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 iii
... Solution of Nonlinear Equations in Several Variables David Kinderlehrer and Guido Stampacchia, An Introduction to Variational Inequalities and Their Applications F. Natterer, The Mathematics of Computerized Tomography Avinash C. Kak and ...
... Solution of Nonlinear Equations in Several Variables David Kinderlehrer and Guido Stampacchia, An Introduction to Variational Inequalities and Their Applications F. Natterer, The Mathematics of Computerized Tomography Avinash C. Kak and ...
Page viii
... Solution ................................ .. 56 Conservation of Energy 61 Energy Curves 67 Phase Plane of a Linear ... Solution of the Logistic Equation .................................................. .. 155 Explicit Solution of the ...
... Solution ................................ .. 56 Conservation of Energy 61 Energy Curves 67 Phase Plane of a Linear ... Solution of the Logistic Equation .................................................. .. 155 Explicit Solution of the ...
Page xiii
... solution is then interpreted, and the validity of the mathematical model is questioned. Often the mathematical model must be modified and the process of formulation, solution, and interpretation continued. Thus we will be illustrating ...
... solution is then interpreted, and the validity of the mathematical model is questioned. Often the mathematical model must be modified and the process of formulation, solution, and interpretation continued. Thus we will be illustrating ...
Page 12
... solution of this differential equation is x = 0, cos cot + 02 sin cot, (5.2) where co':-Ii m and where c1 and c2 are arbitrary constants. However, for those readers who did not recognize that equation 5.2 is the general solution of ...
... solution of this differential equation is x = 0, cos cot + 02 sin cot, (5.2) where co':-Ii m and where c1 and c2 are arbitrary constants. However, for those readers who did not recognize that equation 5.2 is the general solution of ...
Page 14
... solution of d2x_ x = c, cos cot + c2 sin cot, where to : A/k/m and c1 and c2 are arbitrary constants. The general solution is a linear combination of two oscillatory functions, a cosine and a sine. An equivalent expression for the solution ...
... solution of d2x_ x = c, cos cot + c2 sin cot, where to : A/k/m and c1 and c2 are arbitrary constants. The general solution is a linear combination of two oscillatory functions, a cosine and a sine. An equivalent expression for the solution ...
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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