StudyGuide3

# StudyGuide3 - SC/MATH 2271 3.0 Diﬀerential Equations for...

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Unformatted text preview: SC/MATH 2271 3.0 Diﬀerential Equations for Scientists and Engineers Winter 2010 Study Guide for Midterm 3 The third midterm exam will cover lecture material from February 22 through March 12, corresponding to the following sections from the text: 6.1, 6.2, 6.3 (but not 6.3.2), 11.1, 11.3. See the web page for a list of suggested exercises from the text. Note that Chapter 11 involves many of the concepts from linear algebra discussed earlier in the course; you need to know these. Particular topics that may appear on the test include the following: • Determining whether a given point x0 is an ordinary point or a singular point (and if the latter whether a regular singular point or not) or a second order, linear ODE. • Power series solutions of linear diﬀerential equations, expanded about an ordinary point, as for Airy’s equation. • Power series solutions of linear diﬀerential equations, expanded about a regular singular point, as for Bessel’s equation. • The deﬁnition and basic property of the gamma function. • Notions such as inner product (also called scalar product), norm and orthogonal projection, as they apply to functions in the vector space L2 ([0, 1]). • The meaning of convergence in norm of a series of functions versus pointwise convergence, as well as the notion of completeness of an orthogonal set of functions. • Fourier sine series and Fourier cosine series for functions in L2 ([0, 1]). 1 ...
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## This note was uploaded on 09/04/2011 for the course MATH 2271 taught by Professor Petergibson during the Winter '10 term at York University.

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