From Divergent Power Series to Analytic Functions

From Divergent Power Series to Analytic Functions
Title From Divergent Power Series to Analytic Functions PDF eBook
Author Werner Balser
Publisher Springer
Pages 117
Release 2006-11-15
Genre Mathematics
ISBN 3540485945

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Multisummability is a method which, for certain formal power series with radius of convergence equal to zero, produces an analytic function having the formal series as its asymptotic expansion. This book presents the theory of multisummabi- lity, and as an application, contains a proof of the fact that all formal power series solutions of non-linear meromorphic ODE are multisummable. It will be of use to graduate students and researchers in mathematics and theoretical physics, and especially to those who encounter formal power series to (physical) equations with rapidly, but regularly, growing coefficients.

Graduate Mathematical Physics

Graduate Mathematical Physics
Title Graduate Mathematical Physics PDF eBook
Author James J. Kelly
Publisher John Wiley & Sons
Pages 482
Release 2008-09-26
Genre Science
ISBN 3527618902

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This up-to-date textbook on mathematical methods of physics is designed for a one-semester graduate or two-semester advanced undergraduate course. The formal methods are supplemented by applications that use MATHEMATICA to perform both symbolic and numerical calculations. The book is written by a physicist lecturer who knows the difficulties involved in applying mathematics to real problems. As many as 40 exercises are included at the end of each chapter. A student CD includes a basic introduction to MATHEMATICA, notebook files for each chapter, and solutions to selected exercises. * Free solutions manual available for lecturers at www.wiley-vch.de/supplements/

Formal and Analytic Solutions of Diff. Equations

Formal and Analytic Solutions of Diff. Equations
Title Formal and Analytic Solutions of Diff. Equations PDF eBook
Author Galina Filipuk
Publisher Springer
Pages 273
Release 2018-09-24
Genre Mathematics
ISBN 3319991485

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These proceedings provide methods, techniques, different mathematical tools and recent results in the study of formal and analytic solutions to Diff. (differential, partial differential, difference, q-difference, q-difference-differential.... ) Equations. They consist of selected contributions from the conference "Formal and Analytic Solutions of Diff. Equations", held at Alcalá de Henares, Spain during September 4-8, 2017. Their topics include summability and asymptotic study of both ordinary and partial differential equations. The volume is divided into four parts. The first paper is a survey of the elements of nonlinear analysis. It describes the algorithms to obtain asymptotic expansion of solutions of nonlinear algebraic, ordinary differential, partial differential equations, and of systems of such equations. Five works on formal and analytic solutions of PDEs are followed by five papers on the study of solutions of ODEs. The proceedings conclude with five works on related topics, generalizations and applications. All contributions have been peer reviewed by anonymous referees chosen among the experts on the subject. The volume will be of interest to graduate students and researchers in theoretical and applied mathematics, physics and engineering seeking an overview of the recent trends in the theory of formal and analytic solutions of functional (differential, partial differential, difference, q-difference, q-difference-differential) equations in the complex domain.

Loeb Measures in Practice: Recent Advances

Loeb Measures in Practice: Recent Advances
Title Loeb Measures in Practice: Recent Advances PDF eBook
Author Nigel J. Cutland
Publisher Springer
Pages 118
Release 2004-10-11
Genre Mathematics
ISBN 3540445315

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This expanded version of the 1997 European Mathematical Society Lectures given by the author in Helsinki, begins with a self-contained introduction to nonstandard analysis (NSA) and the construction of Loeb Measures, which are rich measures discovered in 1975 by Peter Loeb, using techniques from NSA. Subsequent chapters sketch a range of recent applications of Loeb measures due to the author and his collaborators, in such diverse fields as (stochastic) fluid mechanics, stochastic calculus of variations ("Malliavin" calculus) and the mathematical finance theory. The exposition is designed for a general audience, and no previous knowledge of either NSA or the various fields of applications is assumed.

Superconvergence in Galerkin Finite Element Methods

Superconvergence in Galerkin Finite Element Methods
Title Superconvergence in Galerkin Finite Element Methods PDF eBook
Author Lars Wahlbin
Publisher Springer
Pages 179
Release 2006-11-14
Genre Mathematics
ISBN 3540494014

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This book is essentially a set of lecture notes from a graduate seminar given at Cornell in Spring 1994. It treats basic mathematical theory for superconvergence in the context of second order elliptic problems. It is aimed at graduate students and researchers. The necessary technical tools are developed in the text although sometimes long proofs are merely referenced. The book gives a rather complete overview of the field of superconvergence (in time-independent problems). It is the first text with such a scope. It includes a very complete and up-to-date list of references.

Complex Differential and Difference Equations

Complex Differential and Difference Equations
Title Complex Differential and Difference Equations PDF eBook
Author Galina Filipuk
Publisher Walter de Gruyter GmbH & Co KG
Pages 520
Release 2019-11-18
Genre Mathematics
ISBN 3110609614

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With a balanced combination of longer survey articles and shorter, peer-reviewed research-level presentations on the topic of differential and difference equations on the complex domain, this edited volume presents an up-to-date overview of areas such as WKB analysis, summability, resurgence, formal solutions, integrability, and several algebraic aspects of differential and difference equations.

The Minnesota Notes on Jordan Algebras and Their Applications

The Minnesota Notes on Jordan Algebras and Their Applications
Title The Minnesota Notes on Jordan Algebras and Their Applications PDF eBook
Author Max Koecher
Publisher Springer Science & Business Media
Pages 198
Release 1999-09-17
Genre Mathematics
ISBN 9783540663607

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This volume contains a re-edition of Max Koecher's famous Minnesota Notes. The main objects are homogeneous, but not necessarily convex, cones. They are described in terms of Jordan algebras. The central point is a correspondence between semisimple real Jordan algebras and so-called omega-domains. This leads to a construction of half-spaces which give an essential part of all bounded symmetric domains. The theory is presented in a concise manner, with only elementary prerequisites. The editors have added notes on each chapter containing an account of the relevant developments of the theory since these notes were first written.