\magnification=\magstep1
\overfullrule=0pt
\centerline{Mathematics 134 -- Intensive Calculus for Science 2}
\centerline{Things to Know -- Final Exam}
\centerline{April 30, 2001}
\bigskip
\noindent
{\it General Information}
\bigskip
\item{$\bullet$} The final exam will be given in our regular
class room 8:30am - 11:30am on Saturday, May 5.  
\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 {\it 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 can up a daytime or
evening review session during study week.  I am not free 
Thursday evening, but most other times are possible.
\bigskip
\noindent
{\it Topics to Be Covered}
\bigskip
\item{1)}  The Fundamental Theorem of Calculus:  If $F(x)$
is an antiderivative of a continuous function $f(x)$ on $[a,b]$, then 
$$\int_a^b f(x)\ dx = F(b) - F(a)$$
\item{2)}  Antiderivatives graphically and numerically
\item{3)}  The power, sum, and constant multiple rules for antiderivatives
\item{4)}  Indefinite integrals by substitution, parts
and using the table of integrals
\item{5)}  Improper integrals (integrals over infinite intervals,
and integrals of functions with discontinuities in the interval 
$[a,b]$) -- be able to identify which kind of improper integral
you have, and set up the appropriate limits to evaluate them/determine
whether they converge or not
\item{6)}  Integrals for computing volumes of solids with known 
cross-sections:  $V = \int_a^b A(x)\ dx$, where $A(x)$ is the 
cross-section area function. Volumes of solids of revolution are 
a special case of this.
\item{7)}  Integrals for computing total mass/center of mass of
wires and plates of given shapes, given the mass density function
\item{8)}  Density functions of distributions, cumulative 
distribution function, median, mean.
\item{9)}  Taylor polynomials and Taylor approximations
\item{10)}  Taylor series and interval of convergence
\item{11)}  ``Shortcuts'' (substitution, algebraic
manipulations, term-by-term integration and differentiation)
for computing Taylor series from 
the known series for 
$$e^x,\ \sin(x),\ \cos(x),\ {1\over (1-x)},\ (1+x)^p.$$
\item{12)}  Differential equations 
\itemitem{a)}  What it means for a function to be a solution of
a differential equation
\itemitem{b)}  Graphical meaning of solutions via slope fields
\itemitem{c)}  Approximate values of solutions via Euler's Method
\itemitem{d)}  Formulas for solutions via separation of variables
\itemitem{e)}  Applications to growth/decay problems
\bigskip
\noindent
{\it Suggestions on How to Study}
\bigskip
\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)}  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.
\item{C)}  Also look at your graded problem sets and the
write-ups from the group discussion days. 
\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. 
{\it Everything on the final 
will be very close to something we did along the way somewhere!}
\bye    
