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Differential Equations, Dynamical Systems, and Linear Algebra.
This book is about dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. A prominent role is played by the structure theory of linear operators on finite-dimensional vector spaces; the authors have included a sel...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Burlington :
Elsevier,
1974.
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| Colección: | Pure and Applied Mathematics.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
| LEADER | 00000cam a2200000Mu 4500 | ||
|---|---|---|---|
| 001 | EBOOKCENTRAL_ocn476217324 | ||
| 003 | OCoLC | ||
| 005 | 20240329122006.0 | ||
| 006 | m o d | ||
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| 008 | 091207s1974 vtu o 000 0 eng d | ||
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| 019 | |a 742292301 |a 815688085 |a 823117065 | ||
| 020 | |a 9780080873763 |q (electronic bk.) | ||
| 020 | |a 0080873766 |q (electronic bk.) | ||
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| 035 | |a (OCoLC)476217324 |z (OCoLC)742292301 |z (OCoLC)815688085 |z (OCoLC)823117065 | ||
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| 049 | |a UAMI | ||
| 100 | 1 | |a Hirsch, Morris W. | |
| 245 | 1 | 0 | |a Differential Equations, Dynamical Systems, and Linear Algebra. |
| 260 | |a Burlington : |b Elsevier, |c 1974. | ||
| 300 | |a 1 online resource (373 pages). | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Pure and Applied Mathematics | |
| 520 | |a This book is about dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. A prominent role is played by the structure theory of linear operators on finite-dimensional vector spaces; the authors have included a self-contained treatment of that subject. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Front Cover; Differential Equations, Dynamical Systems, and Linear Algebra; Copyright Page; Contents; Preface; CHAPTER 1. FIRST EXAMPLES; 1. The Simplest Examples; 2. Linear Systems with Constant Coefficients; Notes; CHAPTER 2. NEWTON'S EQUATION AND KEPLER'S LAW; 1. Harmonic Oscillators; 2. Some Calculus Background; 3. Conservative Force Fields; 4. Central Force Fields; 5. States; 6. Elliptical Planetary Orbits; Notes; CHAPTER 3. LINEAR SYSTEMS WITH CONSTANT COEFFICIENTS AND REAL EIGENVALUES; 1. Basic Linear Algebra; 2. Real Eigenvalues | |
| 505 | 8 | |a 3. Differential Equations with Real, Distinct Eigenvalues4. Complex Eigenvalues; CHAPTER 4. LINEAR SYSTEMS WITH CONSTANT COEFFICIENTS AND COMPLEX EIGENVALUES; 1. Complex Vector Spaces; 2. Real Operators with Complex Eigenvalues; 3. Application of Complex Linear Algebra to Differential Equations; CHAPTER 5. LINEAR SYSTEMS AND EXPONENTIALS OF OPERATORS; 1. Review of Topology in Rn; 2. New Norms for Old; 3. Exponentials of Operators; 4. Homogeneous Linear Systems; 5. A Nonhomogeneous Equation; 6. Higher Order Systems; Notes; CHAPTER 6. LINEAR SYSTEMS AND CANONICAL FORMS OF OPERATORS | |
| 505 | 8 | |a 1. The Primary Decomposition2. The S + N Decomposition; 3. Nilpotent Canonical Forms; 4. Jordan and Real Canonical Forms; 5. Canonical Forms and Differential Equations; 6. Higher Order Linear Equations; 7. Operators on Function Spaces; CHAPTER 7. CONTRACTIONS AND GENERIC PROPERTIES OF OPERATORS; 1. Sinks and Sources; 2. Hyperbolic Flows; 3. Generic Properties of Operators; 4. The Significance of Genericity; CHAPTER 8. FUNDAMENTAL THEORY; 1. Dynamical Systems and Vector Fields; 2. The Fundamental Theorem; 3. Existence and Uniqueness; 4. Continuity of Solutions in Initial Conditions | |
| 505 | 8 | |a 5. On Extending Solutions6. Global Solutions; 7. The Flow of a Differential Equation; Notes; CHAPTER 9. STABILITY OF EQUILIBRIA; 1. Nonlinear Sinks; 2. Stability; 3. Liapunov Functions; 4. Gradient Systems; 5. Gradients and Inner Products; Notes; CHAPTER 10. DIFFERENTIAL EQUATIONS FOR ELECTRICAL CIRCUITS; 1. An RLC Circuit; 2. Analysis of the Circuit Equations; 3. Van der Pol's Equation; 4. Hopf Bifurcation; 5. More General Circuit Equations; Notes; CHAPTER 11. THE POINCARÉ-BENDIXSON THEOREM; 1. Limit Sets; 2. Local Sections and Flow Boxes; 3. Monotone Sequences in Planar Dynamical Systems | |
| 505 | 8 | |a 4. The Poincaré-Bendixson Theorem5. Applications of the Poincaré-Bendixson Theorem; Notes; CHAPTER 12. ECOLOGY; 1. One Species; 2. Predator and Prey; 3. Competing Species; Notes; CHAPTER 13. PERIODIC ATTRACTORS; 1. Asymptotic Stability of Closed Orbits; 2. Discrete Dynamical Systems; 3. Stability and Closed Orbits; CHAPTER 14. CLASSICAL MECHANICS; 1. The n-Body Problem; 2. Hamiltonian Mechanics; Notes; CHAPTER 15. NONAUTONOMOUS EQUATIONS AND DIFFERENTIABILITY OF FLOWS; 1. Existence, Uniqueness, and Continuity for Nonautonomous Differential Equations | |
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Differential equations. | |
| 650 | 0 | |a Algebras, Linear. | |
| 650 | 4 | |a Algebras, Linear. | |
| 650 | 4 | |a Differential equations. | |
| 650 | 6 | |a Équations différentielles. | |
| 650 | 6 | |a Algèbre linéaire. | |
| 650 | 7 | |a Algebras, Linear |2 fast | |
| 650 | 7 | |a Differential equations |2 fast | |
| 700 | 1 | |a Smale, Stephen. | |
| 758 | |i has work: |a Differential equations, dynamical systems, and linear algebra (Text) |1 https://id.oclc.org/worldcat/entity/E39PCFwGX33XyC7CdYBjRfPwBX |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 1 | |z 9780123495501 | |
| 830 | 0 | |a Pure and Applied Mathematics. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=404189 |z Texto completo |
| 938 | |a 123Library |b 123L |n 39915 | ||
| 938 | |a EBL - Ebook Library |b EBLB |n EBL404189 | ||
| 938 | |a ProQuest MyiLibrary Digital eBook Collection |b IDEB |n 176362 | ||
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