\documentclass[11pt]{article}
\usepackage{fullpage}

\begin{document}
\title{Engineering and Science Mathematics 1A}
\author{Review for Final Exam}
\date{Exam date: Monday, December 13, 2010 from 12:30--14:30}
\maketitle

\begin{enumerate}

\item Limits, one-sided limits.  Like on the first midterm exam.
  L'H\^opital's rule or Taylor series might help, but are not
  essential if you know the basic trigonometric limits.

\item Continuity: When is a function continuous, can a discontinuous
function be extended to be continuous?  Intermediate value property.

\item Derivative: Definition, differentiation rules, be able to
  compute a Taylor polynomial of a given function.

\item Applied minimax problems.

\item Curve sketching:  Domain and range of a function, horizontal and
  vertical asymptotes.  Finding critical points: when does a critical
point correspond to a minimum, when to a maximum?  Concavity, Points
of inflection.  

\item Implicit differentiation, error propagation.

\item Techniques of integration.  The exam problems will be taken from
  among the \emph{Miscellaneous Problems} from the chapter
  ``Techniques of Integration'' in Edwards \& Penney.

\item Improper integrals.  Problems will be taken from the excises of
  the corresponding section in Edwards \& Penney.  (See scan of the
  Homework 8 assignment.)

\item Find the area under a graph; find volume, surface area via
  integration. 

\item Differential Equations: be able to solve a separable first order
  differential equation.  Look particularly at the models of
  population growth.  

\item Series: Geometric series, harmonic series; test convergence via
  the integral test or comparison test.  (There are a few more
  important tests which we did not cover in class, so those will not
  be on the exam.)  Taylor series.

\end{enumerate}

Exam rules:
\begin{itemize}
\item No notes and calculators.
\item Paper will be supplied.
\item Respect the Code of Academic Integrity.  It will be enforced.
\end{itemize}
\end{document}
