Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 69
... increases as t increases . Arrows are added to the phase plane diagram to indicate the direction the solution changes with time . In the phase plane shown in Fig . 20-4 , since x increases , the solution x ( t ) moves to the right as ...
... increases as t increases . Arrows are added to the phase plane diagram to indicate the direction the solution changes with time . In the phase plane shown in Fig . 20-4 , since x increases , the solution x ( t ) moves to the right as ...
Page 152
... 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 popula- tion , the birth rate equals the death rate and ...
... 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 popula- tion , the birth rate equals the death rate and ...
Page 218
... increases , r increases ; see Fig . 47-13 . If a / b > 0 , then as increases , r decreases as shown in Fig . 47-14 . The time - dependent equations determine the temporal evolution of the solution . For example at x = 0 , dx / dt + by ...
... increases , r increases ; see Fig . 47-13 . If a / b > 0 , then as increases , r decreases as shown in Fig . 47-14 . The time - dependent equations determine the temporal evolution of the solution . For example at x = 0 , dx / dt + by ...
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