Lectures On Analytic Differential Equations
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Lectures On Analytic Differential Equations
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Author : I︠U︡. S. Ilʹi︠a︡shenko
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Lectures On Analytic Differential Equations written by I︠U︡. S. Ilʹi︠a︡shenko and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
The book combines the features of a graduate-level textbook with those of a research monograph and survey of the recent results on analysis and geometry of differential equations in the real and complex domain. As a graduate textbook, it includes self-contained, sometimes considerably simplified demonstrations of several fundamental results, which previously appeared only in journal publications (desingularization of planar analytic vector fields, existence of analytic separatrices, positive and negative results on the Riemann-Hilbert problem, Ecalle-Voronin and Martinet-Ramis moduli, solution of the Poincare problem on the degree of an algebraic separatrix, etc.). As a research monograph, it explores in a systematic way the algebraic decidability of local classification problems, rigidity of holomorphic foliations, etc. Each section ends with a collection of problems, partly intended to help the reader to gain understanding and experience with the material, partly drafting demonstrations of the mor The exposition of the book is mostly geometric, though the algebraic side of the constructions is also prominently featured. on several occasions the reader is introduced to adjacent areas, such as intersection theory for divisors on the projective plane or geometric theory of holomorphic vector bundles with meromorphic connections. The book provides the reader with the principal tools of the modern theory of analytic differential equations and intends to serve as a standard source for references in this area.
Lectures On Analytic Differential Equations
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Author : I͡U. S. Ilʹi͡ashenko
language : en
Publisher: American Mathematical Soc.
Release Date :
Lectures On Analytic Differential Equations written by I͡U. S. Ilʹi͡ashenko and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
Each section ends with a collection of problems, partly intended to help the reader to gain understanding and experience with the material, partly drafting demonstrations of the more recent results surveyed in the text." "The exposition of the book is mostly geometric, though the algebraic side of the constructions is also prominently featured. On several occasions the reader is introduced to adjacent areas, such as intersection theory for divisors on the projective plane or geometric theory of holomorphic vector bundles with meromorphic connections. The book provides the reader with the principal tools of the modern theory of analytic differential equations and intends to serve as a standard source for references in this area."--BOOK JACKET.
Lectures On Analytic Differential Equations
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Author : I͡U. S. Ilʹi͡ashenko
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Lectures On Analytic Differential Equations written by I͡U. S. Ilʹi͡ashenko and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with MATHEMATICS categories.
The authors combine the features of a graduate-level textbook with those of a research monograph and survey of the results on analysis and geometry of differential equations in the real and complex domain.
Lectures On Partial Differential Equations
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Author : Vladimir I. Arnold
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Lectures On Partial Differential Equations written by Vladimir I. Arnold 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 2013-06-29 with Mathematics categories.
Choice Outstanding Title! (January 2006) Like all of Vladimir Arnold's books, this book is full of geometric insight. Arnold illustrates every principle with a figure. This book aims to cover the most basic parts of the subject and confines itself largely to the Cauchy and Neumann problems for the classical linear equations of mathematical physics, especially Laplace's equation and the wave equation, although the heat equation and the Korteweg-de Vries equation are also discussed. Physical intuition is emphasized. A large number of problems are sprinkled throughout the book, and a full set of problems from examinations given in Moscow are included at the end. Some of these problems are quite challenging! What makes the book unique is Arnold's particular talent at holding a topic up for examination from a new and fresh perspective. He likes to blow away the fog of generality that obscures so much mathematical writing and reveal the essentially simple intuitive ideas underlying the subject. No other mathematical writer does this quite so well as Arnold.
Basic Modern Theory Of Linear Complex Analytic Q Difference Equations
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Author : Jacques Sauloy
language : en
Publisher: American Mathematical Society
Release Date : 2024-11-06
Basic Modern Theory Of Linear Complex Analytic Q Difference Equations written by Jacques Sauloy 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 2024-11-06 with Mathematics categories.
The roots of the modern theories of differential and $q$-difference equations go back in part to an article by George D. Birkhoff, published in 1913, dealing with the three ?sister theories? of differential, difference and $q$-difference equations. This book is about $q$-difference equations and focuses on techniques inspired by differential equations, in line with Birkhoff's work, as revived over the last three decades. It follows the approach of the Ramis school, mixing algebraic and analytic methods. While it uses some $q$-calculus and is illustrated by $q$-special functions, these are not its main subjects. After a gentle historical introduction with emphasis on mathematics and a thorough study of basic problems such as elementary $q$-functions, elementary $q$-calculus, and low order equations, a detailed algebraic and analytic study of scalar equations is followed by the usual process of transforming them into systems and back again. The structural algebraic and analytic properties of systems are then described using $q$-difference modules (Newton polygon, filtration by the slopes). The final chapters deal with Fuchsian and irregular equations and systems, including their resolution, classification, Riemann-Hilbert correspondence, and Galois theory. Nine appendices complete the book and aim to help the reader by providing some fundamental yet not universally taught facts. There are 535 exercises of various styles and levels of difficulty. The main prerequisites are general algebra and analysis as taught in the first three years of university. The book will be of interest to expert and non-expert researchers as well as graduate students in mathematics and physics.
Lectures On Partial Differential Equations
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Author : I. G. Petrovsky
language : en
Publisher: Courier Corporation
Release Date : 2012-12-13
Lectures On Partial Differential Equations written by I. G. Petrovsky and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-13 with Mathematics categories.
Graduate-level exposition by noted Russian mathematician offers rigorous, readable coverage of classification of equations, hyperbolic equations, elliptic equations, and parabolic equations. Translated from the Russian by A. Shenitzer.
Five Lectures In Complex Analysis
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Author : Contreras Márquez Contreras
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Five Lectures In Complex Analysis written by Contreras Márquez Contreras and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
This volume contains state-of-art survey papers in complex analysis based on lectures given at the second Winter School on Complex Analysis and Operator Theory held in February 2008 at the University of Sevilla, Sevilla, Spain. --
Textrm C Algebras And Finite Dimensional Approximations
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Author : Nathanial P. Brown
language : en
Publisher: American Mathematical Society
Release Date : 2025-01-16
Textrm C Algebras And Finite Dimensional Approximations written by Nathanial P. Brown 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 2025-01-16 with Mathematics categories.
$mathrm{C}^*$-approximation theory has provided the foundation for many of the most important conceptual breakthroughs and applications of operator algebras. This book systematically studies (most of) the numerous types of approximation properties that have been important in recent years: nuclearity, exactness, quasidiagonality, local reflexivity, and others. Moreover, it contains user-friendly proofs, insofar as that is possible, of many fundamental results that were previously quite hard to extract from the literature. Indeed, perhaps the most important novelty of the first ten chapters is an earnest attempt to explain some fundamental, but difficult and technical, results as painlessly as possible. The latter half of the book presents related topics and applications—written with researchers and advanced, well-trained students in mind. The authors have tried to meet the needs both of students wishing to learn the basics of an important area of research as well as researchers who desire a fairly comprehensive reference for the theory and applications of $mathrm{C}^*$-approximation theory.
Geometric Complex Analysis
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Author : Jisoo Byun
language : en
Publisher: Springer
Release Date : 2018-09-08
Geometric Complex Analysis written by Jisoo Byun and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-08 with Mathematics categories.
The KSCV Symposium, the Korean Conference on Several Complex Variables, started in 1997 in an effort to promote the study of complex analysis and geometry. Since then, the conference met semi-regularly for about 10 years and then settled on being held biannually. The sixth and tenth conferences were held in 2002 and 2014 as satellite conferences to the Beijing International Congress of Mathematicians (ICM) and the Seoul ICM, respectively. The purpose of the KSCV Symposium is to organize the research talks of many leading scholars in the world, to provide an opportunity for communication, and to promote new researchers in this field.
Training Manual On Transport And Fluids
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Author : John C. Neu
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-11-30
Training Manual On Transport And Fluids written by John C. Neu and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-30 with Mathematics categories.
I have learned a lot from John Neu over the past years, and his book reflects very well his sense of style and purpose. --Walter Craig, McMaster University, Hamilton, Ontario, Canada and Fields Institute for Research in Mathematical Sciences, Toronto, Ontario, Canada John Neu's book presents the basic ideas of fluid mechanics, and of the transport of matter, in a clear and reader-friendly way. Then it proposes a collection of problems, starting with easy ones and gradually leading up to harder ones. Each problem is solved with all the steps explained. In the course of solving these problems, many fundamental methods of analysis are introduced and explained. This is an ideal book for use as a text, or for individual study. --Joseph B. Keller, Stanford University This book presents elementary models of transport in continuous media and a corresponding body of mathematical technique. Physical topics include convection and diffusion as the simplest models of transport; local conservation laws with sources as the general framework of continuum mechanics; ideal fluid as the simplest model of a medium with mass; momentum and energy transport; and finally, free surface waves, in particular, shallow water theory. There is a strong emphasis on dimensional analysis and scaling. Some topics, such as physical similarity and similarity solutions, are traditional. In addition, there are reductions based on scaling, such as incompressible flow as a limit of compressible flow, and shallow water theory derived asymptotically from the full equations of free surface waves. More and deeper examples are presented as problems, including a series of problems that model a tsunami approaching the shore. The problems form an embedded subtext to the book. Each problem is followed by a detailed solution emphasizing process and craftsmanship. The problems express the practice of applied mathematics as the examination and re-examination of simple but essential ideas in many interrelated examples.