Differential Equations, Dynamical Systems, and an Introduction to Chaos. (Record no. 10013)
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| 000 -LEADER | |
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| fixed length control field | 06319nam a22004813i 4500 |
| 001 - CONTROL NUMBER | |
| control field | EBC5754594 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | MiAaPQ |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240724113647.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m o d | |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cnu|||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240724s2012 xx o ||||0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9780123820112 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9780123820105 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (MiAaPQ)EBC5754594 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (Au-PeEL)EBL5754594 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)958520620 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | MiAaPQ |
| Language of cataloging | eng |
| Description conventions | rda |
| -- | pn |
| Transcribing agency | MiAaPQ |
| Modifying agency | MiAaPQ |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA372 .H577 2013 |
| 082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 515.35 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Hirsch, Morris W. |
| 245 10 - TITLE STATEMENT | |
| Title | Differential Equations, Dynamical Systems, and an Introduction to Chaos. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 3rd ed. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | San Diego : |
| Name of producer, publisher, distributor, manufacturer | Elsevier Science & Technology, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2012. |
| 264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Date of production, publication, distribution, manufacture, or copyright notice | ©2013. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (433 pages) |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Cover -- Differential Equations, Dynamical Systems, and an Introduction to Chaos -- Copyright -- Table of Contents -- Preface to Third Edition -- Preface -- 1 First-Order Equations -- 1.1 The Simplest Example -- 1.2 The Logistic Population Model -- 1.3 Constant Harvesting and Bifurcations -- 1.4 Periodic Harvesting and Periodic Solutions -- 1.5 Computing the Poincaré Map -- 1.6 Exploration: A Two-Parameter Family -- Exercises -- 2 Planar Linear Systems -- 2.1 Second-Order Differential Equations -- 2.2 Planar Systems -- 2.3 Preliminaries from Algebra -- 2.4 Planar Linear Systems -- 2.5 Eigenvalues and Eigenvectors -- 2.6 Solving Linear Systems -- 2.7 The Linearity Principle -- Exercises -- 3 Phase Portraits for Planar Systems -- 3.1 Real Distinct Eigenvalues -- 3.2 Complex Eigenvalues -- 3.3 Repeated Eigenvalues -- 3.4 Changing Coordinates -- Exercises -- 4 Classification of Planar Systems -- 4.1 The Trace-Determinant Plane -- 4.2 Dynamical Classification -- Case 1 -- Case 2 -- Case 3 -- 4.3 Exploration: A 3D Parameter Space -- Exercises -- 5 Higher-Dimensional Linear Algebra -- 5.1 Preliminaries from Linear Algebra -- 5.2 Eigenvalues and Eigenvectors -- 5.3 Complex Eigenvalues -- 5.4 Bases and Subspaces -- 5.5 Repeated Eigenvalues -- 5.6 Genericity -- Exercises -- 6 Higher-Dimensional Linear Systems -- 6.1 Distinct Eigenvalues -- 6.2 Harmonic Oscillators -- 6.3 Repeated Eigenvalues -- 6.4 The Exponential of a Matrix -- 6.5 Nonautonomous Linear Systems -- Exercises -- 7 Nonlinear Systems -- 7.1 Dynamical Systems -- 7.2 The Existence and Uniqueness Theorem -- 7.3 Continuous Dependence of Solutions -- 7.4 The Variational Equation -- 7.5 Exploration: Numerical Methods -- 7.6 Exploration: Numerical Methods and Chaos -- Exercises -- 8 Equilibria in Nonlinear Systems -- 8.1 Some Illustrative Examples -- 8.2 Nonlinear Sinks and Sources -- 8.3 Saddles. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 8.4 Stability -- 8.5 Bifurcations -- 8.6 Exploration: Complex Vector Fields -- Exercises -- 9 Global Nonlinear Techniques -- 9.1 Nullclines -- 9.2 Stability of Equilibria -- 9.3 Gradient Systems -- 9.4 Hamiltonian Systems -- 9.5 Exploration: The Pendulum with Constant Forcing -- Exercises -- 10 Closed Orbits and Limit Sets -- 10.1 Limit Sets -- 10.2 Local Sections and Flow Boxes -- 10.3 The Poincaré Map -- 10.4 Monotone Sequences in Planar Dynamical Systems -- 10.5 The Poincaré-Bendixson Theorem -- 10.6 Applications of Poincaré-Bendixson -- 10.7 Exploration: Chemical Reactions that Oscillate -- Exercises -- 11 Applications in Biology -- 11.1 Infectious Diseases -- 11.2 Predator-Prey Systems -- 11.3 Competitive Species -- 11.4 Exploration: Competition and Harvesting -- 11.5 Exploration: Adding Zombies to the SIR Model -- Exercises -- 12 Applications in Circuit Theory -- 12.1 An RLC Circuit -- 12.2 The Liénard Equation -- 12.3 The van der Pol Equation -- 12.4 A Hopf Bifurcation -- 12.5 Exploration: Neurodynamics -- Exercises -- 13 Applications in Mechanics -- 13.1 Newton's Second Law -- 13.2 Conservative Systems -- 13.3 Central Force Fields -- 13.4 The Newtonian Central Force System -- 13.5 Kepler's First Law -- 13.6 The Two-Body Problem -- 13.7 Blowing up the Singularity -- 13.8 Exploration: Other Central Force Problems -- 13.9 Exploration: Classical Limits of Quantum Mechanical Systems -- 13.10 Exploration: Motion of a Glider -- Exercises -- 14 The Lorenz System -- 14.1 Introduction -- 14.2 Elementary Properties of the Lorenz System -- 14.3 The Lorenz Attractor -- 14.4 A Model for the Lorenz Attractor -- 14.5 The Chaotic Attractor -- 14.6 Exploration: The Rössler Attractor -- Exercises -- 15 Discrete Dynamical Systems -- 15.1 Introduction -- 15.2 Bifurcations -- 15.3 The Discrete Logistic Model -- 15.4 Chaos -- 15.5 Symbolic Dynamics. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 15.6 The Shift Map -- 15.7 The Cantor Middle-Thirds Set -- 15.8 Exploration: Cubic Chaos -- 15.9 Exploration: The Orbit Diagram -- Exercises -- 16 Homoclinic Phenomena -- 16.1 The Shilnikov System -- 16.2 The Horseshoe Map -- 16.3 The Double Scroll Attractor -- 16.4 Homoclinic Bifurcations -- 16.5 Exploration: The Chua Circuit -- Exercises -- 17 Existence and Uniqueness Revisited -- 17.1 The Existence and Uniqueness Theorem -- 17.2 Proof of Existence and Uniqueness -- 17.3 Continuous Dependence on Initial Conditions -- 17.4 Extending Solutions -- 17.5 Nonautonomous Systems -- 17.6 Differentiability of the Flow -- Exercises -- Bibliography -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- K -- L -- M -- N -- O -- P -- R -- S -- T -- U -- V -- W -- Z. |
| 588 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Description based on publisher supplied metadata and other sources. |
| 590 ## - LOCAL NOTE (RLIN) | |
| Local note | Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Differential equations. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Algebras, Linear. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Chaotic behavior in systems. |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Smale, Stephen. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Devaney, Robert L. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Hirsch, Morris W. |
| Title | Differential Equations, Dynamical Systems, and an Introduction to Chaos |
| Place, publisher, and date of publication | San Diego : Elsevier Science & Technology,c2012 |
| International Standard Book Number | 9780123820105 |
| 797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN) | |
| Corporate name or jurisdiction name as entry element | ProQuest (Firm) |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5754594">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5754594</a> |
| Public note | Click to View |
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