Linear Differential Equations In The Complex Domain
DOWNLOAD
Download Linear Differential Equations In The Complex Domain PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Linear Differential Equations In The Complex Domain book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Linear Differential Equations In The Complex Domain
DOWNLOAD
Author : Yoshishige Haraoka
language : en
Publisher: Springer Nature
Release Date : 2020-11-16
Linear Differential Equations In The Complex Domain written by Yoshishige Haraoka and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-16 with Mathematics categories.
This book provides a detailed introduction to recent developments in the theory of linear differential systems and integrable total differential systems. Starting from the basic theory of linear ordinary differential equations and integrable systems, it proceeds to describe Katz theory and its applications, extending it to the case of several variables. In addition, connection problems, deformation theory, and the theory of integral representations are comprehensively covered. Complete proofs are given, offering the reader a precise account of the classical and modern theory of linear differential equations in the complex domain, including an exposition of Pfaffian systems and their monodromy problems. The prerequisites are a course in complex analysis and the basics of differential equations, topology and differential geometry. This book will be useful for graduate students, specialists in differential equations, and for non-specialists who want to use differential equations.
Linear Differential Equations In The Complex Domain
DOWNLOAD
Author : Yasutaka Sibuya
language : en
Publisher: American Mathematical Soc.
Release Date : 2008-06-26
Linear Differential Equations In The Complex Domain written by Yasutaka Sibuya 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 2008-06-26 with Mathematics categories.
This book is a translation of a 1976 book originally written in Japanese. The main attention is paid to intrinsic aspects of problems related to linear ordinary differential equations in complex domains. Examples of the problems discussed in the book include the Riemann problem on the Riemann sphere, a characterization of regular singularities, and a classification of meromorphic differential equations. Since the original book was published, many new ideas have developed, such as applications of D-modules, Gevrey asymptotics, cohomological methods, $k$-summability, and studies of differential equations containing parameters. Five appendices, added in the present edition, briefly cover these new ideas. In addition, more than 100 references have been added. This book introduces the reader to the essential facts concerning the structure of solutions of linear differential equations in the complex domain and illuminates the intrinsic meaning of older results by means of more modern ideas. A useful reference for research mathematicians, this book would also be suitable as a textbook in a graduate course or seminar.
Principal Solutions Of Ordinary Differential Equations In The Complex Domain
DOWNLOAD
Author : Walter Strodt
language : en
Publisher: American Mathematical Soc.
Release Date : 1957
Principal Solutions Of Ordinary Differential Equations In The Complex Domain written by Walter Strodt 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 1957 with Differential equations categories.
Ordinary Differential Equations
DOWNLOAD
Author : Amritava Gupta
language : en
Publisher: Academic Publishers
Release Date : 1981
Ordinary Differential Equations written by Amritava Gupta and has been published by Academic Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Differential equations categories.
Principal Solutions Of Ordinary Differential Equations In The Complex Domain
DOWNLOAD
Author : Walter Charles Strodt
language : en
Publisher:
Release Date : 1957
Principal Solutions Of Ordinary Differential Equations In The Complex Domain written by Walter Charles Strodt and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1957 with categories.
Ordinary Differential Equations And Dynamical Systems
DOWNLOAD
Author : Gerald Teschl
language : en
Publisher: American Mathematical Society
Release Date : 2024-01-12
Ordinary Differential Equations And Dynamical Systems written by Gerald Teschl 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 2024-01-12 with Mathematics categories.
This book provides a self-contained introduction to ordinary differential equations and dynamical systems suitable for beginning graduate students. The first part begins with some simple examples of explicitly solvable equations and a first glance at qualitative methods. Then the fundamental results concerning the initial value problem are proved: existence, uniqueness, extensibility, dependence on initial conditions. Furthermore, linear equations are considered, including the Floquet theorem, and some perturbation results. As somewhat independent topics, the Frobenius method for linear equations in the complex domain is established and Sturm–Liouville boundary value problems, including oscillation theory, are investigated. The second part introduces the concept of a dynamical system. The Poincaré–Bendixson theorem is proved, and several examples of planar systems from classical mechanics, ecology, and electrical engineering are investigated. Moreover, attractors, Hamiltonian systems, the KAM theorem, and periodic solutions are discussed. Finally, stability is studied, including the stable manifold and the Hartman–Grobman theorem for both continuous and discrete systems. The third part introduces chaos, beginning with the basics for iterated interval maps and ending with the Smale–Birkhoff theorem and the Melnikov method for homoclinic orbits. The text contains almost three hundred exercises. Additionally, the use of mathematical software systems is incorporated throughout, showing how they can help in the study of differential equations.
Contributions To The Asymptotic Theory Of Ordinary Differential Equations In The Complex Domain
DOWNLOAD
Author : Walter Strodt
language : en
Publisher: American Mathematical Soc.
Release Date : 1954
Contributions To The Asymptotic Theory Of Ordinary Differential Equations In The Complex Domain written by Walter Strodt 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 1954 with Difference equations categories.
Formal And Analytic Solutions Of Differential Equations
DOWNLOAD
Author : Galina Filipuk
language : en
Publisher: World Scientific
Release Date : 2022-03-03
Formal And Analytic Solutions Of Differential Equations written by Galina Filipuk and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-03 with Mathematics categories.
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.
Painlev Differential Equations In The Complex Plane
DOWNLOAD
Author : Valeriĭ Ivanovich Gromak
language : en
Publisher: Walter de Gruyter
Release Date : 2002
Painlev Differential Equations In The Complex Plane written by Valeriĭ Ivanovich Gromak and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Functions of complex variables categories.
This book is the first comprehensive treatment of Painlevé differential equations in the complex plane. Starting with a rigorous presentation for the meromorphic nature of their solutions, the Nevanlinna theory will be applied to offer a detailed exposition of growth aspects and value distribution of Painlevé transcendents. The subsequent main part of the book is devoted to topics of classical background such as representations and expansions of solutions, solutions of special type like rational and special transcendental solutions, Bäcklund transformations and higher order analogues, treated.
Introduction To Stokes Structures
DOWNLOAD
Author : Claude Sabbah
language : en
Publisher: Springer
Release Date : 2012-10-03
Introduction To Stokes Structures written by Claude Sabbah and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-03 with Mathematics categories.
This research monograph provides a geometric description of holonomic differential systems in one or more variables. Stokes matrices form the extended monodromy data for a linear differential equation of one complex variable near an irregular singular point. The present volume presents the approach in terms of Stokes filtrations. For linear differential equations on a Riemann surface, it also develops the related notion of a Stokes-perverse sheaf. This point of view is generalized to holonomic systems of linear differential equations in the complex domain, and a general Riemann-Hilbert correspondence is proved for vector bundles with meromorphic connections on a complex manifold. Applications to the distributions solutions to such systems are also discussed, and various operations on Stokes-filtered local systems are analyzed.