EGM6321 - Principles of Engineering Analysis 1, Fall 2009
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Mtg 33: Thurs, 5Nov09
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(1)
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(2)
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Where:
and
becomes
Similarly for
Orthogonality of Legendre polynomial
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(3)
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Where
kronecker delta
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(4)
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(5)
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Orthogonality of
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(1)
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is diagonal with diagonal coefficient:
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(2)
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(3)
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F is complete, i.e. any continuous function, f, can be expressed as an infinite series of function in F:
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(4)
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Eq(4) is an equality due to the completeness of F
p29-5:
Where
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(5)
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Where n=0,1,2...n
HW:
Show that if
is odd, then f is odd
Show that if
is even, then f is even
HW: Show that
is even for k=0,1,2... and
is odd
Eq.(5) P.33-2
, f even
for
, since
is odd
It turns out that
for all
due to linear independance of
and the orthogonality of
Linear independance of
is a polynomial of order n
set of all polynomials of degree (order)
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(1)
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HW:
Given
Find
such that
Plot
Where
figure 1 and
figure 2
Othogonality of
Eq.(3) P.33-1
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(2)
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