Calculus III

First Day Handout

Calc III study probs

Calc III challenge probs

Class List

Midterm Rockets and Maple Labs

In Class Demos


Posted Grades

Help Sessions 



5/1/04 All homeworks etc. have been graded and are in the folder holder outside my office for you.  Pre-final grades should be posted very shortly.
4/15/04 The revised Maple Lab 4 is now posted.  Omit the problems from 16.5 and 16.7 from the challenge problems.
4/5/04 Hour test correction:

no. 5.  It should be spherical, not polar, coordinates.

3/24/04 Maple lab 2 revisions are due Wednesday, April 7.
3/23/04 Additional extra credit talks:  You should begin receiving Senior seminar announcements soon by email.  These are usually held Wednesdays from 2:30 to 3:30.  To get credit, attend, and write a 2 or 3 paragraph synopsis of the talk.  The nice thing here is that the speakers are other students so, A) the talks will be more accessible, and B) if not, they live here so you can ask questions easily.
3/23/04 Hour test:  The third hour test will be on Tuesday, March 30, from 4 to 6 in JEM 373 (next door to our usual classroom).  It will cover 15.1 through 15.8 (not 15.9).  Remember that on-line Drills available Here!!  These are from the 5th edition of the book (we have the 4rth), so the chapter numbers may be off.  The content is basically the same.  There is also a triple integral maplet in the In Class Demos that would provide very good practice.

The Maple lab and challenge problems will be due Monday, April 5.  Omit 3.5 and 3.6 from the Maple lab, and 15.9 #20 from the challenge problems.  Remember that doing the lab and challenge problems ahead of time will help you prepare for the hour test as well.


EXTRA CREDIT TALK  OVERHEADS: Rectangle Visibility Graphs-


Date: Monday, March 22, 2004           

Time: 2:30 - 3:30 p.m.  

Location:  Science 111, St. Michaels campus


Title: Rectangle Visibility Graphs:  Characterization,

     Construction,  and Compaction


Speaker: Sue Whitesides , department of computer science, McGill University


Abstract: Non-overlapping axis-aligned rectangles in the plane define

  visibility graphs in which vertices are associated with

  rectangles and edges are associated with visibility in either

  the horizontal or vertical direction. The recognition problem

  for such graphs is known to be NP-complete.


  This talk introduces the notion of a “topological rectangle

  visibility graph”.  This notion is designed to capture more

  precise visibility information from sets of axis-aligned

  rectangles than does the usual notion of a rectangle visibility

  graph.  We give a combinatorial characterization of topological

  rectangle visibility graphs that are indeed realizable as sets

  of axis-aligned rectangles.  Our characterization gives rise to

  a polynomial time algorithm for recognizing topological

  visibility graphs that are realizable, and in the case of

  realizable graphs, for constructing a realizing set of

  rectangles on the unit grid.  The bounding box of these

  rectangles has optimum length in each dimension.


  Our algorithm provides a rectangle compaction tool: given a set

  of rectangles, one computes the associated topological

  rectangle visibility graph, and then runs the algorithm to get

  an optimally compact set of rectangles with the same visibility



3/4/04 REMINDER--There will be a graph drawing talk by Sue Whitesides on Monday, March 22 (exact time TBA, but I probably something like 3:30 to 4:30).  This talk is EXTRA-CREDIT.


The second hour test will be on Tuesday, March 2, from 4 to 6 in JEM 373 (next door to our usual classroom).  It will cover 14.1 through 14.7 (no Lagrange multipliers).  Remember that on-line Drills available Here!!  These are from the 5th edition of the book (we have the 4rth), so the chapter numbers may be off.  The content is basically the same.

2/25/04 A revised version of Maple Lab 2 has been posted.  The new due date, for both the Maple Lab and the challenge problems for Chapter 14 is March 12.
2/19/04 Grades to date have been posted.  Please check them for accuracy.  Also, since the rocket project is now extra credit, there is a new grading breakdown:

Regular homework --15%, Challenge problems --20%, Maple Labs--20%,  

hour test average --25%, final exam--20%.


The next two hour tests will be on Tuesday 3/2 and Tuesday 3/30 at 4:00, in JEM 373 (NOTE this is not our usual room!!).

2/19/04 Here are the Maple intro solutions:

calc3/labs/Maple Intro Calc III part 1 ans.mws

calc3/labs/Maple Intro Calc III part 2 ans.mws

calc3/labs/Maple Intro Calc III part 3 ans.mws

calc3/labs/Maple Intro Calc III part 4 ans.mws

2/17/04 I do have to report for Jury Duty tomorrow, so class is canceled Wed, 2/18.  Please check this site in the remote chance that I am selected to serve  on cases scheduled for the 19th or 20th.(Assume there will be class on those dates unless there is an announcement posted here.)  We will discuss options to compensate for this missed class and the one cancelled due to illness on 2/9/04.
2/8/04 Class is cancelled tomorrow (Monday, 2/9/04).  Please continue to work on your own and with one another on the Maple Intro's below.


Here is the “crash course” in Maple you asked for.  Please work through these by Feb 16 and turn in the exercises then.  Keep them handy as references for the homework and future labs.

Maple Intro Calc III part 1--Basics,

Maple Intro Calc III part 2--Graphing,

Maple Intro Calc III part 3—Diff and Int,

Maple Intro Calc III part 4--Vectors


Here are the overheads from Jeff Dinitz' talk: Overheads


Here is the abstract for the

Required Talk


Date: Monday, February 9, 2004         

Time:  2:30 -3:30 p.m. 

Location:  Science 111, St. Michaels campus


Title: Polygonal knot theory and stuck unknots



Speaker: Heather Johnston, department of mathematics, Vassar College


Abstract:   Although knot theory has been studied for over 100 years,

polygonal knot theory and its combinatorial approach began in the

1990's.  We fix the length and number of edges of a polygon in

three-space and model each configuration as a set of rigid sticks

joined by very flexible hinges.   Those configurations that cannot be

moved into a convex planar configuration are called stuck.  We are

interested in those stuck polygons that are stuck only due to the

rigidity of the sticks.  For a stuck unknot the same configuration

could be unravelled if it were made of string rather than sticks.  We

will prove the existence of stuck unknots and discuss their

classification, which is still a work in progress.





The challenge problems from chapter 12 will be due Wed, Feb 4 as originally scheduled.  The challenge problems from chapter 13 will be due Mon, Feb 9.


The first hour test will be on Thursday, February 5.  It will cover 12.1 through 13.3.  Here is a practice test with solutions (it may have one or two questions from 13.4 on it): pg1 , pg2pg3  pg4. In addition to the practice test, On-line Drills available Here!!



!! Required Talk !!

Going to talks to learn about cutting edge developments in mathematics in an integral part of being a working mathematician.  There will be three such talks for this course, all on SCI 111, on the following Mondays:  Feb 2, Feb 9, and Mar 22.  The first two will be from 2:30 to 3:30.

The talks on Feb 2 and Mar 22 are optional--extra credit is available if you do attend however.

The talk on Feb 9, which will be on knot theory,  is Required !

To compensate for the time, and to allow a little extra time for the rocket project,  we will not meet for normal class on Friday, March 5 or Monday, March 8.

Here is the abstract for the first talk:

Title: Generating uniform and perfect one-factorizations from starters

 Speaker:  Jeff Dinitz, department of mathematics, UVM

 Abstract:   A one-factorization is uniform if the union of any two one-factors give isomorphic 2-regular graphs.  It is perfect if this union is always a Hamiltonian circuit.  In this talk we will discuss how to construct such one-factorizations using elementary properties of finite fields.  This is joint work with Peter Dukes at the University of Toronto and is a current work in progress.


Tweetle Beetles


I just added two new links above, one for applications of abstract algebra (the first two links in in are good Hudson River possibilities), and one that is a direct link to the computer exercises that accompany our text.


!!Hudson River Talks!!  

Please consider participating in the Hudson River Undergraduate Conference--talk to me about topic possibilities ASAP if you are even remotely interested.   This is a lot of fun, and it is exciting to do the exploration leading up to the talk.  Extra credit may be negotiated.  You can see some previous year's talks at student talks. More information about the event (including deadlines) is at


STUDENT SUMMER RESEARCH INTERNSHIPS AVAILABLE  (Second round opportunities--I think the deadline is something like Feb 17.)

Summer Research Opportunity--$3500 plus $1000 in supplies for May 15 - June 30.  I would be thrilled down to my toes to help you come up with a project and be your advisor.  Returning students only.


If you find you are a little rusty after the summer, here are some review suggestions.

For calc I, see . Under announcements, look at the study guide for the final. There are lots of drill and practices. Anything you don't understand, go to the inclass demos for review. For Calc II, the techniques of integration, polar coordinates, and parameterized functions are VERY important, but the sequences and series stuff is less so. A good integration review can be found at .


A note from math dept chair Jim H:

Welcome back and hello,

For many years we've run math help sessions at night. These provide a chance for students in calculus classes, or in the 101 and 102 classes, to get somy help with their material on a drop-in basis. These sessions are staffed by students, so this is where you come in!

Are you interested in working one or two? We always pair people up, so you won't be lonely, and we get many people who have done it before that come back again, so it must be fun. If you have had through Calc III, and would be interested in making a little extra money (I am told, about $7-$8 per hour), working one or two nights in a one-on-one or small group setting, then I'd like to hear from you. Tell me what classes you've had, please, and what nights you could work.

Also, we are looking for folks who might be interested in grading homeworks or quizzes. You work with a faculty member, again in conjunction with a calculus, or 101, or 102 class. You will be grading quizzes or homework papers, following the instructions of the course instructor. If you are interested in this, please also write and tell me which classes you've had.

Thanks, Jim Hefferon. 


Be sure to click 'refresh' when you visit this site to be sure you get the most recent changes.


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


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.