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

EGM6321 - Principles of Engineering Analysis 1, Fall 2009

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Mtg 33: Thurs, 5Nov09


 

(1)



 

(2)



Where:   and   becomes  

Similarly for  

Orthogonality of Legendre polynomial

 

(3)



Where   kronecker delta

 

(4)



 

(5)


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

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)  

 

(1)



HW:  

 

Given  

Find   such that  

Plot  

Where   figure 1 and   figure 2

Othogonality of   Eq.(3) P.33-1

 

(2)

References

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