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 |
NEWTONS LAW AS APPLIED TO A SPRINGMASS SYSTEM | 6 |
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Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic ... Richard Haberman No preview available - 1998 |
Common terms and phrases
analyze approximation Assume c₁ c₂ calculated conservation of cars Consider corresponding d2x dt2 de/dt density wave velocity depends derived determine dq/dp dx dt dx/dt equilibrium population equilibrium position equilibrium solution example exercise exponential Figure flow-density force formula friction function growth rate highway increases initial conditions initial density initial traffic density initial value problem integral intersect isoclines logistic equation mass mathematical model maximum method of characteristics motion moving Newton's nonlinear pendulum number of cars observer occurs ordinary differential equation oscillation P/Pmax P₁ partial differential equation period phase plane Pmax potential energy problem qualitative region result sharks shock velocity Show shown in Fig simple harmonic motion Sketch the solution sketched in Fig slope solve species spring spring-mass system stable straight line Suppose Taylor series tion traffic flow traffic light trajectories Umax Umaxt unstable equilibrium variables velocity-density x₁ yields zero др