University of Florida/Egm6321/F10.TEAM1.WILKS/Mtg33

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EGM6321 - Principles of Engineering Analysis 1, Fall 2009[edit]

Mtg 33: Thurs, 5Nov09


Page 33-1

[edit]

(1)



(2)



Where: and becomes

Similarly for

Orthogonality of Legendre polynomial

(3)



Where kronecker delta

(4)



(5)


Page 33-2

[edit]

Orthogonality of

(1)



is diagonal with diagonal coefficient:

(2)



(3)


F is complete, i.e. any continuous function, f, can be expressed as an infinite series of function in F:

(4)



Eq(4) is an equality due to the completeness of F

p29-5:

Where

(5)



Where n=0,1,2...n

Page 33-3

[edit]

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

Page 33-4

[edit]

Linear independance of

is a polynomial of order n

set of all polynomials of degree (order)

(1)



HW:



Given

Find such that

Plot

Where figure 1 and figure 2

Othogonality of Eq.(3) P.33-1

(2)

References[edit]