Mathematics for Dynamic Modeling
Published on 10. May 2014
294 pages
978-1-4832-6786-9 (ISBN)
Description
Mathematics for Dynamic Modeling provides an introduction to the mathematics of dynamical systems. This book presents the mathematical formulations in terms of linear and nonlinear differential equations. Organized into two parts encompassing nine chapters, this book begins with an overview of the notions of equilibrium and stability in differential equation modeling that occur in the guise of simple models in the plane. This text then focuses on nonlinear models in which the limiting behavior of orbits can be more complicated. Other chapters consider the problems that illustrate the concepts of equilibrium and stability, limit cycles, chaos, and bifurcation. This book discusses as well a variety of topics, including cusp catastrophes, strange attractors, and reaction-diffusion and shock phenomena. The final chapter deals with models that are based on the notion of optimization. This book is intended to be suitable for students in upper undergraduate and first-year graduate course in mathematical modeling.
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Edward J. Beltrami
Mathematics for Dynamic Modeling
Book
05/2000
Academic Press
€54.47
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Content
PrefacePart 1 First Thoughts on Equilibria and Stability Chapter One Simple Dynamic Models 1.1 Back and Forth, Up and Down 1.2 The Harmonic Oscillator 1.3 Stable Equilibria, I 1.4 What Comes Out Is What Goes In 1.5 Exercises Chapter Two Stable and Unstable Motion, I 2.1 The Pendulum 2.2 When Is a Linear System Stable? 2.3 When Is a Nonlinear System Stable? 2.4 The Phase Plane 2.5 Exercises Chapter Three Stable and Unstable Motion, II 3.1 Liapunov Functions 3.2 Stable Equilibria, II 3.3 Feedback 3.4 Exercises Chapter Four Growth and Decay 4.1 The Logistic Model 4.2 Discrete Versus Continuous 4.3 The Struggle for Life, I 4.4 Stable Equilibria, III 4.5 Exercises A Summary of Part 1Part 2 Further Thoughts and Extensions Chapter Five Motion in Time and Space 5.1 Conservation of Mass, II 5.2 Algae Blooms 5.3 Pollution in Rivers 5.4 Highway Traffic 5.5 A Digression on Traveling Waves 5.6 Morphogenesis 5.7 Tidal Dynamics 5.8 Exercises Chapter Six Cycles and Bifurcation 6.1 Self-Sustained Oscillations 6.2 When Do Limit Cycles Exist? 6.3 The Struggle for Life, II 6.4 The Flywheel Governor 6.5 Exercises Chapter Seven Bifurcation and Catastrophe 7.1 Fast and Slow 7.2 The Pumping Heart 7.3 Insects and Trees 7.4 The Earth's Magnet 7.5 Exercises Chapter Eight Chaos 8.1 Not All Attractors Are Limit Cycles or Equilibria 8.2 Strange Attractors 8.3 Deterministic or Random? 8.4 Exercises Chapter Nine There Is a Better Way 9.1 Conditions Necessary for Optimality 9.2 Fish Harvesting 9.3 Bang-Bang Controls 9.4 ExercisesAppendix Ordinary Differential Equations: A Review First-Order Equations (The Case k = 1) The Case k = 2 The Case k = 3References and a Guide to Further Readings Ordinary Differential Equations Introductions to Differential Equation Modeling More Advanced Modeling Books Hard to ClassifyNotes on the Individual ChaptersIndex
