[Articles
by W G Spunde]
Point-wise calculus
Quote Quad, 24 (1), 1993, pps. 259-266
Proceedings
of the ACM SIGAPL International Conference on APL
(Toronto, August, 1993)
Abstract
The work of Richard Neidinger implementing automatic differentiation
in APL as a vector arithmetic is reformulated and extended. For functions
of a single variable, an arithmetic is developed for function samples,
nested vectors whose components hold the values, at any number of gjven
sample points, of a function and its derivatives up to any specified order.
It is argued that, for teaching purposes, this sampling provides a more
intuitive introduction to mathematical functions and the rules of calculus
than do algebraic formulae and that for certain calculations (such as the
computation of polynomial approximations of high degree) the formulation
provides superior algorithms for computation, As such, it offers an alternative
approach to the teaching of elementary college mathematics.
