# Numerical analysis and Gaussian quadrature

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A function of two variables f(x,y) is integrated over the square [0,2] x [-1,1]. ex: integral from 0 to 2 , integral from -1 to 1 f(x,y) dx dy. (I wanted to input integral symbols there but didn't know how). Build a 25- point numerical integration scheme based on 5- point Gaussian quadrature in the x and y directions. Specify the quadrature points and the summation weights.

Note: f(x,y) is not given meaning it may be any function of 2 variables over the square [0,2] x [-1,1]

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##### Solution Summary

This solution answers questions involving numerical analysis and Guassian quadratures. Step by step calculations are provided.

##### Solution Preview

The last equation I = sum(sum( wi*wj*f(zi,nj+1) ) ) from i = 1,n; j = 1,n is the 25 point numerical integration scheme. It is derived and it states that we can integrate a function by using 25 points. These points are attained when we expand this sum. In this problem, n = 5. We can get the first five points for when i = 1.

i = 1:

I1 = ...

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