Differential equations, dynamical systems, and linear algebra / / Morris W. Hirsch and Stephen Smale

• Record Nr.: UNINA9911108840803321
• Autore: Hirsch Morris W. <1933->
• Pubbl/distr/stampa: New York, : Academic Press, 1974
• ISBN: 1-281-76362-4; 9786611763626; 0-08-087376-6
• Descrizione fisica: 1 online resource (373 p.)
• Collana: Pure and applied mathematics ; ; v. 60
• Altri autori (Persone): SmaleStephen <1930->; HirschMorris W. <1933->
• Disciplina: 510.8 s515.35; 510/.8 s 515/.35; 512.5; 515.35; 515/.35
• Soggetti: Differential equations; Algebras, Linear
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: 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 COEFICIENTS AND REAL EIGENVALUES; 1. Basic Linear Algebra; 2. Real Eigenvalues; 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; 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; 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; 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; 2. Differentiability of the Flow of Autonomous Equations
• Sommario/riassunto: 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.

The gene illusion : genetic research in psychiatry and psychology under the microscope / / Jay Joseph

• Record Nr.: UNINA9911102691903321
• Autore: Joseph Jay
• Pubbl/distr/stampa: New York, : Algora Pub., 2004
• ISBN: 0-87586-345-0; 1-4175-6159-9
• Edizione: [1st ed.]
• Descrizione fisica: 1 online resource (417 p.)
• Disciplina: 616.89/042; 616.89042
• Soggetti: Mental illness - Genetic aspects; Genetic psychology; Twins - Psychology - Research - Methodology
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and indexes.
• Nota di contenuto: ""Acknowledgments""; ""List of Abbreviations""; ""The Gene Illusion""; ""The Gene Illusion""; ""Genetic Research""; ""in Psychiatry and Psychology Under the Microscope""; ""Jay Joseph, Psy.D.""; ""Table of Contents""; ""Chapter 1. Introduction""; ""Outline of the Chapters""; ""Family Studies""; ""Terms Used in the Book""; ""Chapter 2. Twin Research: Misunderstanding Twins, From Galton to the 21st Century""; ""Twin Research from 1870 to 1924""; ""Galton""; ""Thorndike""; ""Origins of the Twin Method""; ""Developments in Twin Research, 1924-1945""; ""Early Criticism of the Twin Method""; ""Developments in North America"" ""Twins Reared Apart""; ""The Co-twin Control Method""; ""Twin Research in Germany""; ""Twin Research From 1945-1960""; ""Kallmann""; ""Selected Topics in Twin Research""; ""Twin Research From 1960 to 1980""; ""Don Jackson's Critique of Schizophrenia Twin Research""; ""Nadir""; ""Twin Research Makes a Comeback""; ""Twin Research in the 1970's""; ""Twin Research from 1980 to the Present""; ""Conclusions""; ""Chapter 3. The Twin Method: An Environmentally Confounded Research Technique""; ""The Equal Environment Assumption (EEA)""; ""Two Definitions""; ""Do Identical and Fraternal Twins Create Differing Environments?"" ; ""Kendler's Theoretical Retreat""; ""A Critique of the Trait-Relevant Equal Environment Assumption""; ""Family Studies and the Trait-Relevant EEA""; ""What Leading Twin Researchers Say About the EEA""; ""Attempts to Test the Validity of the Equal Environment Assumption""; ""Loehlin and Nichols, 1976""; ""Scarr and Carter-Saltzman""; ""Conclusions""; ""Chapter 4: Genetic Studies of Twins Reared Apart: A Critical Review""; ""Part I: Identical Twins Reared Apart as Folklore""; ""Influence of the Cohort""; ""Part II: Scientific Studies of Twins Reared Apart"" ""The Myth of the Separated Identical Twins""; ""The Minnesota Study of Twins Reared Apart""; ""Secret Data, Secret Lives""; ""Environmental Factors Contributing to MZA Resemblance""; ""What About the DZA Correlations?""; ""MZTs (or DZAs) as the Control Group: The Invalidating Flaw of All Twins Reared Apart Studies""; ""What a Valid MZA Study Might Look Like""; ""Conclusions""; ""Chapter 5. The Heritability Concept: A Measure of Inheritance or Inherently Misleading?""; ""What Heritability Is and What It Is Not""; ""Origins of the Heritability Concept"" ""What is the Purpose of a Heritability Coefficient?""; ""An Exchange on the Meaning of Heritability""; ""A Heritability Estimate: The Product of Environmentally Confounded Research""; ""Heritability and Psychiatric Disorders""; ""Conclusions""; ""Chapter 6. The Genetics of Schizophrenia I: Overview""; ""History and Prevalence of Schizophrenia""; ""The Genetic Theory of Schizophrenia""; ""Schizophrenia Twin Research""; ""Three Low Concordance Rate Studies""; ""Schizophrenia Twin Researchers' Interpretations of Concordance Rate Differences""; ""Same Sex- and Opposite-Sex Fraternal Twin Concordance Rates""
• Sommario/riassunto: Genetic factors are increasingly presented as an important influence on psychiatric disorders, personality, intelligence, and various types of socially unacceptable behavior - as if that were an unassailable fact, proven by research. Jay Joseph's timely,