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\textbf{MATH 425: Complex Variables \hfill Spring 2004}

\bigskip

\begin{tabular}{lll}
\hline
Jan  14--16
 & 1--5\\
 &  \begin{minipage}{5in}
     Sums and Products,
     Basic Algebraic Properties,
     Moduli,
     Complex Conjugates
\end{minipage}\\
\hline
Jan 19--23
 & 6--10\\
 &  \begin{minipage}{5in}
     Exponential Form,
     Roots of Complex Numbers,
     Regions in the Complex Plane
\end{minipage}\\
\hline
Jan 26--30
 & 11--19\\
 &  \begin{minipage}{5in}
     Functions of a Complex Variable,
     Mappings,
     Limits,
     The Point at Infinity,
     Continuity,
     Derivatives
\end{minipage}\\
 & \textbf{Quiz 1}\\
\hline
Feb 2--6
 & 20--25\\
 &  \begin{minipage}{5in}
     Cauchy-Riemann Equations,
     Analytic Functions,
     Harmonic Functions
\end{minipage}\\
\hline
Feb 9--13
 & 26--31\\
 &  \begin{minipage}{5in}
     The Exponential Function,
     The Logarithmic Function,
     Branches and Derivatives of Logarithms,
     Some Identities Involving Logarithms,
     Complex Exponents,
     Trigonometric Functions,
     Hyperbolic Functions
\end{minipage}\\
 & \textbf{Quiz 2}\\
\hline
Feb 16--20
 & 32--37\\
 &  \begin{minipage}{5in}
     Derivatives of Functions $w(t)$,
     Definite Integrals of Functions $w(t)$,
     Contour Integrals,
     Upper Bounds for Moduli of Contour Integrals,
     Antiderivatives
\end{minipage}\\
\hline
Feb 23--27
 & 38--45\\
 &  \begin{minipage}{5in}
     Cauchy-Goursat Theorem,
     Simply and Multiply Connected Domains,
     Cauchy Integral Formula,
     Derivatives of Analytic Functions,
\end{minipage}\\
 & \textbf{Midterm Exam}\\
\hline
Mar 1--5
 & 46--50\\
 &  \begin{minipage}{5in}
     Liouville's Theorem,
     Fundamental Theorem of Algebra,
     Maximum Modulus Principle
\end{minipage}\\
\hline
Mar  6--14  & \emph{Mid-semester Break}\\
\hline
Mar 15--19
 & 51--54,57\\
 &  \begin{minipage}{5in}
     Convergence of Sequences,
     Convergence of Series,
     Taylor Series,
     Absolute Convergence of Series
\end{minipage}\\
 & \textbf{Quiz 3}\\
\hline
Mar 22--26
 & 59--61, 55--56\\
 &  \begin{minipage}{5in}
     Integration and Differentiation of Power Series,
     Uniqueness of Series Representations,
     Multiplication and Division of Power Series
\end{minipage}\\
\hline
Mar 29---Apr 2
 & 62--67\\
 &  \begin{minipage}{5in}
     Laurent Series,
     Residues,
     Cauchy's Residue Theorem,
     Isolated Singular Points
\end{minipage}\\
 & \textbf{Quiz 4}\\
\hline
Apr 5--8
 & 68--70\\
 &  \begin{minipage}{5in}
     Residues at Poles,
     Zeros of Analytic Functions,
     Zeros and Poles,
     Behavior of $f$ Near Isolated Singular Points
\end{minipage}\\
\hline
Apr 9--12 & \emph{Easter Holiday}\\
\hline
Apr 13--16
 & 71--75\\
 &  \begin{minipage}{5in}
     Evaluation of Improper Integrals,
     Examples,
     Jordan's Lemma
\end{minipage}\\
\hline
Apr 19--23
 & 76--80\\
 &  \begin{minipage}{5in}
     Indented Paths,
     Definite Integrals Involving Sines and Cosines,
     Argument Principle
\end{minipage}\\
 & \textbf{Quiz 5}\\
\hline
Apr 26--28
 & 83--88?\\
 &  \begin{minipage}{5in}
     Argument Principle,
     Rouche's Theorem
\end{minipage}\\
\hline
May 5 & \textbf{Final Exam} 4:15--6:15\\
\hline
\end{tabular}

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