Principal Solutions of Ordinary Differential Equations in the Complex Domain PDF Download
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Author: Walter Strodt
Publisher: American Mathematical Soc.
ISBN: 0821812262
Category : Differential equations
Languages : en
Pages : 111
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Book Description
Author: Walter Strodt
Publisher: American Mathematical Soc.
ISBN: 0821812262
Category : Differential equations
Languages : en
Pages : 111
Get Book Here
Book Description
Author: Walter Charles Strodt
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 107
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Book Description
Author: Einar Hille
Publisher: Courier Corporation
ISBN: 9780486696201
Category : Mathematics
Languages : en
Pages : 514
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Book Description
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.
Author: Gerald Teschl
Publisher: American Mathematical Society
ISBN: 147047641X
Category : Mathematics
Languages : en
Pages : 370
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Book Description
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 Poincaré–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.
Author: Walter Charles Strodt
Publisher: American Mathematical Soc.
ISBN: 0821812130
Category : Difference equations
Languages : en
Pages : 86
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Book Description
Author: Library of Congress. Copyright Office
Publisher:
ISBN:
Category : Copyright
Languages : en
Pages : 868
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Book Description
Author: Università di Padova. Seminario matematico
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 586
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Author: Yoshishige Haraoka
Publisher: Springer Nature
ISBN: 3030546632
Category : Mathematics
Languages : en
Pages : 396
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Book Description
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.
Author: Edward Lindsay Ince
Publisher:
ISBN:
Category : Differential equations
Languages : en
Pages : 578
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Book Description
