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\centerline{Mathematics 136, section 4 -- AP Calculus}
\centerline{Information on Final Exam}
\centerline{December 9, 2003}
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\noindent
{\it Background}
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The final exam for this section of AP Calculus will be given {\it at 
8:30 a.m. on Friday, December 19, in
our regular classroom -- Swords 302\/}. The exam will be comprehensive,
covering all the material we have studied since the beginning of the 
semester.  In addition to the material covered on the three midterms,
this includes the topics of Taylor polynomials and Taylor series
from the last week.

 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 in-class exams. 
I may include some questions asking for definitions
of terms or statements of theorems. 
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\noindent
{\it 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)} Total change of a function, Riemann sums, the definite
integral (know the definition), antiderivatives
\item{6)} The Fundamental Theorem of Calculus, and
\item{7)} 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{8)}  Applications of integration (setting up problems via
Riemann sums; in limit a definite integral is obtained) -- volumes
by slices, arclengths, physical examples like mass from
non-constant density functions, center of mass of a wire.
\item{9)}  Differential equations -- slope fields and solutions
\item{10)}  Solving differential equations via separation of variables
and integration, including population growth models. 
\item{11)}  Geometric series, power series and the Ratio Test
for the interval of convergence
\item{12)} Taylor series, Taylor polynomials, approximations
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\noindent
{\it Suggestion on How to Study}
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Begin by reviewing the class notes.  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, and the following problems for items
11 and 12 above:  p. 410/1-14, p. 428/11-21; p. 440/1,3,5,7,11,13;
p. 451/1,3,5,6,9.  Also be sure you understand how you can 
use a Taylor polynomial to approximate a value of a function
at an $x$ close to the $a$ used to construct the polynomial.
Then take a couple of hours and try the practice
exam problems below.
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{\it Practice Exam}
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\input PracticeFinal.tex

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{\it Review Session}
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I will be happy to run an evening review session for the 
final during exam week if there is interest. 
We can discuss this in class on Tuesday, December 9.
\bye  

