Ordinary Differential Equations in the Complex Domain

Author: Einar Hille

Publisher: Courier Corporation

ISBN: 9780486696201

Category: Mathematics

Page: 484

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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.
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Linear Differential Equations in the Complex Domain

Problems of Analytic Continuation

Author: Yasutaka Sibuya

Publisher: American Mathematical Soc.

ISBN: 0821846760

Category: Mathematics

Page: 267

View: 1033

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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.
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Ordinary Differential Equations

Author: Edward L. Ince

Publisher: Courier Corporation

ISBN: 0486158217

Category: Mathematics

Page: 576

View: 8902

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Among the topics covered in this classic treatment are linear differential equations; solution in an infinite form; solution by definite integrals; algebraic theory; Sturmian theory and its later developments; much more. "Highly recommended" — Electronics Industries.
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Linear Differential Equations and Group Theory from Riemann to Poincare

Author: Jeremy Gray

Publisher: Springer Science & Business Media

ISBN: 0817647732

Category: Mathematics

Page: 338

View: 2598

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This book is a study of how a particular vision of the unity of mathematics, often called geometric function theory, was created in the 19th century. The central focus is on the convergence of three mathematical topics: the hypergeometric and related linear differential equations, group theory, and on-Euclidean geometry. The text for this second edition has been greatly expanded and revised, and the existing appendices enriched. The exercises have been retained, making it possible to use the book as a companion to mathematics courses at the graduate level.
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Heun's Differential Equations

Author: F. M. Arscott,Slavyanov S. Yu.,D. Schmidt,G. Wolf,P. Maroni,A. Duval

Publisher: Clarendon Press

ISBN: 9780198596950

Category: Mathematics

Page: 354

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Heun's equation is a second-order differential equation which crops up in a variety of forms in a wide range of problems in applied mathematics. These include integral equations of potential theory, wave propagation, electrostatic oscillation, and Schrodinger's equation. This volume brings together important research work for the first time, providing an important resource for all those interested in this mathematical topic. Both the current theory and the main areas of application are surveyed, and includes contributions from authoritative researchers.
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Surveys in Modern Mathematics

Author: Victor Prasolov,Yulij Ilyashenko

Publisher: Cambridge University Press

ISBN: 9781139441124

Category: Mathematics

Page: N.A

View: 5790

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This collection of articles from the Independent University of Moscow is derived from the Globus seminars held there. They are given by world authorities, from Russia and elsewhere, in various areas of mathematics and are designed to introduce graduate students to some of the most dynamic areas of mathematical research. The seminars aim to be informal, wide-ranging and forward-looking, getting across the ideas and concepts rather than formal proofs, and this carries over to the articles here. Topics covered range from computational complexity, algebraic geometry, dynamics, through to number theory and quantum groups. The volume as a whole is a fascinating and exciting overview of contemporary mathematics.
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Asymptotic Expansions for Ordinary Differential Equations

Author: Wolfgang Wasow

Publisher: Courier Dover Publications

ISBN: 0486824586

Category: Mathematics

Page: 384

View: 8330

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This outstanding text concentrates on the mathematical ideas underlying various asymptotic methods for ordinary differential equations that lead to full, infinite expansions. "A book of great value." — Mathematical Reviews. 1976 revised edition.
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Special Functions

A Unified Theory Based on Singularities

Author: Sergei IUr?evich Slavianov,Sergeĭ IUrʹevich Slavianov,Sergej Jur'evič Slavjanov,Sergej U. Slavianov,Sergeĭ I{u0361}Urʹevich Slavi{u0361}anov,Sergeĭ I︠U︡rʹevich Slavi︠a︡nov,Sergei Yu Slavyanov,Wolfgang Lay

Publisher: Oxford University Press on Demand

ISBN: 9780198505730

Category: Mathematics

Page: 293

View: 9851

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The subject of this book is the theory of special functions, not considered as a list of functions exhibiting a certain range of properties, but based on the unified study of singularities of second-order ordinary differential equations in the complex domain. The number and characteristics of the singularities serve as a basis for classification of each individual special function. Links between linear special functions (as solutions of linear second-order equations), and non-linear special functions (as solutions of Painlev� equations) are presented as a basic and new result. Many applications to different areas of physics are shown and discussed. The book is written from a practical point of view and will address all those scientists whose work involves applications of mathematical methods. Lecturers, graduate students and researchers will find this a useful text and reference work.
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