<p>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.</p>

Power Series from a Computational Point of View (Universitext)

Science & Math

Smith, Kennan T.

Mathematics

Springer

This edition is a comprehensive introduction to the basic ideas of modern mathematical analysis. Coverage proceeds form the elementary level to advanced and research levels. Additions to this edition include Rademacher's theorem on differentiability of Lipschitz Functions, deeper formulas on change of variables in multiple integrals, and recent results on the extension of differentiable functions.

Primer of modern analysis: (Directions for knowing all dark things, Rhind Papyrus, 1800 B.C.)

Astronomy & Space Science

Bogden & Quigley

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