Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic FlowThe author uses mathematical techniques along with observations and experiments to give an in-depth look at models for mechanical vibrations, population dynamics, and traffic flow. Equal emphasis is placed on the mathematical formulation of the problem and the interpretation of the results. In the sections on mechanical vibrations and population dynamics, the author emphasizes the nonlinear aspects of ordinary differential equations and develops the concepts of equilibrium solutions and their stability. He introduces phase plane methods for the nonlinear pendulum and for predator-prey and competing species models. Haberman develops the method of characteristics to analyze the nonlinear partial differential equations that describe traffic flow. Fan-shaped characteristics describe the traffic situation that occurs when a traffic light turns green and shock waves describe the effects of a red light or traffic accident. Although it was written over 20 years ago, this book is still relevant. It is intended as an introduction to applied mathematics, but can be used for undergraduate courses in mathematical modeling or nonlinear dynamical systems or to supplement courses in ordinary or partial differential equations. |
From inside the book
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Page vii
... Applied to a Spring-Mass System ............................................. .. 6 4. Gravity 9 5. Oscillation of a Spring-Mass System 12 6. Dimensions and Units 16 7. Qualitative and Quantitative Behavior of a Spring-Mass System ...
... Applied to a Spring-Mass System ............................................. .. 6 4. Gravity 9 5. Oscillation of a Spring-Mass System 12 6. Dimensions and Units 16 7. Qualitative and Quantitative Behavior of a Spring-Mass System ...
Page xi
... applied math SIAM encourages, it is a special pleasure to welcome his classic Mathematical Models to a book series that was initiated with the related classic by Lin and Segel. My students and I can attest that this carefully crafted ...
... applied math SIAM encourages, it is a special pleasure to welcome his classic Mathematical Models to a book series that was initiated with the related classic by Lin and Segel. My students and I can attest that this carefully crafted ...
Page xii
... applied to various problems in science and engineering. To use mathematics, one needs to understand the physical context. Here problems in mechanical vibrations, population dynamics, and traffic flow are developed from first principles ...
... applied to various problems in science and engineering. To use mathematics, one needs to understand the physical context. Here problems in mechanical vibrations, population dynamics, and traffic flow are developed from first principles ...
Page xiii
... applied this text attempts to iLtroduce to the reader some of the fundamental concepts and techniques of applied mathematics. In each area, relevant observations and experiments are discussed. In this way a mathematical model is ...
... applied this text attempts to iLtroduce to the reader some of the fundamental concepts and techniques of applied mathematics. In each area, relevant observations and experiments are discussed. In this way a mathematical model is ...
Page xiv
... applied mathematics. Phase plane methods are introduced and linearization procedures are explained in both parts. On the other hand, the mathematical models of traffic flow involve first-order (nonlinear) partial differential equations ...
... applied mathematics. Phase plane methods are introduced and linearization procedures are explained in both parts. On the other hand, the mathematical models of traffic flow involve first-order (nonlinear) partial differential equations ...
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Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic ... Richard Haberman No preview available - 1998 |
Common terms and phrases
amplitude analysis applied approximately Assume birth calculated called cars characteristics Consider constant continuous corresponding curve decreases delay depends derived described determine differential equation discussed distance energy equal equilibrium population equilibrium position equivalent example exercise experiments expression Figure first fish flow force formulate friction function given growth rate hence highway illustrated increases initial initial conditions integral isoclines known length light limit linear manner mass mathematical model maximum measured method motion moving nonlinear number of cars observer obtained occurs oscillation partial differential equation pendulum period phase plane possible probability problem region result roots sharks shock Show shown in Fig simple sketched sketched in Fig solution solve species spring spring-mass system stable straight line Suppose tion traffic density traflic trajectories unstable variables velocity yields zero