Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 122
... mathematical model . This randomness in the model would predict different results in each experiment . However , in this text , there will not be much discussion of such probabilistic models . Instead , we will almost exclusively pursue ...
... mathematical model . This randomness in the model would predict different results in each experiment . However , in this text , there will not be much discussion of such probabilistic models . Instead , we will almost exclusively pursue ...
Page 150
... model of stochastic births shows one manner in which uncertainty can be introduced in a mathematical model . Let us just mention another way without pursuing its consequences . We have assumed that each individual randomly gives birth ...
... model of stochastic births shows one manner in which uncertainty can be introduced in a mathematical model . Let us just mention another way without pursuing its consequences . We have assumed that each individual randomly gives birth ...
Page 285
... mathematical models along these lines . Some experiments have indicated that u = u ( p ) is reasonable while traffic ... model to include these kinds of effects also have been attempted . In addition u = u ( p , x , t ) implies that if p ...
... mathematical models along these lines . Some experiments have indicated that u = u ( p ) is reasonable while traffic ... model to include these kinds of effects also have been attempted . In addition u = u ( p , x , t ) implies that if p ...
Contents
Mechanical Vibrations 1 | 3 |
NEWTONS LAW | 4 |
AS APPLIED TO A SPRINGMASS SYSTEM | 6 |
Copyright | |
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Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic ... Richard Haberman No preview available - 1998 |
Common terms and phrases
amplitude applied approximation Assume calculated called cars characteristics conservation Consider constant continuous corresponding curve decreases density wave depends derived described determine differential equation discussed distance dx dt dx/dt energy equal equilibrium population equilibrium position equivalent example exercise expression Figure force formula friction function given growth rate hence highway illustrated increases indicate initial conditions integral intersect 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 Pmax possible problem region result road satisfies shock Show shown in Fig simple sketched sketched in Fig slope solution solve species spring spring-mass system stable straight line Suppose tion traffic density traffic flow trajectories Umax unstable valid variables yields zero