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%  Midterm 1 for the course "Calculus (I)", 
%  Spring semester, 2013, Wei-Cheng Wang.


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\noindent
{\scriptsize Calculus II, Spring 2014} \hfill 

\begin{center}
\large
Guide to Midterm Exam 1
\normalsize
\end{center}

\noindent
%Oct 20 2011, 10:10AM  
Review all your homework problems and quizzes.
Then check the following topics and ask yourself if you understand them.
If not sure,
you can find related examples from your
class note and/or homework problems and practice them.

% \vspace{.3in}

%           The questions!

% \noindent
\vspace{.5cm}

\begin{enumerate}

\item
Review section 9.2, study procedure of solving first order 
linear differential equations.

\item 
Study
integral test, ratio test, root test, Leibniz test and their proof.
Makeup a few examples for each test.

\item 
Study the statement of Taylor's Theorem (formula) and its proof.

\item 
Clarify the relation between a function and its Taylor series.
For example,  
how do you generate a Taylor series from a given function?
when and where does a function equal
the Taylor series it generates?
Examples?

\item 
Memorize Taylor series of basic functions on page 620.
Then perform differentiation/integration on them and see
if you can recognize them from the resulting
new series. 
Also study the multiplication of two Taylor series.

\item 
Review the application of Taylor series in approximating 
integrals and the error estimate.

\item 
Review calculus of parametrized curves, including slope of 
a parametrized curve, higher order derivatives, and application
in surface of revolution and polar coordinates.
\end{enumerate}

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