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. |
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Page iii
... Experiments Tamer Basar and Geert Jan Olsder, Dynamic Noncooperatioe Game Theory, Second Edition Emanuel Parzen, Stochastic Processes Petar Kokotovié, l-lassan K. Khalil, and John O'Reilly, Singular Perturbation Methods in Control ...
... Experiments Tamer Basar and Geert Jan Olsder, Dynamic Noncooperatioe Game Theory, Second Edition Emanuel Parzen, Stochastic Processes Petar Kokotovié, l-lassan K. Khalil, and John O'Reilly, Singular Perturbation Methods in Control ...
Page ix
... 265 Flow Equals Density Times Velocity 273 Conservation of the Number of Cars 275 A Velocity-Density Relationship 282 Experimental Observations 286 Traffic Flow 289 ix 2: Contents 64. Steady-State Car-Following Models 293 * 65. Partial.
... 265 Flow Equals Density Times Velocity 273 Conservation of the Number of Cars 275 A Velocity-Density Relationship 282 Experimental Observations 286 Traffic Flow 289 ix 2: Contents 64. Steady-State Car-Following Models 293 * 65. Partial.
Page xiii
... experiments are discussed. In this way a mathematical model is carefully formulated. The resulting mathematical problem is solved, requiring at times the introduction of new mathematical methods. The solution is then interpreted, and ...
... experiments are discussed. In this way a mathematical model is carefully formulated. The resulting mathematical problem is solved, requiring at times the introduction of new mathematical methods. The solution is then interpreted, and ...
Page 3
... experiments or observations. However, when theory and experiment quantitatively agree, then we can usually be more confident in the validity of the theory. In this manner mathematics becomes an integral part of the scientific method ...
... experiments or observations. However, when theory and experiment quantitatively agree, then we can usually be more confident in the validity of the theory. In this manner mathematics becomes an integral part of the scientific method ...
Page 4
... experimental observations culminated in Newton's second law of motion describing how a particle reacts to a force. Newton discovered that the motion of a point mass is well described by the now famous formula 6 __ d _. F _ E(mv), (2.1) ...
... experimental observations culminated in Newton's second law of motion describing how a particle reacts to a force. Newton discovered that the motion of a point mass is well described by the now famous formula 6 __ d _. F _ E(mv), (2.1) ...
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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