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\centerline{Mathematics 126 -- Calculus for Social Science 2}
\centerline{Things to Know -- Final Exam}
\centerline{December 3, 2001}
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\noindent
{\it General Information}
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\item{$\bullet$} The final exam will be given in our regular
classroom 8:30am - 11:30am on Friday, December 7.  
\item{$\bullet$} This will be a {\it comprehensive exam} -- it will
cover all of the material from Chapters 6-10 of the text
that we have studied this semester.  See the
detailed list of topics below.
\item{$\bullet$} The final will be similar in format to the 
three full period midterm exams, but roughly twice as long.
\item{$\bullet$} If you are well prepared and work steadily, it
should be possible to complete the exam in about 2 hours.  But you
will have the full-three hour period to work on the exam if 
you need that much time.
\item{$\bullet$} If there is interest, we could try to set up 
a review session during study week.
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\noindent
{\it Topics to Be Covered}
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\item{1)} Antiderivatives by basic formulas like power rule, rule for
exponentials, etc.
\item{2)} Antiderivatives by substitution
\item{3)} Applied problems where you need to compute an antiderivative
and use it to answer another question (for instance, Section 6.1,/68, 69,
Section 6.2/55, 57, etc.)
\item{4)} Definite integrals -- be prepared to do a Riemann sum calculation
with a small number of subintervals (say $n = 4,5$), for 
a relatively simple function
\item{5)} The Fundamental Theorem of Calculus -- know a precise statement
of this.  I will not ask for the full proof/justification we did
in class, though.
\item{6)} Applications of definite integrals to average values of functions,
area between curves.
\item{7)} Present and Future Value of income streams -- know how 
to compute these with integrals in cases where the rate of 
income generation varies with time (not just the "annuity" formulas
on pages 526 and 527, which assume a constant payment in each
time period). The integral(s) might require the technique of integration
by parts to evaluate. 
\item{8)} Integration by parts 
\item{9)} Integration with a table.  Some of these
will require some algebra, and/or a preliminary substitution before
the appropriate table entry can be identified.  I will make copies of 
the table of integrals from the text and distribute them with the 
exam sheet.
\item{10)} Numerical integration.  Know how to use the 
Trapezoidal and Simpson's Rules to compute approximations to integrals,
also know how to use the ``error bounds'' given in the box on page 576 
of the text.  (I'll put the formulas from page 576 on the sheet
with the table of integrals, so you won't need to memorize them.)
\item{11)} Improper integrals
\item{12)} Differential equations.  Know
how to verify that given functions are 
solutions of differential equations, general solutions, particular
solutions satisfying given initial conditions.
\item{13)} Separable differential equations.  Know how
to solve by separation of variables and integration.
\item{14)} Applications of separable differential equations --
\item{15)} Probability distributions of random variables (density functions) --
\item{16)} Expected value and standard deviation 
\item{17)} Normal distributions and applications  (I will provide a copy of
the table of values of the function $F(z) = P(Z <= z)$
for the standard normal $Z$ -- mean 0, standard deviation 1 --
from pages 900-901 of the text)
for you to use on the exam.  You should know the transformation
formula for converting a normally distributed random variable with
a different mean and standard deviation to the standard one.)
\item{18)} Functions of several variables, level curves, etc.  
\item{19)} Partial derivatives.  
\item{20)} Finding maxima/minima of functions of two variables -- 
critical points, the second derivative test, applied story problems.
\item{21)} Constrained max/min problems and the method of Lagrange
Multipliers.
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\noindent
{\it Suggestions on How to Study}
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\item{A)}  Reread your class notes and work through the 
examples we did in class -- everything on the final 
will be very close to something we did along the way somewhere!
\item{B)}  Also look at your graded problem sets and the
write-ups from the group discussion days. 
\item{C)}  Look over your quizzes and exams, especially any 
questions you had difficulty with.  Read the comments and 
corrections -- they're there to help you figure out what you 
did wrong and how to solve the problem correctly.  Consult the 
review sheets for the 3 exams for practice problems.  (The
3 review sheets are posted on the course homepage if you 
have misplaced your copies.)
{\it Everything on the final 
will be very close to something we did along the way somewhere!}
\item{D)}  Look over the practice exams for the three full-period
midterms.
\item{E)}  Don't panic!  There is a lot of material here, but 
not all that many key ideas. 
\bye    
