Nevanlinna Theory, Normal Families, and Algebraic Differential Equations

Nevanlinna Theory, Normal Families, and Algebraic Differential Equations

Author: Norbert Steinmetz

Publisher: Springer

Published: 2017-07-24

Total Pages: 249

ISBN-13: 3319598007

DOWNLOAD EBOOK

This book offers a modern introduction to Nevanlinna theory and its intricate relation to the theory of normal families, algebraic functions, asymptotic series, and algebraic differential equations. Following a comprehensive treatment of Nevanlinna’s theory of value distribution, the author presents advances made since Hayman’s work on the value distribution of differential polynomials and illustrates how value- and pair-sharing problems are linked to algebraic curves and Briot–Bouquet differential equations. In addition to discussing classical applications of Nevanlinna theory, the book outlines state-of-the-art research, such as the effect of the Yosida and Zalcman–Pang method of re-scaling to algebraic differential equations, and presents the Painlevé–Yosida theorem, which relates Painlevé transcendents and solutions to selected 2D Hamiltonian systems to certain Yosida classes of meromorphic functions. Aimed at graduate students interested in recent developments in the field and researchers working on related problems, Nevanlinna Theory, Normal Families, and Algebraic Differential Equations will also be of interest to complex analysts looking for an introduction to various topics in the subject area. With examples, exercises and proofs seamlessly intertwined with the body of the text, this book is particularly suitable for the more advanced reader.


Book Synopsis Nevanlinna Theory, Normal Families, and Algebraic Differential Equations by : Norbert Steinmetz

Download or read book Nevanlinna Theory, Normal Families, and Algebraic Differential Equations written by Norbert Steinmetz and published by Springer. This book was released on 2017-07-24 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a modern introduction to Nevanlinna theory and its intricate relation to the theory of normal families, algebraic functions, asymptotic series, and algebraic differential equations. Following a comprehensive treatment of Nevanlinna’s theory of value distribution, the author presents advances made since Hayman’s work on the value distribution of differential polynomials and illustrates how value- and pair-sharing problems are linked to algebraic curves and Briot–Bouquet differential equations. In addition to discussing classical applications of Nevanlinna theory, the book outlines state-of-the-art research, such as the effect of the Yosida and Zalcman–Pang method of re-scaling to algebraic differential equations, and presents the Painlevé–Yosida theorem, which relates Painlevé transcendents and solutions to selected 2D Hamiltonian systems to certain Yosida classes of meromorphic functions. Aimed at graduate students interested in recent developments in the field and researchers working on related problems, Nevanlinna Theory, Normal Families, and Algebraic Differential Equations will also be of interest to complex analysts looking for an introduction to various topics in the subject area. With examples, exercises and proofs seamlessly intertwined with the body of the text, this book is particularly suitable for the more advanced reader.

Nevanlinna Theory and Complex Differential Equations

Nevanlinna Theory and Complex Differential Equations

Author: Ilpo Laine

Publisher: Walter de Gruyter

Published: 2011-06-01

Total Pages: 353

ISBN-13: 3110863146

DOWNLOAD EBOOK

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.


Book Synopsis Nevanlinna Theory and Complex Differential Equations by : Ilpo Laine

Download or read book Nevanlinna Theory and Complex Differential Equations written by Ilpo Laine and published by Walter de Gruyter. This book was released on 2011-06-01 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Algebraic Approach to Differential Equations

Algebraic Approach to Differential Equations

Author: D?ng Tr ng Lˆ

Publisher: World Scientific

Published: 2010

Total Pages: 320

ISBN-13: 9814273244

DOWNLOAD EBOOK

Mixing elementary results and advanced methods, Algebraic Approach to Differential Equations aims to accustom differential equation specialists to algebraic methods in this area of interest. It presents material from a school organized by The Abdus Salam International Centre for Theoretical Physics (ICTP), the Bibliotheca Alexandrina, and the International Centre for Pure and Applied Mathematics (CIMPA).


Book Synopsis Algebraic Approach to Differential Equations by : D?ng Tr ng Lˆ

Download or read book Algebraic Approach to Differential Equations written by D?ng Tr ng Lˆ and published by World Scientific. This book was released on 2010 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mixing elementary results and advanced methods, Algebraic Approach to Differential Equations aims to accustom differential equation specialists to algebraic methods in this area of interest. It presents material from a school organized by The Abdus Salam International Centre for Theoretical Physics (ICTP), the Bibliotheca Alexandrina, and the International Centre for Pure and Applied Mathematics (CIMPA).

Ordinary Differential Equations

Ordinary Differential Equations

Author: Wolfgang Walter

Publisher: Springer Science & Business Media

Published: 2013-03-11

Total Pages: 391

ISBN-13: 1461206014

DOWNLOAD EBOOK

Based on a translation of the 6th edition of Gewöhnliche Differentialgleichungen by Wolfgang Walter, this edition includes additional treatments of important subjects not found in the German text as well as material that is seldom found in textbooks, such as new proofs for basic theorems. This unique feature of the book calls for a closer look at contents and methods with an emphasis on subjects outside the mainstream. Exercises, which range from routine to demanding, are dispersed throughout the text and some include an outline of the solution. Applications from mechanics to mathematical biology are included and solutions of selected exercises are found at the end of the book. It is suitable for mathematics, physics, and computer science graduate students to be used as collateral reading and as a reference source for mathematicians. Readers should have a sound knowledge of infinitesimal calculus and be familiar with basic notions from linear algebra; functional analysis is developed in the text when needed.


Book Synopsis Ordinary Differential Equations by : Wolfgang Walter

Download or read book Ordinary Differential Equations written by Wolfgang Walter and published by Springer Science & Business Media. This book was released on 2013-03-11 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on a translation of the 6th edition of Gewöhnliche Differentialgleichungen by Wolfgang Walter, this edition includes additional treatments of important subjects not found in the German text as well as material that is seldom found in textbooks, such as new proofs for basic theorems. This unique feature of the book calls for a closer look at contents and methods with an emphasis on subjects outside the mainstream. Exercises, which range from routine to demanding, are dispersed throughout the text and some include an outline of the solution. Applications from mechanics to mathematical biology are included and solutions of selected exercises are found at the end of the book. It is suitable for mathematics, physics, and computer science graduate students to be used as collateral reading and as a reference source for mathematicians. Readers should have a sound knowledge of infinitesimal calculus and be familiar with basic notions from linear algebra; functional analysis is developed in the text when needed.

Theory of Differential Equations

Theory of Differential Equations

Author: Andrew Russell Forsyth

Publisher: Cambridge University Press

Published: 2012-07-19

Total Pages: 551

ISBN-13: 110769681X

DOWNLOAD EBOOK

The fourth of six volumes in Forsyth's Theory of Differential Equations series, concentrating specifically on ordinary linear equations.


Book Synopsis Theory of Differential Equations by : Andrew Russell Forsyth

Download or read book Theory of Differential Equations written by Andrew Russell Forsyth and published by Cambridge University Press. This book was released on 2012-07-19 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fourth of six volumes in Forsyth's Theory of Differential Equations series, concentrating specifically on ordinary linear equations.

Applications of Nevanlinna Theory to Differential Polynomials, Differential Equations and Deficient Values

Applications of Nevanlinna Theory to Differential Polynomials, Differential Equations and Deficient Values

Author: Anand Prakash Singh

Publisher:

Published: 1976

Total Pages: 248

ISBN-13:

DOWNLOAD EBOOK


Book Synopsis Applications of Nevanlinna Theory to Differential Polynomials, Differential Equations and Deficient Values by : Anand Prakash Singh

Download or read book Applications of Nevanlinna Theory to Differential Polynomials, Differential Equations and Deficient Values written by Anand Prakash Singh and published by . This book was released on 1976 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Galois’ Dream: Group Theory and Differential Equations

Galois’ Dream: Group Theory and Differential Equations

Author: Michio Kuga

Publisher: Springer Science & Business Media

Published: 1993

Total Pages: 164

ISBN-13: 9780817636883

DOWNLOAD EBOOK

First year, undergraduate, mathematics students in Japan have for many years had the opportunity of a unique experience---an introduction, at an elementary level, to some very advanced ideas in mathematics from one of the leading mathematicians of the world. English reading students now have the opportunity to enjoy this lively presentation, from elementary ideas to cartoons to funny examples, and to follow the mind of an imaginative and creative mathematician into a world of enduring mathematical creations.


Book Synopsis Galois’ Dream: Group Theory and Differential Equations by : Michio Kuga

Download or read book Galois’ Dream: Group Theory and Differential Equations written by Michio Kuga and published by Springer Science & Business Media. This book was released on 1993 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: First year, undergraduate, mathematics students in Japan have for many years had the opportunity of a unique experience---an introduction, at an elementary level, to some very advanced ideas in mathematics from one of the leading mathematicians of the world. English reading students now have the opportunity to enjoy this lively presentation, from elementary ideas to cartoons to funny examples, and to follow the mind of an imaginative and creative mathematician into a world of enduring mathematical creations.

Ordinary Differential Equations

Ordinary Differential Equations

Author: A. K. Nandakumaran

Publisher: Cambridge University Press

Published: 2017-05-11

Total Pages: 352

ISBN-13: 110834416X

DOWNLOAD EBOOK

Written in a clear, logical and concise manner, this comprehensive resource allows students to quickly understand the key principles, techniques and applications of ordinary differential equations. Important topics including first and second order linear equations, initial value problems and qualitative theory are presented in separate chapters. The concepts of two point boundary value problems, physical models and first order partial differential equations are discussed in detail. The text uses tools of calculus and real analysis to get solutions in explicit form. While discussing first order linear systems, linear algebra techniques are used. The real-life applications are interspersed throughout the book to invoke reader's interest. The methods and tricks to solve numerous mathematical problems with sufficient derivations and explanation are provided. The proofs of theorems are explained for the benefit of the readers.


Book Synopsis Ordinary Differential Equations by : A. K. Nandakumaran

Download or read book Ordinary Differential Equations written by A. K. Nandakumaran and published by Cambridge University Press. This book was released on 2017-05-11 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written in a clear, logical and concise manner, this comprehensive resource allows students to quickly understand the key principles, techniques and applications of ordinary differential equations. Important topics including first and second order linear equations, initial value problems and qualitative theory are presented in separate chapters. The concepts of two point boundary value problems, physical models and first order partial differential equations are discussed in detail. The text uses tools of calculus and real analysis to get solutions in explicit form. While discussing first order linear systems, linear algebra techniques are used. The real-life applications are interspersed throughout the book to invoke reader's interest. The methods and tricks to solve numerous mathematical problems with sufficient derivations and explanation are provided. The proofs of theorems are explained for the benefit of the readers.

Non-Linear Partial Differential Equations

Non-Linear Partial Differential Equations

Author: E.E. Rosinger

Publisher: Elsevier

Published: 1990-11-22

Total Pages: 403

ISBN-13: 0080872751

DOWNLOAD EBOOK

A massive transition of interest from solving linear partial differential equations to solving nonlinear ones has taken place during the last two or three decades. The availability of better computers has often made numerical experimentations progress faster than the theoretical understanding of nonlinear partial differential equations. The three most important nonlinear phenomena observed so far both experimentally and numerically, and studied theoretically in connection with such equations have been the solitons, shock waves and turbulence or chaotical processes. In many ways, these phenomena have presented increasing difficulties in the mentioned order. In particular, the latter two phenomena necessarily lead to nonclassical or generalized solutions for nonlinear partial differential equations.


Book Synopsis Non-Linear Partial Differential Equations by : E.E. Rosinger

Download or read book Non-Linear Partial Differential Equations written by E.E. Rosinger and published by Elsevier. This book was released on 1990-11-22 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: A massive transition of interest from solving linear partial differential equations to solving nonlinear ones has taken place during the last two or three decades. The availability of better computers has often made numerical experimentations progress faster than the theoretical understanding of nonlinear partial differential equations. The three most important nonlinear phenomena observed so far both experimentally and numerically, and studied theoretically in connection with such equations have been the solitons, shock waves and turbulence or chaotical processes. In many ways, these phenomena have presented increasing difficulties in the mentioned order. In particular, the latter two phenomena necessarily lead to nonclassical or generalized solutions for nonlinear partial differential equations.

First Order Algebraic Differential Equations

First Order Algebraic Differential Equations

Author: M. Matsuda

Publisher: Springer

Published: 2006-11-15

Total Pages: 118

ISBN-13: 3540393110

DOWNLOAD EBOOK


Book Synopsis First Order Algebraic Differential Equations by : M. Matsuda

Download or read book First Order Algebraic Differential Equations written by M. Matsuda and published by Springer. This book was released on 2006-11-15 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: