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Complex Differential and Difference Equations

Complex Differential and Difference Equations
Author: Galina Filipuk
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 473
Release: 2019-11-18
Genre: Mathematics
ISBN: 3110611422

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With a balanced combination of longer survey articles and shorter, peer-reviewed research-level presentations on the topic of differential and difference equations on the complex domain, this edited volume presents an up-to-date overview of areas such as WKB analysis, summability, resurgence, formal solutions, integrability, and several algebraic aspects of differential and difference equations.


Nevanlinna Theory and Complex Differential Equations

Nevanlinna Theory and Complex Differential Equations
Author: Ilpo Laine
Publisher: Walter de Gruyter
Total Pages: 353
Release: 2011-06-01
Genre: Mathematics
ISBN: 3110863146

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The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.


Complex Delay-Differential Equations

Complex Delay-Differential Equations
Author: Kai Liu
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 302
Release: 2021-06-08
Genre: Mathematics
ISBN: 3110560569

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This book presents developments and new results on complex differential-difference equations, an area with important and interesting applications, which also gathers increasing attention. Key problems, methods, and results related to complex differential-difference equations are collected to offer an up-to-date overview of the field.


Complex Analysis and Differential Equations

Complex Analysis and Differential Equations
Author: Luis Barreira
Publisher: Springer Science & Business Media
Total Pages: 417
Release: 2012-04-23
Genre: Mathematics
ISBN: 1447140087

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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.


Differential-Difference Equations

Differential-Difference Equations
Author: Bellman
Publisher: Academic Press
Total Pages: 484
Release: 1963-01-01
Genre: Mathematics
ISBN: 0080955142

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Differential-Difference Equations


Ordinary Differential Equations in the Complex Domain

Ordinary Differential Equations in the Complex Domain
Author: Einar Hille
Publisher: Courier Corporation
Total Pages: 514
Release: 1997-01-01
Genre: Mathematics
ISBN: 9780486696201

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Graduate-level text offers full treatments of existence theorems, representation of solutions by series, theory of majorants, dominants and minorants, questions of growth, much more. Includes 675 exercises. Bibliography.


Partial Differential Equations and Complex Analysis

Partial Differential Equations and Complex Analysis
Author: Steven G. Krantz
Publisher: CRC Press
Total Pages: 322
Release: 1992-07-02
Genre: Mathematics
ISBN: 9780849371554

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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.


Partial Differential Equations and Complex Analysis

Partial Differential Equations and Complex Analysis
Author: Steven G. Krantz
Publisher: CRC Press
Total Pages: 320
Release: 2018-05-04
Genre: Mathematics
ISBN: 1351425811

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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.


Advances in Differential and Difference Equations with Applications 2020

Advances in Differential and Difference Equations with Applications 2020
Author: Dumitru Baleanu
Publisher: MDPI
Total Pages: 348
Release: 2021-01-20
Genre: Computers
ISBN: 3039368702

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It is very well known that differential equations are related with the rise of physical science in the last several decades and they are used successfully for models of real-world problems in a variety of fields from several disciplines. Additionally, difference equations represent the discrete analogues of differential equations. These types of equations started to be used intensively during the last several years for their multiple applications, particularly in complex chaotic behavior. A certain class of differential and related difference equations is represented by their respective fractional forms, which have been utilized to better describe non-local phenomena appearing in all branches of science and engineering. The purpose of this book is to present some common results given by mathematicians together with physicists, engineers, as well as other scientists, for whom differential and difference equations are valuable research tools. The reported results can be used by researchers and academics working in both pure and applied differential equations.