Introduction To Complex Theory Of Differential Equations
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Introduction To Complex Theory Of Differential Equations
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Author : Anton Savin
language : en
Publisher: Birkhäuser
Release Date : 2017-03-28
Introduction To Complex Theory Of Differential Equations written by Anton Savin and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-28 with Mathematics categories.
This book discusses the complex theory of differential equations or more precisely, the theory of differential equations on complex-analytic manifolds. Although the theory of differential equations on real manifolds is well known – it is described in thousands of papers and its usefulness requires no comments or explanations – to date specialists on differential equations have not focused on the complex theory of partial differential equations. However, as well as being remarkably beautiful, this theory can be used to solve a number of problems in real theory, for instance, the Poincaré balayage problem and the mother body problem in geophysics. The monograph does not require readers to be familiar with advanced notions in complex analysis, differential equations, or topology. With its numerous examples and exercises, it appeals to advanced undergraduate and graduate students, and also to researchers wanting to familiarize themselves with the subject.
Linear Differential Equations In The Complex Domain
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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.
Introduction To Theory Of Ordinary Differential Equation
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Author : V. DHARMAIAH
language : en
Publisher: PHI Learning Pvt. Ltd.
Release Date : 2012-09-19
Introduction To Theory Of Ordinary Differential Equation written by V. DHARMAIAH and has been published by PHI Learning Pvt. Ltd. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-19 with Mathematics categories.
This systematically-organized text on the theory of differential equations deals with the basic concepts and the methods of solving ordinary differential equations. Various existence theorems, properties of uniqueness, oscillation and stability theories, have all been explained with suitable examples to enhance students’ understanding of the subject. The book also discusses in sufficient detail the qualitative, the quantitative, and the approximation techniques, linear equations with variable and constants coefficients, regular singular points, and homogeneous equations with analytic coefficients. Finally, it explains Riccati equation, boundary value problems, the Sturm–Liouville problem, Green’s function, the Picard’s theorem, and the Sturm–Picone theorem. The text is supported by a number of worked-out examples to make the concepts clear, and it also provides a number of exercises help students test their knowledge and improve their skills in solving differential equations. The book is intended to serve as a text for the postgraduate students of mathematics and applied mathematics. It will also be useful to the candidates preparing to sit for the competitive examinations such as NET and GATE.
An Introduction To Several Complex Variables And Partial Differential Equations
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Author : H Begehr
language : en
Publisher: Chapman and Hall/CRC
Release Date : 1997-07-09
An Introduction To Several Complex Variables And Partial Differential Equations written by H Begehr and has been published by Chapman and Hall/CRC this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-07-09 with Mathematics categories.
Complex Analysis And Differential Equations
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Author : Luis Barreira
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-04-23
Complex Analysis And Differential Equations written by Luis Barreira 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 2012-04-23 with Mathematics categories.
This text provides an accessible, self-contained and rigorous introduction to complex analysis and differential equations. Topics covered include holomorphic functions, Fourier series, ordinary and partial differential equations. The text is divided into two parts: part one focuses on complex analysis and part two on differential equations. Each part can be read independently, so in essence this text offers two books in one. In the second part of the book, some emphasis is given to the application of complex analysis to differential equations. Half of the book consists of approximately 200 worked out problems, carefully prepared for each part of theory, plus 200 exercises of variable levels of difficulty. Tailored to any course giving the first introduction to complex analysis or differential equations, this text assumes only a basic knowledge of linear algebra and differential and integral calculus. Moreover, the large number of examples, worked out problems and exercises makes this the ideal book for independent study.
Partial Differential Equations And Complex Analysis
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Author : Steven G. Krantz
language : en
Publisher: CRC Press
Release Date : 2018-05-04
Partial Differential Equations And Complex Analysis written by Steven G. Krantz and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-04 with Mathematics categories.
Ever since the groundbreaking work of J.J. Kohn in the early 1960s, there has been a significant interaction between the theory of partial differential equations and the function theory of several complex variables. Partial Differential Equations and Complex Analysis explores the background and plumbs the depths of this symbiosis. The book is an excellent introduction to a variety of topics and presents many of the basic elements of linear partial differential equations in the context of how they are applied to the study of complex analysis. The author treats the Dirichlet and Neumann problems for elliptic equations and the related Schauder regularity theory, and examines how those results apply to the boundary regularity of biholomorphic mappings. He studies the ?-Neumann problem, then considers applications to the complex function theory of several variables and to the Bergman projection.
Introduction To Fractional And Pseudo Differential Equations With Singular Symbols
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Author : Sabir Umarov
language : en
Publisher: Springer
Release Date : 2015-08-18
Introduction To Fractional And Pseudo Differential Equations With Singular Symbols written by Sabir Umarov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-18 with Mathematics categories.
The book systematically presents the theories of pseudo-differential operators with symbols singular in dual variables, fractional order derivatives, distributed and variable order fractional derivatives, random walk approximants, and applications of these theories to various initial and multi-point boundary value problems for pseudo-differential equations. Fractional Fokker-Planck-Kolmogorov equations associated with a large class of stochastic processes are presented. A complex version of the theory of pseudo-differential operators with meromorphic symbols based on the recently introduced complex Fourier transform is developed and applied for initial and boundary value problems for systems of complex differential and pseudo-differential equations.
Ordinary Differential Equations
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Author : Jane Cronin
language : en
Publisher: CRC Press
Release Date : 2007-12-14
Ordinary Differential Equations written by Jane Cronin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-14 with Mathematics categories.
Designed for a rigorous first course in ordinary differential equations, Ordinary Differential Equations: Introduction and Qualitative Theory, Third Edition includes basic material such as the existence and properties of solutions, linear equations, autonomous equations, and stability as well as more advanced topics in periodic solutions of
Partial Differential Equations
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Author : Aleksei A. Dezin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Partial Differential Equations written by Aleksei A. Dezin 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.
Let me begin by explaining the meaning of the title of this book. In essence, the book studies boundary value problems for linear partial differ ential equations in a finite domain in n-dimensional Euclidean space. The problem that is investigated is the question of the dependence of the nature of the solvability of a given equation on the way in which the boundary conditions are chosen, i.e. on the supplementary requirements which the solution is to satisfy on specified parts of the boundary. The branch of mathematical analysis dealing with the study of boundary value problems for partial differential equations is often called mathematical physics. Classical courses in this subject usually consider quite restricted classes of equations, for which the problems have an immediate physical context, or generalizations of such problems. With the expanding domain of application of mathematical methods at the present time, there often arise problems connected with the study of partial differential equations that do not belong to any of the classical types. The elucidation of the correct formulation of these problems and the study of the specific properties of the solutions of similar equations are closely related to the study of questions of a general nature.
Painlev Differential Equations In The Complex Plane
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Author : Valerii I. Gromak
language : en
Publisher: Walter de Gruyter
Release Date : 2008-08-22
Painlev Differential Equations In The Complex Plane written by Valerii I. 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 2008-08-22 with Mathematics 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 separately for each of these six equations. The final chapter offers a short overview of applications of Painlevé equations, including an introduction to their discrete counterparts. Due to the present important role of Painlevé equations in physical applications, this monograph should be of interest to researchers in both mathematics and physics and to graduate students interested in mathematical physics and the theory of differential equations.