Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 141
... obtained by a method similar to that developed in Sec . 33 . ( a ) Use the notation Ñ Ñ ( mAt ) , and hence Nm + 1 = AÑm . Try a solu- Ñ „ = Ñm + 1 tion to this system of difference equations in the form Ñm = rmề , where is a constant ...
... obtained by a method similar to that developed in Sec . 33 . ( a ) Use the notation Ñ Ñ ( mAt ) , and hence Nm + 1 = AÑm . Try a solu- Ñ „ = Ñm + 1 tion to this system of difference equations in the form Ñm = rmề , where is a constant ...
Page 286
... obtained by two observers ( with a machine's assistance ) a short distance apart , as is shown in Fig . 62-2 . The velocity of each vehicle was obtained by recording the times at which they passed each observer ( v = d / ( t2 — t1 ) ...
... obtained by two observers ( with a machine's assistance ) a short distance apart , as is shown in Fig . 62-2 . The velocity of each vehicle was obtained by recording the times at which they passed each observer ( v = d / ( t2 — t1 ) ...
Page 373
... obtained using the shock condition : - = dxsr [ q ] dt [ p ] - Pou ( po ) Po = u ( po ) . ( 82.2 ) As we know , this shock wave travels at the same velocity as each car ( of density po ) . Thus if the light stayed red forever , then we ...
... obtained using the shock condition : - = dxsr [ q ] dt [ p ] - Pou ( po ) Po = u ( po ) . ( 82.2 ) As we know , this shock wave travels at the same velocity as each car ( of density po ) . Thus if the light stayed red forever , then we ...
Contents
NEWTONS | 6 |
OSCILLATION OF A SPRINGMASS SYSTEM | 12 |
QUALITATIVE AND QUANTITATIVE BEHAVIOR | 18 |
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Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic ... Richard Haberman No preview available - 1998 |
Common terms and phrases
amplitude of oscillation analyze approximation Assume birth c₁ calculation characteristics Consider constant coefficient corresponding d2x dt2 damping de/dt decreases delay depend derived determine difference equation discussed dx dt dx/dt energy integral equilibrium population equilibrium solution equivalent example exercise exponential Figure formula function growth rate Hint increases initial conditions initial value problem isoclines linearized stability analysis logistic equation mass mathematical model maximum method of characteristics motion moving N₁ Newton's nonlinear pendulum number of cars obtained occur ordinary differential equations oscillation P₁ partial differential equation period phase plane Pmax population growth potential energy r₁ result sharks shock Show shown in Fig simple harmonic motion Sketch the solution sketched in Fig slope solution curves solve species spring spring-mass system stable straight line Suppose Taylor series tion traffic flow trajectories Umax unstable equilibrium position variables vector x₁ yields zero