Merkzettel Warenkorb
  • Produktbild: Basic Theory of Ordinary Differential Equations
  • Produktbild: Basic Theory of Ordinary Differential Equations
- 12%

Basic Theory of Ordinary Differential Equations

Aus der Reihe Universitext
12% sparen

74,99 € UVP 85,59 €

inkl. gesetzl. MwSt., Versandkostenfrei

Lieferung nach Hause

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

24.10.2012

Verlag

Springer Us

Seitenzahl

469

Maße (L/B/H)

23,5/15,5/2,7 cm

Gewicht

727 g

Auflage

Softcover reprint of the original 1st ed. 1999

Sprache

Englisch

ISBN

978-1-4612-7171-0

Beschreibung

Rezension

"This book in pure mathematics will guide the reader on a newly marked path through classic and awesome terrain---first so well described by Coddington and Levinson---toward research in the important and useful areas of power series solutions and asymptotics. The path not taken would be marked by at least one explicit mention of a Poincaré map, a resonance in celestial mechanics, an average, a traveling wave, or a transversal intersection of separatrices."--MATHEMATICAL REVIEWS

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

24.10.2012

Verlag

Springer Us

Seitenzahl

469

Maße (L/B/H)

23,5/15,5/2,7 cm

Gewicht

727 g

Auflage

Softcover reprint of the original 1st ed. 1999

Sprache

Englisch

ISBN

978-1-4612-7171-0

Herstelleradresse

Springer-Verlag KG
Sachsenplatz 4-6
1201 Wien
AT

Email: GPSR Kontakt

Kundinnen und Kunden meinen

0 Bewertungen

Informationen zu Bewertungen

Zur Abgabe einer Bewertung ist eine Anmeldung im Konto notwendig. Die Authentizität der Bewertungen wird von uns nicht überprüft. Wir behalten uns vor, Bewertungstexte, die unseren Richtlinien widersprechen, entsprechend zu kürzen oder zu löschen.

Die Bewertungen sind nach Format, Anzahl Sterne und Datum sortiert.

Verfassen Sie die erste Bewertung zu diesem Artikel

Helfen Sie anderen Kund*innen durch Ihre Meinung

Kundinnen und Kunden meinen

0 Bewertungen filtern
  • Produktbild: Basic Theory of Ordinary Differential Equations
  • Produktbild: Basic Theory of Ordinary Differential Equations
  • 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.