UNIVERSITY OF NOTRE DAME
Department of Civil Engineering
and Geological Sciences
CE 30125
September 5, 2010
J.J. Westerink
Due: September 10, 2010
Homework Set #1
Backgound:
Taylor series provide a very useful and powerfull tool in order to not only derive approximations
in discrete space, but also to provide valuable information about the errors that we make by using a discrete
approximation. There are two key things that we want to oberve: (1) errors get larger as we apply larger
discrete distances or move away from the expansion point; (2) errors have associated convergence rates  often
dominated by the leading order truncated term. This information will be extremely usefull in obtaining esti
mates of how large the numerical error is for our solution and will also provide guidance as to how build our
discrete “grids” or networks of nodes at which the numerical solutions are computed.
Problem 1
Consider the function
a) Develop
2, 4, and 6 term Taylor series expansions
about
x
= 0.
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 Fall '08
 Westerink,J
 Civil Engineering, Numerical Analysis, Taylor series expansions, gauss elimination, expansion point, Backgound

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