Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 89
... calculations to a minimum , prevents us from developing additional terms in this approximation . The use of the binomial expansion facilitates the above calculation . * Thus T ( E ) = 2√ 1 or , equivalently , u12 ( 1 E 1 u ) 1/2 [ 1 + ...
... calculations to a minimum , prevents us from developing additional terms in this approximation . The use of the binomial expansion facilitates the above calculation . * Thus T ( E ) = 2√ 1 or , equivalently , u12 ( 1 E 1 u ) 1/2 [ 1 + ...
Page 166
... Calculating the population for the following year , yields N2 = N1 ( 1.2 — .0025N 。) = 15 ( 1.175 ) = 17.625 N2 Additional results have been calculated from the difference equation using a computer No N1 = 10.0 N8 = 15.0 = 39.4 N ...
... Calculating the population for the following year , yields N2 = N1 ( 1.2 — .0025N 。) = 15 ( 1.175 ) = 17.625 N2 Additional results have been calculated from the difference equation using a computer No N1 = 10.0 N8 = 15.0 = 39.4 N ...
Page 287
... calculated . * The data for all cars moving between 14.5 and 15.5 miles per hour was collected , for example , and the average of the distance to the preceding car was calculated . In this manner an average density for cars moving at 15 ...
... calculated . * The data for all cars moving between 14.5 and 15.5 miles per hour was collected , for example , and the average of the distance to the preceding car was calculated . In this manner an average density for cars moving at 15 ...
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