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    Differential Equations, Dynamical Systems, and an Introduction to Chaos

    Differential Equations, Dynamical Systems, and an Introduction to Chaos

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    Bog E-bog
    • Format
    • Bog, hardback
    • Engelsk

    Beskrivelse

    Hirsch, Devaney, and Smale’s classic Differential Equations, Dynamical Systems, and an Introduction to Chaos has been used by professors as the primary text for undergraduate and graduate level courses covering differential equations. It provides a theoretical approach to dynamical systems and chaos written for a diverse student population among the fields of mathematics, science, and engineering. Prominent experts provide everything students need to know about dynamical systems as students seek to develop sufficient mathematical skills to analyze the types of differential equations that arise in their area of study. The authors provide rigorous exercises and examples clearly and easily by slowly introducing linear systems of differential equations. Calculus is required as specialized advanced topics not usually found in elementary differential equations courses are included, such as exploring the world of discrete dynamical systems and describing chaotic systems.

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    Detaljer
    • SprogEngelsk
    • Sidetal432
    • Udgivelsesdato26-04-2012
    • ISBN139780123820105
    • Forlag Academic Press Inc
    • FormatHardback
    Størrelse og vægt
  • Vægt790 g
    • coffee cup img
    10 cm
    book img
    15,2 cm
    22,9 cm

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    Hamiltonian systems Symbolic dynamics Chaos Oscillating chemical reactions Two-body problem Variation of parameters Circuit theory Poincaré-Bendixson theorem Numerical methods Poincare Map Canonical Form Limit cycle Gliders Diffeomorphism Hamiltonian system Center Linearization Euler's method Dynamical system Saddle Differential equation Limit set Hopf Bifurcation Déterminant Asymptotic Stability Linear Independence Conjugacy Harmonic Oscillator Bifurcation Hyperbolic system Eigenvalue Homeomorphism Nonautonomous systems Eigenvector Sink Lorenz system Fixed-point Genericity 2 × 2 matrix Bifurcation Diagram Cantor middlethirds set change of coordinates conservative systems Double Scroll Attractor competing species model dense periodic points discrete logistic population model exponential of a matrix Chua circuit Existence and Uniqueness Theorem complex eigenvalues continuous dependence on initial conditions Higher-dimensional linear system of differential equations Frequency Ratio ideal pendulum heteroclinic bifurcation Homoclinic bifurcation Horseshoe Map ω-limit set Invertible matrix Kepler's first law logistic population model Liapunov Stability Equilibrium Point Liénard equation Lorenz attractor Linearity Principle flow box local section Nullclines Periodic Point Phase Plane Homoclinic points Picard iteration n × n matrix gradient system improved Euler's method Row Echelon Form Runge-Kutta 4 Shilnikov system RLC circuit equation Rössler attractor sensitive dependence spiral sink spiral center spiral source Slope Field Van Der Pol Equation Trace-determinant plane Iterated functions spiral saddle stable curve variational equation Newton's second law Nonlinear system of differential equations Newtonian central force system Newton's equation Phase Line Orbit Diagram Stable Curve Theorem repeated eigenvalues Planar linear system of differential equations unstable curve SIRS model Source subspace total energy function Transitive

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