\magnification=\magstep1
\centerline{Mathematics 131, section 1 -- Calculus for Physical and 
Life Sciences, 1}
\centerline{Information on Final Examination}
\centerline{December 6, 2004}
\bigskip
\noindent
{\it General Information}
\bigskip
\item{$\bullet$}  The final examination for this class will be
given during the scheduled period 2:30 to 5:30pm on Monday, December 13.
\item{$\bullet$}  Unlike the midterms, this one will be given
in our regular classroom, Swords 328, and each MATH 131 section 
will be getting a separate final exam.
\item{$\bullet$}  The final will be similar in format to the 
midterm exams but perhaps 1.75 times as long.  I expect that
if you are well prepared and you work steadily, then you should 
be able to finish the exam in 2 hours.  However, you will have 
the full 3 hour period to work on the exam if you need that 
much time.
\item{$\bullet$}  As on the midterm, a basic scientific
(non-graphing) calculator will be provided for ``number crunching.''
\item{$\bullet$}  No cell-phones, computers, or other electronic
devices may be used during the exam.  Please do not bring them
with you; they will be subject to confiscation for the period
of the exam if you use them. 
\item{$\bullet$} If there is interest, we could arrange
a review session during the reading period (Wednesday, December 8
through Friday, December 10).  We can discuss this in 
class on Monday, December 6.  
\item{$\bullet$} I will also be available during regular
office hours for questions as you prepare.
\bigskip
\noindent
{\it Topics to be Covered}
\bigskip
\item{$\bullet$}  This will be a {\it comprehensive} final -- 
it will cover all the topics we have studied this semester,
with roughly equal weight given to the three sections of the 
course.  In addition, you should expect a question on
the material on the definite integral (Chapter 5 in the text)
that we studied the past two weeks.  
\item{$\bullet$}  See the review sheets for the three midterms
for a detailed breakdown of the topics we studied earlier.
Those review sheets are now reposted on the course homepage
if you need another copy of any of them.
\item{$\bullet$}  The topics not covered on the previous
exams are:
\itemitem{1.}  Computing total distance from velocity (Section 5.1).
This is the motivation for the introduction of the left- and right-hand
sums and the integral.  
\itemitem{2.}  Definition of the definite integral (Section 5.2).
You should know how to compute left- and right-hand sums for 
basic functions on intervals using a small number of subdivisions
(say $n \le 5$).  
\itemitem{3.}  Interpretations of the definite integral (Section 5.3):  
Integral of rate of change of $f$ gives total change of $f$:
$$\int_a^b f'(t)\ dt = f(b) - f(a),$$
(one version of the Fundamental Theorem of Calculus), 
the integral as signed area, integrals for average values:
$$\overline{y} = {1\over b - a} \int_a^b f(x)\ dx$$
\item{$\bullet$}  Some good practice problems on these
topics:  Section 5.3/3, 11, 13, 27.  Chapter 5 Review:  1, 3, 5, questions like 9-13
(on these, first write an integral that would compute the areas described,
then approximate that integral with left- and right-hand sums), 17.
\bigskip
\noindent
{\it Suggestions on How To Prepare}
\bigskip
\item{$\bullet$}  Get started reviewing early
and do some work on this {\it every day} between now and the date of the final.
Don't try to ``cram'' at the end.  There's a lot of stuff
that you need to know!
\item{$\bullet$}  Go over your corrected problem sets
and the midterm exams with the solutions.  If 
there were questions where you lost a lot 
of points, be sure you understand why what you did was not
correct, and how to solve those questions. 
\item{$\bullet$}  Reread your class notes in addition to the
text, especially
for topics where you lost points on the midterms.  There are a lot of 
worked-out examples and discussions of all of the topics
we have covered there.
\item{$\bullet$}  Be sure you actually do 
enough practice problems so that you have the 
facility to solve exam-type questions in a limited
amount of time.   {\it Even if you 
have saved solutions for practice problems from the midterms},
it is going to be much more beneficial to do practice problems
starting ``from scratch'' rather than just reading old
solutions.  Remember, the goal of the course is to get
you to be able to develop solutions to these problems
yourselves, not just to understand solutions that someone
else (that includes you, one or more months ago!) has written down.  
Another analogy -- as most of you know from your study
of languages, it's much easier to understand 
another language passively than it is to actually 
use a language actively yourself (for instance, to form your
own complete, grammatically correct sentences).  
The goal of this course is to make you reasonably
proficient ``calculus speakers'' and there's no substitute
for active practice on those skills.
\bye
  
