Matrices provide the algebraic structure for solving myriad problems across the sciences. We study matrices and solutions to systems of linear equations as part of understanding linear transformations and general linear spaces. Using the notions of orthogonality, eigenvalues, and eigenvectors, we find least-squares solutions, solve discrete and continuous dynamical systems using exact methods and phase-plane analysis, introduce the Spectral Theorem and Fourier series, and analyze different types of differential equations.
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