Millersville University
Department of Mathematics
MATH 375, Homework 3
October 7, 2003
The completed assignment is due at class time on 10/23/2003. You may use your textbook,
computer programs, and notes. All numerical approximations must be accurate to within 10โ4
unless otherwise stated.
Star S in the Big Dipper (Ursa Major ) has a regular variation in its apparent magnitude. Leon
Campbell and Laizi Jacchia give data for the mean light curve of this star in the book The Story
of Variable Stars (1941). The data are shown in the table below.
Phase Magnitude
โ110 7.98
โ80 8.85
โ40 10.71
โ10 11.70
30 10.01
80 8.23
110 7.86
What is different about this data is that the apparent magnitude of the star is periodic, in other
words the magnitude at phase โ120 is the same as the magnitude at phase 120.
1. Derive a linear system to find the coefficients of a cubic spline interpolant with periodic
boundary conditions. For periodic boundary conditions the first and second derivatives agree
at the boundary.
2. Solve the linear system (using a computer if necessary) to find the appropriate cubic spline
interpolant for the data.
3. What is the error in the cubic spline interpolant if the following additional data are available
for star S?
Phase Magnitude
โ100 8.37
โ60 9.40
โ20 11.39
20 10.84
60 8.53
100 7.89