University of Florida/Egm4313/s12.team11.perez.gp/R4.1

Problem Statement

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Obtain equations (2), (3), (n-2), (n-1), (n), and set up the matrix A as in (1) p.7-21 for the general case, with the matrix coefficients for rows 1, 2, 3, (n-2), (n-1), n, filled in, as obtained from equations (1), (2), (3), (n-2), (n-1), (n).

Given

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As shown in p.7-21, the first equation is:

  (1) p.7-21

According to p.7-20, the general form of the series is:

  (2) p. 7-20

From (2) p.7-20, we can obtain n+1 equations for n+1 unknown coefficients  .

After referring to p.7-22, it can be determined that the matrix to be set up is of the following form:

 

where the rows signify the coefficients  , and the columns signify  .

Solution

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Building the coefficient matrix as shown in p.7-22 of the class notes, we can begin to solve for the coefficients as follows:

Equation associated with  :

j=0:   (1)

Equation associated with  :

j=1:   (2)

Equation associated with  :

j=2:   (3)

Equation associated with  :

j=n-2:   (n-2)

Equation associated with  :

j=n-1:   (n-1)

Equation associated with  :

j=n:   (n)

Using all of the above equations, (1), (2), (3), (n-2), (n-1), (n), we can then determine the A matrix to be: