Millersville University
Department of Mathematics
MATH 375, Numerical Analysis, Homework 2
October 10, 2006
The completed assignment is due at class time on 10/19/2006. Each problem or part of a problem
is worth ten points. You may use your textbook, computer programs, and notes. You may not
work with another person or group of persons. The work you submit must be your individual effort.
1. Make a table of the absolute error of the three-point centered difference formula for f′(0)
where f(x) = sin x−cos xwith h= 10−1, 10−2, .. . , 10−15 . At which value of hdoes the
minimum error occur?
2. Consider the definite integral
Zπ
0
xcos x dx.
Use the following numerical integration methods to approximate the definite integral. For
each method find the absolute error and the theoretical maximum error.
(a) Trapezoidal Rule
(b) Simpson’s Rule
(c) Simpson’s Three-Eighths Rule
(d) Closed Newton-Cotes: n= 4
(e) Midpoint Rule
(f) Open Newton-Cotes: n= 1
(g) Open Newton-Cotes: n= 2
(h) Open Newton-Cotes: n= 3
