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: 5069

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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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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: 2393

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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: André Ronveaux,F. M. Arscott

Publisher: Clarendon Press

ISBN: 9780198596950

Category: Mathematics

Page: 354

View: 5956

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Collating papers from a number of internationally renowned mathematicians, this book surveys both the current theory and the main areas of application of Heun's equation. This crops up in a wide variety of problems in applied mathematics, such as integral equations of potential theory, wave propagation, electrostatic oscillation, and Schrodinger's equation. This major collection will be of interest specifically for those researchers in non-linear Hamiltoniansystems, as well as those working in mathematical biology.
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Asymptotic Expansions for Ordinary Differential Equations

Author: Wolfgang Wasow

Publisher: Courier Dover Publications

ISBN: 0486824586

Category: Mathematics

Page: 384

View: 5329

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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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Ordinary Differential Equations

Author: Edward L. Ince

Publisher: Courier Corporation

ISBN: 9780486603490

Category: Mathematics

Page: 558

View: 997

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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; further developments in the theory of boundary problems; existence theorems, equations of first order; nonlinear equations of higher order; more. "Highly recommended" — Electronics Industries.
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Embeddings and Immersions

Author: Masahisa Adachi

Publisher: American Mathematical Soc.

ISBN: 9780821846124

Category: Mathematics

Page: 183

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This book covers fundamental techniques in the theory of $C^{\infty}$-imbeddings and $C^{\infty}$-immersions, emphasizing clear intuitive understanding and containing many figures and diagrams. Adachi starts with an introduction to the work of Whitney and of Haefliger on $C^{\infty}$-imbeddings and $C^{\infty}$-manifolds. The Smale-Hirsch theorem is presented as a generalization of the classification of $C^{\infty}$-imbeddings by isotopy and is extended by Gromov's work on the subject, including Gromov's convex integration theory. Finally, as an application of Gromov's work, the author introduces Haefliger's classification theorem of foliations on open manifolds. Also described here is the Adachi's work with Landweber on the integrability of almost complex structures on open manifolds. This book would be an excellent text for upper-division undergraduate or graduate courses.
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Classical and Quantum Nonlinear Integrable Systems

Theory and Application

Author: A Kundu

Publisher: CRC Press

ISBN: 9781420034615

Category: Science

Page: 292

View: 645

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Covering both classical and quantum models, nonlinear integrable systems are of considerable theoretical and practical interest, with applications over a wide range of topics, including water waves, pin models, nonlinear optics, correlated electron systems, plasma physics, and reaction-diffusion processes. Comprising one part on classical theories
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