The Basic Theory Of Power Series

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The Basic Theory Of Power Series

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Author : Jesus M. Ruiz
language : en
Publisher:
Release Date : 2009

The Basic Theory Of Power Series written by Jesus M. Ruiz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.

The Basic Theory Of Power Series

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Author : Jesús M. Ruiz
language : en
Publisher: Vieweg+Teubner Verlag
Release Date : 1993-01-01

The Basic Theory Of Power Series written by Jesús M. Ruiz and has been published by Vieweg+Teubner Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-01-01 with Mathematics categories.

Power series techniques are indispensable in many branches of mathematics, in particular in complex and in real analytic geometry, in commutative algebra, in algebraic geometry, in real algebraic geometry. The book covers in a comprehensive way and at an elementary level essentially all the theorems and techniques which are commonly used and needed in any of these branches. In particular it presents Rückert's complex nullstellensatz, Risler's real nullstellensatz, Tougerons' implicit function theorem, and Artin's approximation theorem, to name a few. Up to now a student of any of the subjects mentioned above usually had to learn about power series within the framework of the vast theory of the subject. The present book opens another path: One gets acquaintance with power series in a direct and elementary way, and then disposes of a good box of tools and examples to penetrate any of the subjects mentioned above, and also some others.

The Basic Theory Of Power Series

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Author : Jesús M. Ruiz
language : en
Publisher: Vieweg+Teubner Verlag
Release Date : 1993-03-15

The Basic Theory Of Power Series written by Jesús M. Ruiz and has been published by Vieweg+Teubner Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-03-15 with Mathematics categories.

Power series techniques are indispensable in many branches of mathematics, in particular in complex and in real analytic geometry, in commutative algebra, in algebraic geometry, in real algebraic geometry. The book covers in a comprehensive way and at an elementary level essentially all the theorems and techniques which are commonly used and needed in any of these branches. In particular it presents Rückert's complex nullstellensatz, Risler's real nullstellensatz, Tougerons' implicit function theorem, and Artin's approximation theorem, to name a few. Up to now a student of any of the subjects mentioned above usually had to learn about power series within the framework of the vast theory of the subject. The present book opens another path: One gets acquaintance with power series in a direct and elementary way, and then disposes of a good box of tools and examples to penetrate any of the subjects mentioned above, and also some others.

Basic Theory Of Ordinary Differential Equations

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Author : Po-Fang Hsieh
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Basic Theory Of Ordinary Differential Equations written by Po-Fang Hsieh and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Providing readers with the very basic knowledge necessary to begin research on differential equations with professional ability, the selection of topics here covers the methods and results that are applicable in a variety of different fields. The book is divided into four parts. The first covers fundamental existence, uniqueness, smoothness with respect to data, and nonuniqueness. The second part describes the basic results concerning linear differential equations, while the third deals with nonlinear equations. In the last part the authors write about the basic results concerning power series solutions. Each chapter begins with a brief discussion of its contents and history, and hints and comments for many problems are given throughout. With 114 illustrations and 206 exercises, the book is suitable for a one-year graduate course, as well as a reference book for research mathematicians.

From Divergent Power Series To Analytic Functions

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Author : Werner Balser
language : en
Publisher: Springer
Release Date : 2006-11-15

From Divergent Power Series To Analytic Functions written by Werner Balser and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.

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.

Transcendence In Algebra Combinatorics Geometry And Number Theory

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Author : Alin Bostan
language : en
Publisher: Springer Nature
Release Date : 2021-11-02

Transcendence In Algebra Combinatorics Geometry And Number Theory written by Alin Bostan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-02 with Mathematics categories.

This proceedings volume gathers together original articles and survey works that originate from presentations given at the conference Transient Transcendence in Transylvania, held in Brașov, Romania, from May 13th to 17th, 2019. The conference gathered international experts from various fields of mathematics and computer science, with diverse interests and viewpoints on transcendence. The covered topics are related to algebraic and transcendental aspects of special functions and special numbers arising in algebra, combinatorics, geometry and number theory. Besides contributions on key topics from invited speakers, this volume also brings selected papers from attendees.

Automata Theoretic Aspects Of Formal Power Series

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Author : Arto Salomaa
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Automata Theoretic Aspects Of Formal Power Series written by Arto Salomaa and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.

This book develops a theory of formal power series in noncommuting variables, the main emphasis being on results applicable to automata and formal language theory. This theory was initiated around 196O-apart from some scattered work done earlier in connection with free groups-by M. P. Schutzenberger to whom also belong some of the main results. So far there is no book in existence concerning this theory. This lack has had the unfortunate effect that formal power series have not been known and used by theoretical computer scientists to the extent they in our estimation should have been. As with most mathematical formalisms, the formalism of power series is capable of unifying and generalizing known results. However, it is also capable of establishing specific results which are difficult if not impossible to establish by other means. This is a point we hope to be able to make in this book. That formal power series constitute a powerful tool in automata and language theory depends on the fact that they in a sense lead to the arithmetization of automata and language theory. We invite the reader to prove, for instance, Theorem IV. 5. 3 or Corollaries III. 7. 8 and III. 7.- all specific results in language theory-by some other means. Although this book is mostly self-contained, the reader is assumed to have some background in algebra and analysis, as well as in automata and formal language theory.

Field Theory And Its Classical Problems

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Author : Charles Robert Hadlock
language : en
Publisher: Cambridge University Press
Release Date : 2000-12-07

Field Theory And Its Classical Problems written by Charles Robert Hadlock and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-12-07 with Mathematics categories.

An introduction to the classical notions behind modern Galois theory.

Complex Function Theory

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Author : Donald Sarason
language : en
Publisher: American Mathematical Society
Release Date : 2021-02-16

Complex Function Theory written by Donald Sarason and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-16 with Mathematics categories.

Complex Function Theory is a concise and rigorous introduction to the theory of functions of a complex variable. Written in a classical style, it is in the spirit of the books by Ahlfors and by Saks and Zygmund. Being designed for a one-semester course, it is much shorter than many of the standard texts. Sarason covers the basic material through Cauchy's theorem and applications, plus the Riemann mapping theorem. It is suitable for either an introductory graduate course or an undergraduate course for students with adequate preparation. The first edition was published with the title Notes on Complex Function Theory.

Algebraic Combinatorics

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Author : Chris Godsil
language : en
Publisher: Routledge
Release Date : 2017-10-19

Algebraic Combinatorics written by Chris Godsil and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-19 with Mathematics categories.

This graduate level text is distinguished both by the range of topics and the novelty of the material it treats--more than half of the material in it has previously only appeared in research papers. The first half of this book introduces the characteristic and matchings polynomials of a graph. It is instructive to consider these polynomials together because they have a number of properties in common. The matchings polynomial has links with a number of problems in combinatorial enumeration, particularly some of the current work on the combinatorics of orthogonal polynomials. This connection is discussed at some length, and is also in part the stimulus for the inclusion of chapters on orthogonal polynomials and formal power series. Many of the properties of orthogonal polynomials are derived from properties of characteristic polynomials. The second half of the book introduces the theory of polynomial spaces, which provide easy access to a number of important results in design theory, coding theory and the theory of association schemes. This book should be of interest to second year graduate text/reference in mathematics.