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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... , and Traffic Flow Richard Haberman. q Mathematical Models Mechanical Vibrations, Population Dynamim, . ,l a . ' a b d Richard Haberman C-L-A-S'S-l-C'S In Applied Mathematics 21 F' '3 Mathematical Model; g,. Front Cover.
... , and Traffic Flow Richard Haberman. q Mathematical Models Mechanical Vibrations, Population Dynamim, . ,l a . ' a b d Richard Haberman C-L-A-S'S-l-C'S In Applied Mathematics 21 F' '3 Mathematical Model; g,. Front Cover.
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... Applied Mathematics 92 Richard Haberman Department of Mathematics Southern Methodist University Dallas, Texas is 5mm. Society for ... Applied Mathematics Philadelphia Books in the Classics in Applied Mathematics series are monographs.
... Applied Mathematics 92 Richard Haberman Department of Mathematics Southern Methodist University Dallas, Texas is 5mm. Society for ... Applied Mathematics Philadelphia Books in the Classics in Applied Mathematics series are monographs.
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... Applied Mathematics series are monographs and textbooks declared out of print by their original publishers, though ... Applied Mathematics C. C. Lin and L. A. Segel, Mathematics Applied to Deterministic Problems in the Natural Sciences ...
... Applied Mathematics series are monographs and textbooks declared out of print by their original publishers, though ... Applied Mathematics C. C. Lin and L. A. Segel, Mathematics Applied to Deterministic Problems in the Natural Sciences ...
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Mechanical Vibrations, Population Dynamics, and Traffic Flow Richard Haberman. Classics in Applied Mathematics ... Applied to Continuum Mechanics Rajendra Bhatia, Perturbation Bounds for Matrix Eigenvalues Copyright © 1998 by the ...
Mechanical Vibrations, Population Dynamics, and Traffic Flow Richard Haberman. Classics in Applied Mathematics ... Applied to Continuum Mechanics Rajendra Bhatia, Perturbation Bounds for Matrix Eigenvalues Copyright © 1998 by the ...
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... Applied Mathematics. This SIAM edition is an unabridged republication of the work first published by Prentice—Hall, Inc., Englewood Cliffs, New Jersey, 1977. 10 9 8 7 6 All rights reserved. Printed in the United States of America. No ...
... Applied Mathematics. This SIAM edition is an unabridged republication of the work first published by Prentice—Hall, Inc., Englewood Cliffs, New Jersey, 1977. 10 9 8 7 6 All rights reserved. Printed in the United States of America. No ...
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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