Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 131
... growth models , while part ( b ) is ? What ecological assumption of the model caused parts ( c ) and ( d ) to yield unreasonable results ? = = = aNm . Instead of substituting Nm esm ) . Show that the result is the same . rm , substitute ...
... growth models , while part ( b ) is ? What ecological assumption of the model caused parts ( c ) and ( d ) to yield unreasonable results ? = = = aNm . Instead of substituting Nm esm ) . Show that the result is the same . rm , substitute ...
Page 135
... in the exercises . EXERCISES 34.1 . A certain bacteria is observed to double in number in 8 hours . What is its growth rate ? 34.2 . A population of bacteria is initially N。 and grows at a constant rate Ro . Suppose τ hours later the ...
... in the exercises . EXERCISES 34.1 . A certain bacteria is observed to double in number in 8 hours . What is its growth rate ? 34.2 . A population of bacteria is initially N。 and grows at a constant rate Ro . Suppose τ hours later the ...
Page 152
... growth rate still diminishes as the population density * increases . In some manner , still being investigated by researchers , the increase in density causes the birth rate to decrease , the death rate to increase , or both . At some ...
... growth rate still diminishes as the population density * increases . In some manner , still being investigated by researchers , the increase in density causes the birth rate to decrease , the death rate to increase , or both . At some ...
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 |
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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