Overview
ABSTRACT
It is often difficult to have an idea of the interest of the theoretical notions dealt with in the Mathématiques pour l'ingénieur treaty or in books dedicated to numerical analysis and applied mathematics. These notions are often presented separately and it is difficult to understand how they are linked together. As in other mathematical domains, the functional analysis has allowed for unifying a certain number of concepts, problems and numerical analysis methods which until then were not linked together or, at least, to give them a common basis. From the functional analysis to applications, one understands how everything is linked together.
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Claude BREZINSKI: Doctor of Mathematical Sciences - Professor Emeritus - Paul Painlevé Laboratory UMR CNRS 8524 - Lille University of Science and Technology
INTRODUCTION
It's often difficult to get an idea of the relevance of the various theoretical concepts covered in Mathematics for Engineers, Numerical Analysis and Applied Mathematics. They are usually presented separately from each other, and it's hard to see how they are related and why. The aim of this article is to provide, at least partially, some answers and to serve as a link between different articles in this treatise.
As in other areas of mathematics, functional analysis has made it possible to unify a number of hitherto unrelated concepts, problems and methods of numerical analysis, or at least to give them a common basis.
Our aim here is to show how everything fits together, from functional analysis through to applications. The aim is by no means to be exhaustive, but simply to illustrate this idea with a few examples, most of which have already been studied in other articles. In particular, see
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Functional bases of numerical analysis
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