Power series from a computationalpoint of view

Description:

The purpose of this book is to explain the use of power series in performing concrete calculations, such as approximating definite integrals or solutions to differential equations. This focus may seem narrow but, in fact, such computations require the understanding and use of many of the important theorems of elementary analytic function theory, for example Cauchy's Integral Theorem, Cauchy's Inequalities, and Analytic Continuation and the Monodromy Theorem. These computations provide an effective motivation for learning the theorems, and a sound basis for understanding them.

subjects: Power series,  Analytic functions,  Fonction analytique,  Prolongement analytique,  Série puissance,  Fonctions analytiques,  Séries de puissances,  Numerisches Verfahren,  Potenzreihe,  Potenzreihenentwicklung,  Computational complexity,  Mathematics,  Global analysis (Mathematics)