E so the function and its derivatives do not exists there, also skip the 9th one since it has a confusing wrong answer given),

quiz 3 

VC 1st deriv test drill

VC MVT drill

vc max/min drill 



Bacteria Project Revisions: 

  1. Include the names of you partners in Biology.
  2. Include a copy of the original data you were given by your bio partners.
  3. If you used the Maplets posted on the website to determine the parameters, include screen captures in your report.
  4. Organize information so that it will be easy for your bio partners to understand:
    1. Label data sets and plots
    2. Insert comments above Maple code to explain what you are doing and why.
    3. Introduce the answers to the questions in part 3 so the bio partners will know what you are discussing.
    4. Edit as though this were an English paper (in some sense it is�the point of your writing classes is to develop the skills you need to make reports like this meet professional standards). Use complete sentences, check grammar and spelling, etc.
  5. Analyze all four data sets you were given.  They may not all exhibit logistic growth�that is ok, but you need to explain why you chose whatever other model you did choose.  It may be that no matter how hard you try with various pairs of data points and (and values of M for the logistic curve) you still don�t get a great fit�this is ok as long as you give some explanation of what might be causing the difficulty.
  6. If the are questionable data points, ask your bio partners about it and include the explanation in your report.
4/1/05 Extra Credit Talk--

Date: Thursday, 4/7/05

Time:  3:30 � 4:30 p.m.

Location: SMC Campus, JEM 362

 Title:  A Problem in Extremal Graph Theory

 Speaker:  John Schmidt, Department of Mathematics, Emory University


Graphs have proven to be a very important mathematical model. For example, computer or telephone networks can be viewed as graphs.  Often, one would like to build a graph  that has a certain property.  A natural question then arises:

"How much does one have to spend to build the graph with the desired property?" 

 We will discuss such a question as asked by Paul Erdos and its solution.

No previous knowledge of graph theory is assumed.

3/28/05 Extra credit opportunities:  Extra credit is available for attending any of the Senior Seminar talks and writing up a two or three paragraph synopsis of the talk.  You may attend as many as you would like.
3/21/05 some implicit examples on Maple:   sec3-6 no, sec3-6 no, sec3-6 no (not enough detail for the challenge problem, but enough to get started.)
3/21/05 An example using Maple to plot the tangent line to a function  tangentline
3/21/05 Challenge problems 3.6-3.11 due: 4/1/05, no fooling.
3/2/05 The next hour test will be on Tuesday, March 8, and will cover sections 2.5 through 3.4. 

The second hour test, on Tuesday, October 19,  will cover sections 2.6 through 3.2.

The first part will be similar, both in content and format, to the first hour test (multiple choice).  You should study from the tutorial quizzes at: Chapter tests.  However, there isn't a very large selection there of problems to practice on (although 3.2 is good)--you should do as many of the "drill" problems from the inclass demos as possible, since I am likely to take problems from there for the test as well.   You should be able to compute the slope of the tangent line (derivative) using the limit definition of the derivative.  You should be able to tell if a function is continuous and if it is differentiable.  You should also be able to sketch a graph of a function and the tangent line at a point.

There is also an excellent Maple tutor--go to tools/tutors/calc--single variable/differentiation methods. Do A LOT of practice with the product and quotient rules!

The second part of the test will ask you to prove at least two of the differentiation rules--constant multiple, power, sum, product, quotient, various trig rules.

Here are some good review sources: 


Also do the examples in the inclass demos that will generate different problems for you, for example at the bottom of , and 

These are good for practicing using the limit definition to find the derivative.

Here are some good practice finding tangent lines and using the product and quotient rules with the trig functions.

VC tanlines drill,

VC product rule egs, 

VC quotient rule egs,



3/2/05 Due dates for the next set of challenge problems and lab have been posted.
3/1/05 EXTRA CREDIT TALK--Extra credit is available for attending this talk.  As usual, write up and turn in 2 paragraphs about the talk (due the Tuesday after break) for credit.  This is a very entertaining and easy to understand speaker.

Rick Cleary Talk

2/25/05 Grades to date have been posted.  See me for your code or if you have any questions.
2/25/05 Here are some Maplets that may be useful for the populations project.  WARNING--do NOT use the Curve Fitting tool inside Maple--it will fit to lines or polynomials, NOT the exponential/logistic curves which you need for this project.

calc1/calc I maplets/ExponentialGrowth.mws

calc1/calc I maplets/LimitedGrowth.mws

calc1/calc I maplets/LogisticGrowth.mws

2/15/05 Some "sexy" maple: 

calc1/maple labs/fancy Maple/torus

calc1/maple labs/fancy Maple/surreal shells submit.mws

calc1/maple labs/fancy Maple/

calc1/maple labs/fancy Maple/

2/14/05 In order to provide out-of-class time for the populations project, class will not meet on 2/23.
2/14/05 Populations project due dates:  Part I (section 3.1.2)-due: 3/4.  Part II (section 3.2)- due: 4/1.  Part III (section 3.3.1) - due: 4/22.
2/14/05 WB01703_1.gif (578 bytes) Happy Valentine's Day!
2/10/05 Is there any interest in Tatoos for Pi-Day?  (3/14).  We could probably get the department to order us some.  Let me know ASAP.
2/9/05 The date of the extra credit talk has been changed to next week--2/18/05.
2/8/05 Maple lab 2 is due 2/14/05
2/7/05 Solutions to HT I from last semester:  acdbbcbbadebc.  Note that problems 12 and 13 are from 2.5 which will not be covered on our test.

Extra Credit talk:  David Wood will be speaking at the UVM Math department colloquium this week as well as in the combo seminar.  The colloquium talk is aimed at a general audience and should be quite accessible.


Turn in about a page of notes/observations from the talk for extra credit.


Date: 2/11/05 (Changed to 1/18/05  !!!)

Time:  4:00 � 5:00 p.m.

Location:  004 Kalkin, UVM Campus

Title:  Drawing of Graphs in Two and Three Dimensions

More info

2/2/05 The first hour test is scheduled for Tuesday, February 8.

The test will cover sections 1.1 through at least part of 2.4, and assumes you have a thorough mastery of the appendix reviews. 

 You may use one page of notes, front and back, during the test.  You may also use a calculator on the test--graphing or non-graphing is fine.

The first hour test will be very similar, both in content and format, to the tutorial quizzes at: Chapter tests. You will have to change the chapter in order to get problems from chapter 2.  However, there may also be a "delta-epsilon" problem, of much the same flavor as # 19 - 32 in section 2.4.   Here is an hour test from last semester: HT1f04.pdf.  You should also spend some time with the graphical view at .

Some other good study problems:


1/25/05 Maple printouts--the Maple tutors and assistants, as far as I know, won't print directly from Maple.  If you need a print out of something you have done on one of them, the quickest way I know is to press alt/PrtScrn  (the PrtScrn button is usually on the upper right of the keyboard) while the window is up.  This copies the window to the clipboard, and then you can paste it into another application such as Word, and then print from there.  If you right-click on the image, you can crop it if necessary.  This will work with any active window, not just Maple.
1/24/05 New time for trig review:  7:30 to 8:30 (moved from 8 to 9) TONIGHT, in JEM 364. Trig review notes: 

calc1/inclass demos S05/calc-trig review.xbk

calc1/inclass demos S05/calc trig review.pdf

And a unit circle chart:

1/19/05 You may order a personal copy of Maple 9.5 at a discounted price of $75 if you wish:  Secure ordering address: .  The NEW Promotion Code is: AD7229 Course Name: Math 109 Ellis-Monag
1/19//05 Maple connection hint:  \\\maple95 seems to work if \\raptor\mapl95 does not work.
1/17/05 Due Wednesday 1/19--  a print out of a Maple worksheet with just your name on it so that I know that you are able to get on Maple and get started.
1/17/05 There will be a Maple help session in JEM 142 on 1/20 from 6:30 to 7:30 for the first Maple lab and a trig review session on 1/24 in JEM 364 from 8-9 pm.
1/17/05 The 2/6 hour test date on the First Day Handout was a typo--it should have been 2/8 and has been corrected.   The other two hour test dates, 3/8 and 4/12, are correct.
9/27/04 The link for the resources (eg tutorial quizes) that goes with our book seems to have changed.  I think this is the new link:  Book Resources 
9/22/04 From George Ashline

I wish to bring to your attention that once again this year there will be a conference for undergraduate students interested in mathematics during the Spring semester. The twelfth annual Hudson River Undergraduate Mathematics Conference (HRUMC) will take place on Saturday, April 30, 2005 at Williams College in Williamstown, Massachusetts. The keynote speaker will be Ken Ribet of UC Berkeley. In the past several years, a contingent of students and faculty from St. Michael's has gone to the HRUMC, and several students and faculty members have given presentations at previous conferences. For more information about this meeting, you can check out the conference homepage at At this site, you can find details about last year's conference which was held at Mount Holyoke College.

At the HRUMC, some talks are given on original research in mathematics or a related field (done by students, faculty, or jointly), while others are expositions of interesting work that has been accomplished and discoveries that have been made in mathematics (typically not discussed in regular course work). If you think that you might be interested in giving a talk or attending the conference to see what it's like, please let me or anyone else in the mathematics department know. If you'd like to get more information about this opportunity, just e-mail me back or stop by my office and I'd be happy to discuss it more with you. I have copies of recent conference programs if you'd like to get a feel for what the conference involves and the type of talks given. I look forward to hearing back from some of you about this opportunity.

1/13/05 There will be Help Sessions Mon-Thu 7:30 - 9:00 pm in STE 334, starting date TBA.  Note--this is in St. Eds, and NOT in the hall our class is in.
1/13/05 There will be a trig review--Date TBA
1/13/05 There will be a Maple help session if you would like help with the first lab.  Time/location TBA
8/31/04 Some of the interactive material in the Visual Calculus modules uses ActiveMath, which does not work under Internet explorer.  There is a way to see/use the activemath notebooks.  To start with, you need to be running under Netscape, not Internet Explorer.  If you don't have Netscape, you can down load it for free here:  (choose the full install when prompted)

You also need the LiveMath Plug-in for netscape.  You can download it free here:  (click on the icon for "Windows for Netscape based browsers", assuming you are running some version of Windows).  You only need the freeware--you don't have to buy anything!

CAVEAT:  This worked for me, but comes with no guarantees--it may or may not work with the way your computer is configured.  The helpdesk does not in general support netscape--if you have a problem, you can ask, and they may be able to help you, but DO NOT hassle them if they can't.

PLEASE, PLEASE:  If you happen to be one of the folks that is able to get this to work,  please, please share your resources with classmates you may not be able to.  Thank you!



Some career resources:

Lots of people with exciting real jobs using Math, More people using Math,  Job Listing Services, Comprehensive resources from SIAM, AWM Career resource site.

The department has (in George's office) a CD-ROM and videotape entitled Careers in Mathematics created by three major professional societies of mathematicians (AMS, MAA, and SIAM).  He also has video tapes of a panel and presentation by recent SMC math alums.

There is also this note from George:

"This summer I have been in contact with a number of St. Michael's mathematics alumni in a wide variety of careers, in such areas as statistical data analysis, actuarial consulting, software engineering and other computer-related fields, education (at the secondary and university levels), and even flying (specifically as a USAF pilot). These alumni are willing to be resource/contact people representing a variety of careers. If you wish to be in contact with an SMC alumnus from a particular mathematics-related field, then let me know and I will try to connect you with an appropriate person. I recently have given a few of my advisees e-mail addresses of mathematics alumni who are pursuing careers in an area of interest to them, and could do a similar service for any of you that are interested."


9/11/02 Note:  Be sure to click on "refresh" when you open these pages to be sure you get the most current postings.
1/10/02 The postings on this site have all been tested and all work.  If you have any difficulty getting material off this site, you can try any of the following:

1.  See if someone in your study group was able to print the file you want and make a photocopy of it.

2.  Try using one of the lab computers in case the problem is with how your own computer is configured.

3.  Using Explorer, right click on the link, select "save target as", then save the file to your home computer.  You should be able to open and print it from there.

4.  Contact Cynthia Kelley at 654-2756 or  She is the person for website trouble shooting.


The Student Resource Center runs excellent workshops every semester on study skills, time management, test-taking techniques, etc.  For details:   SRC study skills