Numerical Methods Qualification Exam Problems and Solutions (University of Maryland)/August 2002
Problem 1Edit

Solution 1Edit
Problem 2Edit
Suppose there is a quadrature formula

Solution 2Edit
All nodes lies in (a,b)Edit
Let be the nodes that lie in the interval .
Let which is a polynomial of degree .
Let which is a polynomial of degree .
Then
since is of one sign in the interval since for ,
This implies is of degree since otherwise
from the orthogonality of .
All weights positiveEdit
Problem 3Edit
