## Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic FlowMathematics is a grand subject in the way it can be applied to various problems in science and engineering. To use mathematics, one needs to understand the physical context. The 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. |

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Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic ... Richard Haberman No preview available - 1998 |

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analyze approximately aſb Assume behavior birth calculated conservation of cars Consider constant coefficient corresponding da/dp decreases density wave velocity depends derived determine difference equation discussed dx/dt equilibrium population equilibrium position equilibrium solution equivalent example EXE RCISES exercise exponential Figure fish flow-density force formulate friction function growth rate highway increases initial conditions initial traffic density initial value problem integral intersect isoclines Lincoln Tunnel logistic equation mass mathematical model maximum method of characteristics motion moving nonlinear pendulum number of cars observer occurs ordinary differential equations oscillation partial differential equation phase plane Pmax population growth potential energy predator predator-prey Prmax qualitative region result sharks Show shown in Fig simple harmonic motion Sketch the solution sketched in Fig solve species spring spring-mass system stable straight line Suppose Taylor series tion traffic flow traffic light trajectories unstable equilibrium variables velocity-density yields zero