Formal Power Series and Linear Systems of Meromorphic Ordinary Differential Equations
Author: Werner Balser
Publisher:
Published: 2014-01-15
Total Pages: 324
ISBN-13: 9781475774047
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Formal Power Series and Linear Systems of Meromorphic Ordinary Differential Equations
Author: Werner Balser
Publisher: Springer Science & Business Media
Published: 2008-01-19
Total Pages: 314
ISBN-13: 0387225986
DOWNLOAD EBOOK →Simple Ordinary Differential Equations may have solutions in terms of power series whose coefficients grow at such a rate that the series has a radius of convergence equal to zero. In fact, every linear meromorphic system has a formal solution of a certain form, which can be relatively easily computed, but which generally involves such power series diverging everywhere. In this book the author presents the classical theory of meromorphic systems of ODE in the new light shed upon it by the recent achievements in the theory of summability of formal power series.
Formal And Analytic Solutions Of Differential Equations
Author: Galina Filipuk
Publisher: World Scientific
Published: 2022-03-03
Total Pages: 400
ISBN-13: 1800611374
DOWNLOAD EBOOK →The book provides the reader with an overview of the actual state of research in ordinary and partial differential equations in the complex domain. Topics include summability and asymptotic study of both ordinary and partial differential equations, and also q-difference and differential-difference equations. This book will be of interest to researchers and students who wish to expand their knowledge of these fields.With the latest results and research developments and contributions from experts in their field, Formal and Analytic Solutions of Differential Equations provides a valuable contribution to methods, techniques, different mathematical tools, and study calculations.
Formal and Analytic Solutions of Diff. Equations
Author: Galina Filipuk
Publisher: Springer
Published: 2018-09-24
Total Pages: 274
ISBN-13: 3319991485
DOWNLOAD EBOOK →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.
Intuitive Combinatorial Topology
Author: V.G. Boltyanskii
Publisher: Springer Science & Business Media
Published: 2013-03-09
Total Pages: 153
ISBN-13: 1475756046
DOWNLOAD EBOOK →Topology is a relatively young and very important branch of mathematics, which studies the properties of objects that are preserved through deformations, twistings, and stretchings. This book deals with the topology of curves and surfaces as well as with the fundamental concepts of homotopy and homology, and does this in a lively and well-motivated way. This book is well suited for readers who are interested in finding out what topology is all about.
Higher-Dimensional Algebraic Geometry
Author: Olivier Debarre
Publisher: Springer Science & Business Media
Published: 2013-03-09
Total Pages: 245
ISBN-13: 147575406X
DOWNLOAD EBOOK →The classification theory of algebraic varieties is the focus of this book. This very active area of research is still developing, but an amazing quantity of knowledge has accumulated over the past twenty years. The authors goal is to provide an easily accessible introduction to the subject. The book starts with preparatory and standard definitions and results, then moves on to discuss various aspects of the geometry of smooth projective varieties with many rational curves, and finishes in taking the first steps towards Moris minimal model program of classification of algebraic varieties by proving the cone and contraction theorems. The book is well-organized and the author has kept the number of concepts that are used but not proved to a minimum to provide a mostly self-contained introduction.
Fourier and Wavelet Analysis
Author: George Bachmann
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 510
ISBN-13: 1461205050
DOWNLOAD EBOOK →This comprehensive volume develops all of the standard features of Fourier analysis - Fourier series, Fourier transform, Fourier sine and cosine transforms, and wavelets. The books approach emphasizes the role of the "selector" functions, and is not embedded in the usual engineering context, which makes the material more accessible to a wider audience. While there are several publications on the various individual topics, none combine or even include all of the above.
A Basic Course in Probability Theory
Author: Rabi Bhattacharya
Publisher: Springer Science & Business Media
Published: 2007-07-27
Total Pages: 217
ISBN-13: 0387719385
DOWNLOAD EBOOK →Introductory Probability is a pleasure to read and provides a fine answer to the question: How do you construct Brownian motion from scratch, given that you are a competent analyst? There are at least two ways to develop probability theory. The more familiar path is to treat it as its own discipline, and work from intuitive examples such as coin flips and conundrums such as the Monty Hall problem. An alternative is to first develop measure theory and analysis, and then add interpretation. Bhattacharya and Waymire take the second path.
Classical Theory of Algebraic Numbers
Author: Paulo Ribenboim
Publisher: Springer Science & Business Media
Published: 2013-11-11
Total Pages: 676
ISBN-13: 0387216901
DOWNLOAD EBOOK →The exposition of the classical theory of algebraic numbers is clear and thorough, and there is a large number of exercises as well as worked out numerical examples. A careful study of this book will provide a solid background to the learning of more recent topics.
Sheaves in Geometry and Logic
Author: Saunders MacLane
Publisher: Springer Science & Business Media
Published: 1994-10-27
Total Pages: 650
ISBN-13: 0387977104
DOWNLOAD EBOOK →Sheaves arose in geometry as coefficients for cohomology and as descriptions of the functions appropriate to various kinds of manifolds. Sheaves also appear in logic as carriers for models of set theory. This text presents topos theory as it has developed from the study of sheaves. Beginning with several examples, it explains the underlying ideas of topology and sheaf theory as well as the general theory of elementary toposes and geometric morphisms and their relation to logic.
