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\begin{center}
\textbf{\Large MATH 3912 - Definitions and Theorems (2)}
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\begin{questions}

\fullwidth{\textbf{Definitions}}

\question
The determinant of an $n \times n$ matrix

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\question
A linear vector space $X$

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\question
Vectors $v_1$, $v_2$, $...$, $v_n$ are linearly dependent (or independent)

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\question
The space $L^p([a, b])$, where $p > 0$ and $[a, b]$ is an interval in $\R$

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\question
A function $f: [a, b] \rightarrow \R$ is bounded

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\question
A function $f: [a, b] \rightarrow \R$ is continuous

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\question
A function $f: [a, b]\rightarrow \R$ is uniformly continous

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\question
A function $f: [a, b]\rightarrow \R$ is Lipschitz with power $\alpha$, i.e. $f \in Lip(\alpha)$

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\question
The space $C^n([a, b])$, where $[a, b]$ is an interval in $\R$

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\question
The space $C^\infty([a, b])$, where $[a, b]$ is an interval in $\R$

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\question
A Taylor series for a function $f$ centered at a point $c$

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\question
A power series centered at a point $c$

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\question
A function that is real analytic

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\question
A function of a complex variable that is analytic 

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\question
What is an entire function?

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\question
What is a polynomial?

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\question
What is a functional, and what is a linear functional?

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\question
What is a conformal map?

\end{questions}

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\begin{questions}
\fullwidth{\textbf{Theorems}}

\question
When does a system of linear equations $\Sigma_{j=1}^{n} a_{ij} x_j = b_j$ for $i = 1, 2, \dots, n$ possess a unique solution?

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\question
What conditions can you put on a function $f$ and its domain to ensure it is bounded?

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\question
What conditions can you put on a function $f$ and its domain to ensure it is uniformly continous?

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\question
What is the \textit{Mean Value Theorem} for a function $f:[a, b] \rightarrow R$?

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\question
What is the \textit{First Mean Value Theorem for Integral}?

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\question
What is \textit{Rolle's Theorem}?

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\question
What is the \textit{Generalized Rolle's Theorem}?

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\question
What is Taylor's Theorem?

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\question
What is \textit{Cauchy's Integral Formula}?

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\question
What is the \textit{Fundamental Theorem of Algebra} (and, by the way, what is the Fundamental Theorem of Calculus?)

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\question
What is the \textit{Factorization Theorem} and the \textit{Uniqueness Theorem}?

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\question
What is the image of circles, radius $r \ge 1$, under the (complex) function
$f(z) = {1 \over 2} \left( z + {1 \over z}\right)$?

\end{questions}
\end{document}
