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This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors. }This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors. A unique feature of the book is its emphasis on applications. These include mechanical vibrations, lasers, biological rhythms, superconducting circuits, insect outbreaks, chemical oscillators, genetic control systems, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with the mathematical theory.Richly illustrated, and with many exercises and worked examples, this book is ideal for an introductory course at the junior/senior or first-year graduate level. It is also ideal for the scientist who has not had formal instruction in nonlinear dynamics, but who now desires to begin informal study. The prerequisites are multivariable calculus and introductory physics. }

Chaotic behavior in systems --- Dynamics --- Nonlinear theories --- Chaos --- Dynamique --- Théories non linéaires --- Théories non linéaires --- Nonlinear problems --- Nonlinearity (Mathematics) --- Chaostheorie --- Dynamische systemen --- Vertakkingstheorie --- Chaostheorie. --- Dynamische systemen. --- Vertakkingstheorie. --- Dynamical systems --- Kinetics --- Chaos in systems --- Chaos theory --- Chaotic motion in systems --- Chemical thermodynamics --- fysicochemie --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Differentiable dynamical systems --- System theory --- Calculus --- Mathematical analysis --- Mathematical physics --- Chaotic behavior in systems. --- Dynamics. --- Nonlinear theories. --- Systèmes dynamiques non linéaires. --- Chaos (théorie des systèmes)

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517.987 --- Chaotic behavior in systems --- Dynamics --- Nonlinear theories --- Nonlinear problems --- Nonlinearity (Mathematics) --- Calculus --- Mathematical analysis --- Mathematical physics --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Chaos in systems --- Chaos theory --- Chaotic motion in systems --- Differentiable dynamical systems --- System theory --- 517.987 Measures. Representations of Boolean algebras. Metric theory of dynamic systems --- Measures. Representations of Boolean algebras. Metric theory of dynamic systems --- Chemical thermodynamics --- fysicochemie --- Chaotic behavior in systems. --- Dynamics. --- Nonlinear theories.

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This is the captivating story of mathematics' greatest ever idea: calculus. Without it, there would be no computers, no microwave ovens, no GPS, and no space travel. But before it gave modern man almost infinite powers, calculus was behind centuries of controversy, competition, and even death.Taking us on a thrilling journey through three millennia, professor Steven Strogatz charts the development of this seminal achievement from the days of Archimedes to today's breakthroughs in chaos theory and artificial intelligence. Filled with idiosyncratic characters from Pythagoras to Fourier, Infinite Powers is a compelling human drama that reveals the legacy of calculus on nearly every aspect of modern civilisation, including science, politics, medicine, philosophy, and much besides.

Calculus. --- Differential calculus. --- Counting --- Philosophy --- Calcul infinitésimal. --- Calcul différentiel. --- Calcul --- Philosophie --- History. --- Histoire --- Histoire.

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Mathematics

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