Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 170
... Determine the population for 0≤t < ta . Can you determine the population for mtå ≤t < ( m + 1 ) ta ? 40.2 . Suppose dN dt = - N ( t − tå ) [ a — bN ( t — ta ) ] . Determine a nonzero equilibrium population . What linear delay ...
... Determine the population for 0≤t < ta . Can you determine the population for mtå ≤t < ( m + 1 ) ta ? 40.2 . Suppose dN dt = - N ( t − tå ) [ a — bN ( t — ta ) ] . Determine a nonzero equilibrium population . What linear delay ...
Page 264
... determine the position of a car at later times , which starts ( at t 0 ) at x = = L ? = 57.4 . Determine a velocity field satisfying all the following properties : ( a ) at x ( b ) at x = = 30t , u = 30 ; 45 ; 45t + L , u = ( c ) the ...
... determine the position of a car at later times , which starts ( at t 0 ) at x = = L ? = 57.4 . Determine a velocity field satisfying all the following properties : ( a ) at x ( b ) at x = = 30t , u = 30 ; 45 ; 45t + L , u = ( c ) the ...
Page 301
... Determine the solution of dP / dt 65.3 . Determine the solution of dp / dt = p , which satisfies p ( x , t ) along x = -2t . = 65.4 . Is there a solution of dP / dt : -x2p , such that both p ( x , 0 ) x > 0 and p ( 0 , t ) = cos t for t ...
... Determine the solution of dP / dt 65.3 . Determine the solution of dp / dt = p , which satisfies p ( x , t ) along x = -2t . = 65.4 . Is there a solution of dP / dt : -x2p , such that both p ( x , 0 ) x > 0 and p ( 0 , t ) = cos t for t ...
Contents
Mechanical Vibrations 1 | 3 |
NEWTONS LAW | 4 |
AS APPLIED TO A SPRINGMASS SYSTEM | 6 |
Copyright | |
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Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic ... Richard Haberman No preview available - 1998 |
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amplitude applied approximation Assume calculated called cars characteristics conservation Consider constant continuous corresponding curve decreases density wave depends derived described determine differential equation discussed distance dx dt dx/dt energy equal equilibrium population equilibrium position equivalent example exercise expression Figure force formula friction function given growth rate hence highway illustrated increases indicate initial conditions integral intersect isoclines known length light limit linear manner mass mathematical model maximum measured method motion moving nonlinear number of cars observer obtained occurs oscillation partial differential equation pendulum period phase plane Pmax possible problem region result road satisfies shock Show shown in Fig simple sketched sketched in Fig slope solution solve species spring spring-mass system stable straight line Suppose tion traffic density traffic flow trajectories Umax unstable valid variables yields zero