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\textbf{Reveiw for Final}

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\begin{enumerate}

\item  Final is Friday, August 9.  7:30-9:30AM.

\item  You can have one $4 \times 6$ note card for the final.
\item  I will give you a table of Laplace transforms (I will probably just Xerox the table in the front of the book for you)

\item  First order equations
	\begin{enumerate}
	\item  Separation of variables.
	\item  Direction fields
	\item  Existance and uniqueness theorem.
	\item  Linear first order equations (integrating factors)
	\end{enumerate}

\item  Mathematical models
	\begin{enumerate}
	\item  Population
	\item  Acceleration-velocity
	\item  Springs and masses (and linear systems of differential equations)
	\item  Stability and equilibrium.
	\end{enumerate}

\item  Linear algebra and matrices
	\begin{enumerate}
	\item  Gaussian reductions (reduced row echelon)
	\item  Inverses
	\item  Determinants
	\item  Eigenvalues and Eigenvectors (computing them)
	\item  Vector spaces (what is a vector space and why do we care?)
	\item  Eigenspaces
	\item  Diagonalizable matrices.
	\item  Basis and dimension.
	\item  Linear independence, linear dependence.
	\end{enumerate}

\item  Linear equations
	\begin{enumerate}
	\item  Theory part (complimentary solution, particular solution, general solution)
	\item  Computing part (constant coefficients, homogeneous and nonhomogeneous).
	\end{enumerate}

\item  Linear systems of differential equations.
	\begin{enumerate}
	\item  Theory part (what is a complimentary solution, general solution, particular solution)
	\item  Computing part (finding a solution, constant coefficients only, eigenvalues and eigenvectors!)
	\end{enumerate}

\item  Laplace transforms
	\begin{enumerate}
	\item  Definition of Laplace transform
	\item  Transforming a differential equation into an algebraic equation and solving.
	\item  Inverse Laplace transforms.
	\end{enumerate}





\end{enumerate}







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