Scientific Computing: Theory, Developments and Applications

Abstract

The aim of this work is to provide a short expos´e on a classical area of mathematics — approximation theory — in a way that leads to the recent research results and the modern field of wavelets. We study the idea of approximating “complicated expressions” with “simpler expressions” and we underline how this procedure plays an important role in these areas of mathematics and applications. The focus here is on ideas rather than on technical details. One of the main goals of the present work is to make it clear that mathematics is a subject in a state of continuous evolution. We try to demonstrate the dynamic nature of mathematics and how classical disciplines influence many areas of modern mathematics and its applications. We attempt to organize the work in a way that makes the information accessible smoothly from the Taylor polynomial approximation to wavelets as a natural way of extension.