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Basic Theory of Ordinary Differential Equations (Universitext) - Hsieh, Po-Fang, Sibuya, Yasutaka
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Hsieh, Po-Fang, Sibuya, Yasutaka:

Basic Theory of Ordinary Differential Equations (Universitext) - hardcover

1999, ISBN: 9780387986999

Springer, Gebundene Ausgabe, Auflage: 1999, 480 Seiten, Publiziert: 1999-06-22T00:00:01Z, Produktgruppe: Buch, 1.88 kg, Mathematik, Naturwissenschaften & Technik, Kategorien, Bücher, Frem… More...

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Hsieh, Po-Fang and Yasutaka Shibuya:

Basic theory of ordinary differential equations. - First edition

1999, ISBN: 9780387986999

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Hsieh, Po-Fang and Yasutaka Shibuya:
Basic theory of ordinary differential equations. - First edition


ISBN: 0387986995

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Sibuya, Yasutaka; Hsieh, Po-Fang:
Basic Theory of Ordinary Differential Equations - hardcover

1999, ISBN: 0387986995

1999 Gebundene Ausgabe Differenzialgleichung / Gewöhnliche, Gewöhnliche Differenzialgleichung, Differentialoperator; Eigenvalue; ordinarydifferentialequations; Smoothfunction; different… More...

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Basic Theory of Ordinary Differential Equations - used book

1999, ISBN: 9780387986999

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Details of the book
Basic Theory of Ordinary Differential Equations (Universitext)

Providing readers with the very basic knowledge necessary to begin research on differential equations with professional ability, the selection of topics here covers the methods and results that are applicable in a variety of different fields. The book is divided into four parts. The first covers fundamental existence, uniqueness, smoothness with respect to data, and nonuniqueness. The second part describes the basic results concerning linear differential equations, while the third deals with nonlinear equations. In the last part the authors write about the basic results concerning power series solutions. Each chapter begins with a brief discussion of its contents and history, and hints and comments for many problems are given throughout. With 114 illustrations and 206 exercises, the book is suitable for a one-year graduate course, as well as a reference book for research mathematicians.

Details of the book - Basic Theory of Ordinary Differential Equations (Universitext)

EAN (ISBN-13): 9780387986999
ISBN (ISBN-10): 0387986995
Publishing year: 1999
Publisher: Springer
484 Pages
Weight: 0,882 kg
Language: eng/Englisch

Book in our database since 2007-04-17T10:35:28-04:00 (New York)
Detail page last modified on 2024-03-16T11:51:08-04:00 (New York)
ISBN/EAN: 0387986995

ISBN - alternate spelling:
0-387-98699-5, 978-0-387-98699-9
Alternate spelling and related search-keywords:
Book author: hsieh, yasutaka, fang, fields, basic
Book title: ordinary differential, basic, theory differential equations, something out the ordinary

Information from Publisher

Author: Po-Fang Hsieh
Title: Universitext; Basic Theory of Ordinary Differential Equations
Publisher: Springer; Springer US
469 Pages
Publishing year: 1999-06-22
New York; NY; US
Language: English
142,99 € (DE)

BB; Hardcover, Softcover / Mathematik/Analysis; Mathematische Analysis, allgemein; Verstehen; Differential operator; Eigenvalue; Ordinary Differential Equations; Smooth function; differential equation; maximum; minimum; ordinary differential equation; Analysis; BC

I. Fundamental Theorems of Ordinary Differential Equations.- I-1. Existence and uniqueness with the Lipschitz condition.- I-2. Existence without the Lipschitz condition.- I-3. Some global properties of solutions.- I-4. Analytic differential equations.- Exercises I.- II. Dependence on Data.- II-1. Continuity with respect to initial data and parameters.- II-2. Differentiability.- Exercises II.- III. Nonuniqueness.- III-l. Examples.- III-2. The Kneser theorem.- III-3. Solution curves on the boundary of R(A).- III-4. Maximal and minimal solutions.- III-5. A comparison theorem.- III-6. Sufficient conditions for uniqueness.- Exercises III.- IV. General Theory of Linear Systems.- IV-1. Some basic results concerning matrices.- IV-2. Homogeneous systems of linear differential equations.- IV-3. Homogeneous systems with constant coefficients.- IV-4. Systems with periodic coefficients.- IV-5. Linear Hamiltonian systems with periodic coefficients.- IV-6. Nonhomogeneous equations.- IV-7. Higher-order scalar equations.- Exercises IV.- V. Singularities of the First Kind.- V-1. Formal solutions of an algebraic differential equation.- V-2. Convergence of formal solutions of a system of the first kind.- V-3. TheS-Ndecomposition of a matrix of infinite order.- V-4. TheS-Ndecomposition of a differential operator.- V-5. A normal form of a differential operator.- V-6. Calculation of the normal form of a differential operator.- V-7. Classification of singularities of homogeneous linear systems.- Exercises V.- VI. Boundary-Value Problems of Linear Differential Equations of the Second-Order.- VI- 1. Zeros of solutions.- VI- 2. Sturm-Liouville problems.- VI- 3. Eigenvalue problems.- VI- 4. Eigenfunction expansions.- VI- 5. Jost solutions.- VI- 6. Scattering data.- VI- 7. Reflectionless potentials.- VI- 8. Construction of a potential for given data.- VI- 9. Differential equations satisfied by reflectionless potentials.- VI-10. Periodic potentials.- Exercises VI.- VII. Asymptotic Behavior of Solutions of Linear Systems.- VII-1. Liapounoff’s type numbers.- VII-2. Liapounoff’s type numbers of a homogeneous linear system.- VII-3. Calculation of Liapounoff’s type numbers of solutions.- VII-4. A diagonalization theorem.- VII-5. Systems with asymptotically constant coefficients.- VII-6. An application of the Floquet theorem.- Exercises VII.- VIII. Stability.- VIII- 1. Basic definitions.- VIII- 2. A sufficient condition for asymptotic stability.- VIII- 3. Stable manifolds.- VIII- 4. Analytic structure of stable manifolds.- VIII- 5. Two-dimensional linear systems with constant coefficients.- VIII- 6. Analytic systems in ?n.- VIII- 7. Perturbations of an improper node and a saddle point.- VIII- 8. Perturbations of a proper node.- VIII- 9. Perturbation of a spiral point.- VIII-10. Perturbation of a center.- Exercises VIII.- IX. Autonomous Systems.- IX-1. Limit-invariant sets.- IX-2. Liapounoff’s direct method.- IX-3. Orbital stability.- IX-4. The Poincaré-Bendixson theorem.- IX-5. Indices of Jordan curves.- Exercises IX.- X. The Second-Order Differential Equation $$\\frac{{{d^2}x}}{{d{t^2}}} + h(x)\\frac{{dx}}{{dt}} + g(x) = 0 $$.- X-1. Two-point boundary-value problems.- X-2. Applications of the Liapounoff functions.- X-3. Existence and uniqueness of periodic orbits.- X-4. Multipliers of the periodic orbit of the van der Pol equation.- X-5. The van der Pol equation for a small ?> 0.- X-6. The van der Pol equation for a large parameter.- X-7. A theorem due to M. Nagumo.- X-8. A singular perturbation problem.- Exercises X.- XI. Asymptotic Expansions.- XI-1. Asymptotic expansions in the sense of Poincaré.- XI-2. Gevrey asymptotics.- XI-3. Flat functions in the Gevrey asymptotics.- XI-4. Basic properties of Gevrey asymptotic expansions.- XI-5. Proof of Lemma XI-2-6.- Exercises XI.- XII. Asymptotic Expansions in a Parameter.- XII-1. An existence theorem.- XII-2. Basic estimates.- XII-3. Proof of Theorem XII-1-2.- XII-4. A block-diagonalization theorem.- XII-5. Gevrey asymptotic solutions in a parameter.- XII-6. Analytic simplification in a parameter.- Exercises XII.- XIII. Singularities of the Second Kind.- XIII-1. An existence theorem.- XIII-2. Basic estimates.- XIII-3. Proof of Theorem XIII-1-2.- XIII-4. A block-diagonalization theorem.- XIII-5. Cyclic vectors (A lemma of P. Deligne).- XIII-6. The Hukuhara-Turrittin theorem.- XIII-7. An n-th-order linear differential equation at a singular point of the second kind.- XIII-8. Gevrey property of asymptotic solutions at an irregular singular point.- Exercises XIII.- References.

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