Mathucsbedumoore doug moore march 2003 ii contents the

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Unformatted text preview: ext version of this short book. He hopes to make a list of corrections available at the web site: http://www.math.ucsb.edu/~moore Doug Moore March, 2003 ii Contents The sections marked with asterisks are less central to the main line of discussion, and may be treated briefly or omitted if time runs short. 1 Power Series 1.1 What is a power series? . . . . . . . . 1.2 Solving differential equations by means 1.3 Singular points . . . . . . . . . . . . . 1.4 Bessel’s differential equation . . . . . . ......... of power series ......... ......... . . . . . . . . . . . . . . . . . . . . . . . . 1 1 7 15 22 2 Symmetry and Orthogonality 2.1 Eigenvalues of symmetric matrices . . 2.2 Conic sections and quadric surfaces . . 2.3 Orthonormal bases . . . . . . . . . . . 2.4 Mechanical systems . . . . . . . . . . . 2.5 Mechanical systems with many degrees 2.6 A linear array of weights and springs* ....... ....... ....... ....... of freedom* ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . ....
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