\documentclass{amsart}

\everymath{\displaystyle}

\title{Final Exam Topics}

\author{Math 166: Calculus II}

\date{Spring, 2000}

\begin{document}

\maketitle

\subsection*{Theorems}

\begin{itemize}
\item Fundamental Theorem of Calculus
\item Derivative of an Inverse Function
\item Taylor's Theorem with Remainder
\item L'H\^opital's Rule
\item Linearity of Series
\item Simple Divergence Test
\item Telescoping and Geometric Series
\item Comparison Test and Limit Comparison Test
\item Integral Test
\item Root and Ratio Tests
\item Leibniz's Rule
\item Uniform Convergence of Power Series
\item Continuity of Power Series
\item Termwise Integration and Differentiation of Power Series
\end{itemize}

\subsection*{Definitions}

\begin{itemize}
\item $\log(x)$, $\exp(x)$, $a^x$
\item Hyperbolic Functions
\item Inverse Functions
\item Taylor Polynomials
\item Limits Involving Infinity
\item Sequences and Series
\item Telescoping, Geometric, and Alternating Series
\item Absolute and Conditional Convergence
\item Integrals Involving Infinity
\item Power Series
\item Radius/Interval of Convergence
\end{itemize}

\subsection*{Derivatives}

\begin{itemize}
\item Integrals: $\frac{d}{dx}\int_{g(x)}^{h(x)}f(t)\,dt$
\item Inverse Functions: $\frac{d}{dx}f^{-1}(x)$
\item Exponential Functions: $\frac{d}{dx}g(x)^{f(x)}$
\end{itemize}

\subsection*{Techniques of Integration}

\begin{itemize}
\item Substitution
\item Integration by Parts
\item Partial Fractions
\item Trig Substitutions
\item Integrals Involving Rational Functions of $\sin(x)$ and $\cos(x)$
\item Computing Improper Integrals
\end{itemize}

\subsection*{Taylor Polynomials}

\begin{itemize}
\item Calculating Taylor Polynomials
\item Estimating the Error Term
\item $o$-symbols
\end{itemize}

\subsection*{Limits}

\begin{itemize}
\item Indeterminate Forms
\item Calculating Limits with $o$-symbols
\item L'H\^opital's Rule and Extensions
\item Limits of Sequences
\end{itemize}

\subsection*{Series}

\begin{itemize}
\item Summing Telescoping and Geometric Series
\item Testing Series for Convergence: Absolute and Conditional
\item Determining Radius/Interval of Convergence of a Power Series
\item Determining the Power Series of a Function
\item Standard Power Series: $1/(1\pm x)$, $\log(1\pm x)$, $e^x$,
$\sin(x)$, $\cos(x)$
\item Summing Power Series using Standard Series, Derivatives, and Integrals
\end{itemize}

\end{document}
