%{\begin{center}
%\Large \bf Lab Projects \\
%\end{center}
\chapter*{Lab Projects for Ma113}
\vspace{1cm}
 

\index{ Lab projects} Lab projects are generally stated as a  
topic of investigation rather then as  a specific exercise. You are required to 
perform a detailed analysis of the problem. This will include: setting up the 
problem, making a labeled diagram of the problem with information 
acquired, performing the  necessary calculations and visually displaying the 
results (usually as graphs of functions).  You must then organize this 
information into a  full  written report. 

Lab projects are done by \index{ collaborative groups} collaborative groups of three or four students who 
are expected to organize themselves,  do the work, and prepare the report as 
a group.  Each person in the group must sign the final report and be aware 
that in doing so he or she is guaranteeing that everyone who signed has 
done his or her fair share of the work.  This does not mean that everyone did 
exactly the same number of tasks, spent the same amount of time, etc. It may 
well be the case that one member of the group provides the majority of the 
ideas, another provides the organization and direction, and another actually 
prepares the "write-up".  It does mean  that each person who signs the final 
report is personally satisfied that every author contributed in fair measure 
{\em and fully understands the report}.  

The reports will be  graded with each student in the group receiving the  
group grade.  The grade may be determined either by the written report 
alone 
or in  equal measure by an oral presentation by a randomly selected
 member of the group.  Report grading will be on correctness,
completeness, correct \index{ English} English,  demonstration of understanding of the
problem and solution, and style. Bonus points may be given for originality.

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 The following are  general \index{ guidelines} guidelines and expectations:
 
\vspace{.5cm}

\subsection{The Lab Session:}

\begin{itemize}
\item Get started immediately.  You will not be able to complete the project 
all in the last minute.  Do not waste this valuable time. 
\item Read over the laboratory material carefully before you begin 
discussing or completing any part of it. This should  be done before the lab 
sessions designated for this activity. Give some advanced thought to what 
you are going to do and the anticipated form of the report you are going to 
prepare.
\item Initially you may have some trouble getting started.  Don't panic, a 
discussion with your group partners will usually generate some ideas.  Your 
TA can also give you a `push' in the right direction. There will likely be a 
general discussion on the problem in lecture. Your TA may also be able to 
make suggestions as to how to organize your efforts. 
\item The generality of projects  like these tend to make them quite different 
from the standard "exercises" of the homework.  You will need to make 
assumptions to simplify the problem.  Be sure to discuss such assumptions 
in detail in your final write-up.\\
\item Plan on spending some time outside of lab on  the report. In particular, 
plan on writing the final report outside of class.
\item  Your TA will be happy to go over  complete drafts of your final 
report with you if they are ready at least two days before the submission 
deadline. He or she will then be able to point out areas of concern and make 
suggestions on improving the final submission.

\end{itemize}

\subsection{ The Lab Report:}

The report should be readable by anyone who can understand the 
mathematics with no reference to any other source It must at least 
have the following identifiable features:

\begin{enumerate}

\item {\bf A \index{ Cover Page} Cover Page } signed by each member of 
the team
which produced the report.
A signature on a report
means that each person signing attests to the
fact that each contributed approximately
equally to the work. Each member of the team is 
responsible
for any errors; each member of the team may be 
asked to
explain any detail of a report.


\item A {\bf complete statement of the problem}

\item  An {\bf  analysis} of the problem, complete
with carefully drawn sketch which  contains a 
complete
explanation of the solution, derives and explains
all equations  and  sets  up all calculations
that need to be done. This may be done as part of a 
\index{ Maple worksheet} Maple worksheet and should contain carefully annotated 
graphs
of the pertinent functions.  This is the most 
important part
of the report. 

\item {\bf Details of the calculations} (this can 
be an annotated
Maple worksheet. It must be clear to the reader 
what each calculation
is intended to do. This can be done with comments.
 
The report should be free of any extraneous
calculations. Do not include any intermediate 
calculations unless you need to refer to them or 
you feel that their presence makes the report 
easier to read.

Most of the graphs will be in this section.
It should be clear to the reader why one doing a 
certain graph 
before it is actually done. This can be done with a 
comment.
Features of importance on a graph should be labeled 
and interpreted
either on the graph itself or immediately following 
it. For instance the axes of all graphs should be labeled and a 
caption provided  for each graph which explains its purpose. This labeling 
can be done by  hand on computer-generated drawings. The function(s) 
being  graphed  should be in the \index{ caption} caption or penciled on the graph.

\item {\bf \index{ Conclusions} Conclusions and \index{ interpretations} interpretations }. 
At the  very least this should briefly explain how 
what
has been done answers the original question or 
solves
the original problem. If appropriate, it should 
refer back
to graphs and relate features of the graphs to 
numerical
calculations.  Finally, there should be a 
summary paragraph or sentence describing what has been accomplished and 
(possibly) suggesting directions for further study.
problem(s).


\end{enumerate} 


A good report will not be very long - probably 
three to five typed pages, excluding graphs. 

The report should be free of any extraneous
calculations (e.g. material that should have been
cut out of a worksheet.)

 
Finally, there should be a 
summary paragraph or sentence describing what has been accomplished and 
(possibly) suggesting directions for further study.
problem(s).

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