Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 185
... discussed . In an attempt to understand large ecosystems , we will study situations that involve the interaction of more than one species . We have already discussed models that involve the interaction of different species . In the ...
... discussed . In an attempt to understand large ecosystems , we will study situations that involve the interaction of more than one species . We have already discussed models that involve the interaction of different species . In the ...
Page 246
... discussed in the exercises in which the amplitudes of oscilla- tion decay as time goes on , as though nature seeks ... discussed in this text . Neither will predator - prey models which exhibit delays be discussed . More realistic ...
... discussed in the exercises in which the amplitudes of oscilla- tion decay as time goes on , as though nature seeks ... discussed in this text . Neither will predator - prey models which exhibit delays be discussed . More realistic ...
Page 374
... discussed in Sec . 73. Using this linear relationship , we note that the density wave velocity is dq dp Umax 2x ( 1 - 20 ) . Dmax ) Furthermore the general expression for the shock velocity may be simplified as follows : dxs dt = Umax ...
... discussed in Sec . 73. Using this linear relationship , we note that the density wave velocity is dq dp Umax 2x ( 1 - 20 ) . Dmax ) Furthermore the general expression for the shock velocity may be simplified as follows : dxs dt = Umax ...
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