Calculus I

First Day Handout Homework Homework hints

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Maple Labs

In Class Demos

Notebook Posted Grades Help Sessions

Announcements

12/15/04 Finals have been graded and course letter grades are now available  HERE .  Please let me know if you see any discrepancies.
12/13/04 I will be in my office this evening from 6:30 until about 9:00.

Feel free to come by with any questions.

12/13/04 I have graded everything except lab 6 and chpt 4 challenge problems.  You may come by to pick up the other stuff at my office anytime before 1:30 this afternoon.  I will post grades just as soon as I finish the final lab and challenge problems.  There are some assignments without names,  so it would be very helpful if folks would come by and pick up homework asap since this will help identify the anonymous work....
  A word about the final exam--  A good performance on the final will often provide convincing evidence of having mastered material that may have been a struggle grade-wise earlier in the course, so that sometimes a good final grade exam may be weighted a little more heavily in computing your course grade.

STUDY TIPS for the final exam.  The final exam will emphasize chapter 5.  You can find a practice test at:  chapter quiz.   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 the following drills: 

(There was a link to a set of drills on integrals on this line previously--they were for u-substitution, which we did not get to, but which will be covered in Calc II)

http://archives.math.utk.edu/visual.calculus/4/integrals.2/index.html (mult choice quiz--skip the substitution problems)

 

http://archives.math.utk.edu/visual.calculus/4/ftc.12/index.html 

http://archives.math.utk.edu/visual.calculus/4/ftc.12/index.html 

 

http://archives.math.utk.edu/visual.calculus/1/vertical.1/index.html

http://archives.math.utk.edu/visual.calculus/1/horizontal.3/index.html 

http://archives.math.utk.edu/visual.calculus/2/quotient_rule.3/index.html 

  http://archives.math.utk.edu/visual.calculus/2/chain_rule.4/index.html 

http://archives.math.utk.edu/visual.calculus/3/implicit.4/index.html 

  http://archives.math.utk.edu/visual.calculus/3/logdiff.1/index.html 

   max/min, derivatives and graphing, identifying functions and derivatives, L'Hopital's drill 1, L'Hopital's drill 2, antiderivatives, and antiderivatives with initial values.

 

You should also practice from the various drills listed for hour test I, II, and III below.

It is too scary (and probably not even possible) to do every problem from every drill--just do one  or two 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

Another excellent source of study problems for the final is: http://academics.smcvt.edu/jellis-monaghan/calc1/homework.html#overview

I am in the process of updating these to the current edition, but there shouldn't be many changes--as usual, purple font indicates updated material.

There will also be a "delta-epsilon" problem, of much the same flavor as # 15 - 18 in section 2.4, a related rate problem (section 3.10), an optimization problem, (section 4.7) a graphing problem (section 4.5) (factored derivatives will be given), and a proof of the derivative of some log or trig function or its inverse.  These 5 questions will be worth more than the multiple choice questions.

NO GRAPHING CALCULATORS!!!  You will be sent out of the exam until you find a non-graphing calculator!

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.

 

 

11/22/03 Hour test three post-practice-- Here are 10 problems for each of the non-proof questions on the test.  If you missed a question on the test, you may recover one point on the test for each one of these problems you complete correctly.  You should anticipate problems VERY similar to these on the final exam.

DUE:  Friday, December 3.

1.  Section 3.5 # 35-44 all

2. http://archives.math.utk.edu/visual.calculus/2/chain_rule.2/index.html 

3.  Section 3.7 # 11-20

4.  http://archives.math.utk.edu/visual.calculus/3/implicit.4/index.html 

5. http://archives.math.utk.edu/visual.calculus/3/logdiff.1/index.html 

6. vc max/min drill

7.  VC MVT drill

8.  quiz 3 

9.  quiz 1, (on #7 there as 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)

10. Sec 3.10 # 8, 10, 12 (3 1/3 points each).

 

11/18/04 A hint for the Maple lab:  Recall that sometimes if the solve command doesn't give you an answer you can use, you can often get what you need from the fsolve command on a specific interval.  For example, if you want to know where x^3 -6*x+4=0, you can first plot it, see roughly where it seems to cross the axis, and then use the fsolve command on these intervals, as in:

fsolve(x^3 -6*x+4=0, x=-4..-1);

11/15/04 The third hour test will be on Wednesday, November 17 (this is a change from the date given in the first day handout).  The test will cover sections 3.3-3.8, 3.10, 4.1-4.3.  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.  There will be questions (proofs) for the derivatives of the trig and inverse trig functions.

Here are a some drills:

VC Lhopital drill

VC Lhopital drill inf limits,

quiz 1, (on #7 there as 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

VC tanlines drill,

VC product rule egs, 

VC quotient rule egs,

http://archives.math.utk.edu/visual.calculus/2/chain_rule.4/index.html 

 http://archives.math.utk.edu/visual.calculus/3/implicit.4/index.html 

 http://archives.math.utk.edu/visual.calculus/3/logdiff.1/index.html 

 

11-3-04 I have the first part of the population projects in my office--you should pick them up from me today or tomorrow to check your work before doing the second part.  NOTE: in the logistic curve part, a couple groups  did estimates just from the Maplet--this isn't sufficient, and certainly isn't sufficient for the actual data part.  You need to use the Maplet to get M, B, and k, and then follow the example in the handout to do the analysis.  I will still accept corrections to the first part if you come get it and fix it ASAP.
10-27-04 PowerPoints from the extra credit talk is at: Mary Cox Talk

Get the video from me.  You should work through at least one example of one of the games in your write up.

10/20/04 Here are some Maplets that might be useful for the population project:  ExponentialGrowth.mws, LimitedGrowth.mws, LogisticGrowth.mws.
10/19/04

Extra Credit Talk

Date:  Tuesday, October 26, 2004

Time:  3:30 � 4:30 pm

Location:  Jeanmarie 391, SMC Campus.

 

Title:  The Continued Fraction in Combinatorial Game Theory

 

Speaker:  Mary Cox, UVM.

 

Abstract: The origin of continued fractions is traditionally placed at the time of the creation of Euclid's Algorithm; in fact, continued fractions are intimately related to Euclid's Algorithm.  In the 19th Century, there was an explosion of growth within this subject, with contributions by Jacobi, Perron, Hermite, Gauss, Cauchy, and Stieljes.  Since the beginning of the 20th Century continued fractions have made their appearance in other fields, including chaos theory, within computer algorithms for computing rational approximations to real numbers, solving indeterminate equations, and knot theory.  Very recently, continued fractions have also been used in the relatively young field of combinatorial game theory.

In this talk, we define the general and simple continued fraction, and give a short demonstration of a traditional number theoretic use -- solving Pell's equation.  We then outline the basics of combinatorial game theory, and then demonstrate the use of continued fractions in this area of mathematics by demonstrating the evaluation of a game of Contorted Fractions.

This talk is accessible to a general audience.

10/18/04 Reminder-- you should be measuring your culture (I think it actually is a yeast...) every day.  This stuff is baker's yeast, Saccaromyces cerevisiae.
10/14/04 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 one or more of the differentiation rules--constant multiple, power, sum, product, quotient.

http://archives.math.utk.edu/visual.calculus/1/horizontal.3/index.html 

 

Also do the examples in the inclass demos that will generate different problems for you, for example at the bottom of http://archives.math.utk.edu/visual.calculus/2/definition.8/index.html , and http://archives.math.utk.edu/visual.calculus/2/formulas.3/8.html 

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

 

10/12/04 EXTRA CREDIT TALKS!

As part of the President's Distinguished Lecture Series the Departmentof Mathematics and Statistics is pleased to host Ronald Graham.

He will be speaking at

4:00pm Monday October 18th in Angell B106 on the UVM campus.

A reception will follow in Billing's Apse.

Dr. Graham is the current president of the Mathematical Association of America,past president of the American Mathematical Society, and of the International Jugglers Association. He is in the Guinness Book of World Records for the largest number ever used in a mathematical proof,and in Ripley's Believe it or Not for his skills as a trampolinist and juggler.

For more details on Dr. Graham see: http://www.math.ucsd.edu/~fan/ron/

Title: Searching for the shortest network

Abstract: There are many situations in which one would like to connect a collection of points together by a network having the minimum possible total length. Such problems occur in the design of telephone networks, railroad lines, oil and gas pipeline networks, heating and air-conditioning duct systems, the layout of VLSI chips, and the inference of evolutionary pathways for living organisms, for example. In this talk we give a summary of what is known (and unknown) about this classical problem, and how current developments in computer science have impacted it.

If you only go to one math talk this year, this should be it!

There is also a second, earlier, talk:

Archimedes, Combinatorics and the Stomachion

Professor Ron Graham

University of California at San Diego

Monday, October 18, 2004

2:30-3:20 PM

Room L200 Lafayette
Reception to follow in Billings Apse at 5:00pm

Abstract:

Greek mathematics has long been known for its fundamental contributions to geometry and diophantine equations, for example  However, there is now evidence that ancient Greek mathematicians were also interested in various combinatorial problems. In this talk, I will describe some recent work exploring this theme which arose from the analysis of a puzzle called the Stomachion, which was recently discovered in a long lost manuscript of Archimedes.

 

For extra credit on the next test, attend one or both of the talks and write about 2 or 3 paragraphs describing the talk.

Note--if you absolutely cannot make either of these talks, but would like to take advantage of the extra credit, we have a videotape of one of Ron Graham's lectures at the library, and you can base your write up on that.  Call Number: VTC 2421 to get the video from the library.
 

10/12/04 Midterm Project.  This will be handed out in class.  You need to read the whole thing, and then do the material in sections 3.1, 3.2, and 3.3.  Section 3.1 is due October 22.  Section 3.2 is due November 5.  Section 3.3 is due November 19.  Here is a link to IntelPop:  http://simon.cs.vt.edu/geosim/IntlPop/IntlPop.html.  Here is a list of other population data links you may find useful: http://www.census.gov/ipc/www/idbnew.html 
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 
9/27/04 NOTE NEW LOCATION FOR HELP SESSIONS:  They will meet in STE 106 starting Wed, Sept. 29 (same times--7:30 to 9:00 pm MTWTh).
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 http://www.skidmore.edu/academics/mcs/hrumc.htm. 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.

2/29/03 The first hour test is scheduled for Tuesday, September 28th.  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 will also be a "delta-epsilon" problem, of much the same flavor as # 19 - 32 in section 2.4.  

Some other good study problems:  http://archives.math.utk.edu/visual.calculus/1/vertical.1/index.html

http://archives.math.utk.edu/visual.calculus/0/symmetry.5/

http://archives.math.utk.edu/visual.calculus/0/domain.1/index.html

http://archives.math.utk.edu/visual.calculus/0/shifting.7/index.html

http://archives.math.utk.edu/visual.calculus/0/shifting.4/index.html

http://archives.math.utk.edu/visual.calculus/0/compositions.4/index.html

http://archives.math.utk.edu/visual.calculus/0/shifting.5/index.html

http://archives.math.utk.edu/visual.calculus/0/shifting.5/index.html

http://archives.math.utk.edu/visual.calculus/1/limits.15/index.html

http://archives.math.utk.edu/visual.calculus/1/definition.8/index.html

http://archives.math.utk.edu/visual.calculus/1/definition.7/index.html

http://archives.math.utk.edu/visual.calculus/1/vertical.1/index.html

http://archives.math.utk.edu/visual.calculus/1/continuous.9/index.html

http://archives.math.utk.edu/visual.calculus/1/continuous.3/index.html

You should also spend some time with the graphical view at http://math.hws.edu/javamath/config_applets/EpsilonDelta.html .

The test will cover sections 1.1 through 2.5, and assumes you have a thorough mastery of the the appendix reviews. 

9/17/04

Dear Math Students,

On Saturday, September 25 the Math Department will hold a very special event � our own celebration of the Centennial.

There will be a talk, an honor society induction and a Career Panel � as well as birthday cake to celebrate 100 years of Math at SMC.

A number of Math alums are coming from far and wide to connect with you, our current students � who will follow in their footsteps.

This is a great opportunity to network with alums working in a variety of areas (see below!) � and to learn about applications of math.

This is really an exciting program that should be of special interest to you --let�s have a great turnout on September 25th!

And please invite your friends -- and family if they are visiting.

Zsu Kadas and the Math Faculty

9/15/04

Academic Internships!

Academic interships are a great way for students to strengthen their r�sum�s, increase their marketability and test the career waters.

The academic intership office holds informational meetings in September for Spring internships and in January for Fall internships. This semester�s meetings will be held on September 20, 21, 22, and 23 from 11:45 � 12:15 in Jeanmarie 376. Joanne LaBrake is available in Klein 114, extension 2314 if you have any questions.

 

9/13/04 There will be Help Sessions Mon-Thu 7:30 - 9:00 pm in STE 334, starting Mon, Sept 13.  Note--this is in St. Eds, and NOT in the hall our class is in.
9/9/04 Notes from review session: review9-9-04.pdf, review9-9-04.xbk
9/7/04 There will be a trig review on thursday, september 9 from 7 to 8 pm in JEM 364 (usual MWF classroom).
9/6/04 Please redo the Calculus warmup activity for Wednesday, Sept. 8.
9/6/04 There will be a Maple help session in JEM 142 Monday, Sept 6 from 9-10 pm if you would like help with the first lab.
9/3/04 http://www.cvfair.com/   A link to the fair!
9/3/04 Note:  Append. B,  has been added to the homework due Friday 9/6/04.
9/1/04 Note:  Append. A, 13-37 odd, 47-55 odd  has been added to the homework due Friday 9/3/04.
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:  http://www.netscape.com/download/  (choose the full install when prompted)

You also need the LiveMath Plug-in for netscape.  You can download it free here: http://www.livemath.com/download/  (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!

 

8/27/04 You may order a personal copy of Maple 9.5 at a discounted price of $75 if you wish:  Secure ordering address: http://webstore.maplesoft.com Promotion Code: AD1111

10/30/03

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 ckelley2@smcvt.edu.  She is the person for website trouble shooting.

1/28/00 Click Here for info on how to be notified automatically of any new changes to this website (how to subscribe to the site).
1/16/00

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