University of Florida/Egm4313/

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Problem Statement[edit | edit source]

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[edit | edit source]

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[edit | edit source]

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: