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Ordinary Differential Equations in the Complex Domain

1997-01-01 Mathematics
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Release : 1997-01-01
Genre : Mathematics
Kind : eBook
Book Rating : 201/5 ( reviews)

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Book Synopsis Ordinary Differential Equations in the Complex Domain by : Einar Hille

Download or read book Ordinary Differential Equations in the Complex Domain written by Einar Hille. This book was released on 1997-01-01. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Linear Differential Equations in the Complex Domain

2020-11-16 Mathematics
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Release : 2020-11-16
Genre : Mathematics
Kind : eBook
Book Rating : 632/5 ( reviews)

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Book Synopsis Linear Differential Equations in the Complex Domain by : Yoshishige Haraoka

Download or read book Linear Differential Equations in the Complex Domain written by Yoshishige Haraoka. This book was released on 2020-11-16. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Linear Differential Equations in the Complex Domain

2008-06-26 Mathematics
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Release : 2008-06-26
Genre : Mathematics
Kind : eBook
Book Rating : 760/5 ( reviews)

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Book Synopsis Linear Differential Equations in the Complex Domain by : Yasutaka Sibuya

Download or read book Linear Differential Equations in the Complex Domain written by Yasutaka Sibuya. This book was released on 2008-06-26. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Ordinary Differential Equations

1981 Differential equations
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Release : 1981
Genre : Differential equations
Kind : eBook
Book Rating : 234/5 ( reviews)

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Book Synopsis Ordinary Differential Equations by : Amritava Gupta

Download or read book Ordinary Differential Equations written by Amritava Gupta. This book was released on 1981. Available in PDF, EPUB and Kindle. Book excerpt:

Ordinary Differential Equations and Dynamical Systems

2012-08-30 Mathematics
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Release : 2012-08-30
Genre : Mathematics
Kind : eBook
Book Rating : 283/5 ( reviews)

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Book Synopsis Ordinary Differential Equations and Dynamical Systems by : Gerald Teschl

Download or read book Ordinary Differential Equations and Dynamical Systems written by Gerald Teschl. This book was released on 2012-08-30. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained introduction to ordinary differential equations and dynamical systems suitable for beginning graduate students. The first part begins with some simple examples of explicitly solvable equations and a first glance at qualitative methods. Then the fundamental results concerning the initial value problem are proved: existence, uniqueness, extensibility, dependence on initial conditions. Furthermore, linear equations are considered, including the Floquet theorem, and some perturbation results. As somewhat independent topics, the Frobenius method for linear equations in the complex domain is established and Sturm-Liouville boundary value problems, including oscillation theory, are investigated. The second part introduces the concept of a dynamical system. The Poincare-Bendixson theorem is proved, and several examples of planar systems from classical mechanics, ecology, and electrical engineering are investigated. Moreover, attractors, Hamiltonian systems, the KAM theorem, and periodic solutions are discussed. Finally, stability is studied, including the stable manifold and the Hartman-Grobman theorem for both continuous and discrete systems. The third part introduces chaos, beginning with the basics for iterated interval maps and ending with the Smale-Birkhoff theorem and the Melnikov method for homoclinic orbits. The text contains almost three hundred exercises. Additionally, the use of mathematical software systems is incorporated throughout, showing how they can help in the study of differential equations.

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