Wave Propagation in Linear Media | re-examined

Chapter 7
Mathematica implementation of a
quadrature function
Les mathematiciens n'etudient pas des objets, mais des relations entre les
objets; il leur est donc indi erent de remplacer ces objets par d'autres,
pourvu que les relations ne changent pas. La matiere ne leur importe pas,
la forme seule les interesse. Henry Poincare, quoted in [1]
Based on the ndings of the previous sections, this chapter describes how an automatic
quadrature routine for an extrapolation strategy can be implemented in Mathematica. We
begin the discussion from a user's point of view with the options that control the operation of
the function. The internal structure of the function is another topic of interest, and nally we
shall point out some implementation details. The entire source code of the package is listed
in the appendix. In the last section of the chapter we shall apply the function to examples
known from the literature to verify the correct operation.
7.1 User interface of the function OscInt
The top level function of the package has the same name as the whole package, OscInt. Its
basic syntax is
OscInt[fint, fzero, a, opts],
and its purpose is to nd the numerical value of the integral
I =
Z 1
a
(x) u( (x)) dx ; (7.1)
where u( ) is e j , e ,j or any linear combination of both, in particular sin( ) and cos( ). The
individual input parameters of OscInt have the following meanings:
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