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\multicolumn{3}{c}{\textbf{MATH 228: Intro to Linear Algebra and Differential
Equations\hfill\quad Spring 2003}}\\
\hline
Jan  15--17
 & 1.1 Intro to Systems of Linear Equations\\
 & 1.2 Gaussian Elimination\\
 & 1.3 Matrices and Matrix Operations\\
\hline
Jan 20--24
 & 1.4 Inverses; Rules of Matrix Arithmetic \\
 & 1.5 Elementary Matrices; Finding $A^{-1}$\\
 & 1.6 Further Results on Systems, Invertibility\\
 & 1.7 Diagonal, Triangular, and Symmetric Matrices\\
\hline
Jan 27--31
 & 2.1 The Determinant Function \\
 & 2.2 Evaluating Determinants by Row Reduction\\
 & 2.3 Properties of the Determinant Function\\
 & 2.4 Cofactor Expansion; Cramer's Rule\\
\hline
Feb 3--7
 & 4.1 Euclidean $n$-Space \\
 & 4.2 Linear Transformations from $R^n$ to $R^m$\\
 & 4.3 Properties of Linear Transformations\\
\hline
Feb 10--14
 & 5.1 Real Vector Spaces \\
 & 5.2 Subspaces\\
 & 5.3 Linear Independence\\
 & 5.4 Basis and Dimension\\
\hline
Feb 17--21
 & 5.5 Row Space, Column Space, and Nullspace \\
 & 5.6 Rank and Nullity\\
 & 6.1 Inner Products\\
\hline
Feb 22--23 & \textbf{Exam I}\\
\hline
Feb 24--28
 & 6.2 Angle and Orthogonality\\
 & 6.3 Orthonormal Bases; Gram-Schmidt Process; QR-Decomposition\\
 & 6.4 Best Approximation; Least Squares\\
\hline
Mar 3--7
 & 6.5 Orthogonal Matrices; Change of Basis\\
 & 7.1 Eigenvalues and Eigenvectors \\
 & 7.2 Diagonalization\\
 & 7.3 Orthogonal Diagonalization\\
\hline
Mar  8--16  & \emph{Midsemester Break}\\
\hline
Mar 17--21
 & 8.1 General Linear Transformations\\
 & 8.2 Kernel and Range \\
 & 8.3 Inverse Linear Transformations\\
 & 8.4 Matrices of General Linear Transformations\\
 & 8.5 Similarity\\
\hline
Mar 24--28
 & 1.1--1.3 Intro to Differential Equations\\
 & 2.1 Linear Equations\\
 & 2.2 Separable Equations + 2.3\\
\hline
Mar 31---Apr 4
 & 2.3 Modeling with First Order Equations\\
 & (2.4 Differences Bewteen Linear and Nonlinear Equations) \\
 & 2.5 Autonomous Equations and Population Dynamics\\
 & 2.6 Exact Equations and Integrating Factors\\
\hline
Apr 7--11
 & 3.1 Homogeneous Equations with Constant Coefficients\\
 & 3.2 Fundamental Solutions of Linear Homogeneous Equations\\
 & 3.3 Linear Independence and the Wronskian + 3.4\\
\hline
Apr 12--13 & \textbf{Exam II}\\
\hline
Apr 14--16
 & 3.4 Complex Roots of the Characteristic Equation\\
 & 3.5 Repeated Roots; Reduction of Order + 3.6\\
\hline
Apr 18--21 & \emph{Easter Holiday}\\
\hline
Apr 23--25
 & 3.6 Non-homogeneous Equations; Undetermined Coefficients\\
 & 3.7 Variation of Parameters\\
\hline
Apr 28--30
 & 3.8 Mechanical Vibrations\\
 & 3.9 Forced Vibrations\\
\hline
May    7 & \textbf{Final Exam}\\
\hline
\end{tabular}

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