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\centerline{Mathematics 36, section 5 -- AP Calculus}
\centerline{Information on Final Exam}
\centerline{December 6, 1999}
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\noindent
{\bf Background}
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The final exam for this section of AP Analysis will be given {\it at 
8:30 a.m. on Saturday, December 11, in
our regular classroom -- Beaven 118\/}. The exam will be comprehensive,
covering all the material we have studied since the beginning of the 
semester.  I will write the exam to be roughly twice the length of the 
in-class midterms.  However, you will have the full three-hour
period 8:30 - 11:30 a.m. to work on the exam if you need that much time.
The questions will be similar to those on the 3 inclass exams. 
I may include some questions asking for definitions
of terms or statements of theorems. 
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\noindent
{\bf Topics to be Covered}
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\item{1)}  Functions defined by graphs, tables, formulas,
the ``library of functions''
\item{2)}  Derivatives (know the definition):  know how to sketch 
the graph of the derivative of a function defined by a graph, 
how to approximate values of the derivative given a table for the 
function, how to use the derivative rules on functions defined by 
formulas.  
\item{3)}  The meaning of the signs of $f'(x), f''(x)$.  
\item{4)}  Differentiability = local linearity, tangent lines, 
etc.
\item{5)} Taylor polynomials, approximations, the error bound
\item{6)} Taylor series, 
\item{7)} Total change of a function, Riemann sums, the definite
integral (know the definition), antiderivatives
\item{8)} The Fundamental Theorem of Calculus, and
\item{9)} Integration by substitution, by parts, using the 
table.  A copy of the table of integrals
from the text will be provided with the exam; any integral you 
need to compute will be do-able by some combination of substitution, 
integration by parts, and/or consultation with the table).  
\item{10)}  Applications of integration (setting up problems via
Riemann sums; in limit a definite integral is obtained) -- volumes
by slices, arclengths, physical examples like work, mass from
non-constant density functions, etc.
\item{11)}  Differential equations -- slope fields and solutions
\item{12)}  Solving differential equations via separation of variables
and integration, including population growth models. 
\item{13)}  Parametric curves.
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{\bf Suggestion on How to Study}
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Begin by reviewing the class notes and the discussion write-ups 
and lab reports from 
your groups' work.  Look at the in-class midterm problems and try to 
work out solutions for those again, without refering to your previous
work.  Look over some of the problems from the text from the 
previous review sheets.  Then take a couple of hours and try the practice
exam problems below.
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\input PracticeFinal.tex
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