Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 165
... depends not on the present population but only on the past population . We have assumed the change in population only depends on the previous year's population . In particular , the change does not depend explicitly on the population ...
... depends not on the present population but only on the past population . We have assumed the change in population only depends on the previous year's population . In particular , the change does not depend explicitly on the population ...
Page 289
... depends on traffic density and not on the time or position along the road ; see Fig . 63-1 . Since the traffic flow ( number of cars per hour ) equals density times velocity , the flow also only depends on the density , q = pu ( p ) ...
... depends on traffic density and not on the time or position along the road ; see Fig . 63-1 . Since the traffic flow ( number of cars per hour ) equals density times velocity , the flow also only depends on the density , q = pu ( p ) ...
Page 299
... depend on x and t ( even though there is no explicit appearance of x in either of the first two equations ) . If p only depends on t , then the first two would be ordinary differential equations , the general solutions being : ( 1 ) ( 2 ) ...
... depend on x and t ( even though there is no explicit appearance of x in either of the first two equations ) . If p only depends on t , then the first two would be ordinary differential equations , the general solutions being : ( 1 ) ( 2 ) ...
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