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Approximate symbolic calculations with a functional computing environment

R. Barrère
Journal / Anthology

Mathematics with Vision: Proceedings of the First International Mathematica Symposium
Year: 1995
Page range: 37-44

The expansion of numerical computing techniques on the one hand, and exact computing techniques with computer algebra systems on the other hand, made us forget approximate analytic calculus. Yet, symbolic approximations can be computed by means of functional iterations, perturbation expansions, or variational methods. An advantage of such analytic formulations is due to their capability of processing literal expressions with symbolic parameters, thus improving our mastering of the underlying mathematical models. Moreover, these methods can be implemented in Mathematica as functional operators that can be used like symbolic built-in operators. In prospect, a renewed notion of mathematical modeling and scientific computing is emerging, where calculating and programming tend to blend into a single activity.

*Applied Mathematics
*Mathematics > Calculus and Analysis