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.
 Winter '10
 PeterGibson
 Differential Equations, Equations

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