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Course Goals:

Linear algebra is one of the most useful and practical courses in the mathematics sequence. It is used extensively in computer science (particularly computer graphics), physics, engineering, and even accounting and finance. Although its main objects of study -- linear, or "flat" functions -- seem simple, they also are very powerful tools for understanding non-linear functions. In fact, an important way to investigate a non-linear function is approximate it (locally) by a linear one. Indeed, you are already familiar with this process from differential calculus: the tangent line to a curve is the best linear approximation to the curve at a point, so studying the tangent line tells you a lot about the curve, at least near the point of tangency. This same idea is used to understand the non-linear dynamics of phase spaces in physics, and financial trends in economics.

You already are familiar with some linear algebra from Math 15. (Remember Gauss-Jordan elimination and matrix determinants?) We will revisit these here in a wider context, and introduce a number of new concepts, such as vector space, linear independence, and basis vectors. We will use matrices to represent an important class of functions, and will interpret them geometrically. Our final topic, eigenvectors and eigenvalues, is one of the most useful ones for the physical sciences.

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Created: 06 Jan 2008
Last modified: Jan 6, 2008 3:38:39 PM
Comments to: dpvc@union.edu
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