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
Results 1-5 of 83
Page ii
... Problems for Ordinary Differential Equations K. E. Brenan, S. L. Campbell, and L. R. Petzold, Numerical Solution of Initial'Value Problems in Differential-Algebraic Equations Charles L. Lawson and Richard J. Hanson, Solving Least ...
... Problems for Ordinary Differential Equations K. E. Brenan, S. L. Campbell, and L. R. Petzold, Numerical Solution of Initial'Value Problems in Differential-Algebraic Equations Charles L. Lawson and Richard J. Hanson, Solving Least ...
Page iii
... Problem Richard Haberman, Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow Peter W ... Problems Ivar Stakgold, Boundary Value Problems of Mathematical Physics, Volumes I and II J. M. Ortega and W C ...
... Problem Richard Haberman, Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow Peter W ... Problems Ivar Stakgold, Boundary Value Problems of Mathematical Physics, Volumes I and II J. M. Ortega and W C ...
Page vii
... Problem 20 9. A Two-Mass Oscillator 23 * IO. Friction Z9 11. Oscillations of a Damped System 33 12. Underdamped Oscillations 34 13. Overdamped and Critically Damped Oscillations .............................................. .. 4O 14. A ...
... Problem 20 9. A Two-Mass Oscillator 23 * IO. Friction Z9 11. Oscillations of a Damped System 33 12. Underdamped Oscillations 34 13. Overdamped and Critically Damped Oscillations .............................................. .. 4O 14. A ...
Page xiii
... problem is solved, requiring at times the introduction of new mathematical methods. The solution is then interpreted, and the validity of the mathematical model is questioned. Often the mathematical model must be modified and the ...
... problem is solved, requiring at times the introduction of new mathematical methods. The solution is then interpreted, and the validity of the mathematical model is questioned. Often the mathematical model must be modified and the ...
Page xiv
... problem and the interpretation of the results. I believe, in order to learn mathematics, the reader must take an active part. This is best accomplished by attempting a significant number of the included exercises. Many more problems are ...
... problem and the interpretation of the results. I believe, in order to learn mathematics, the reader must take an active part. This is best accomplished by attempting a significant number of the included exercises. Many more problems are ...
Other editions - View all
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