Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 120
... observed ? Perhaps the number of monkeys in a laboratory as a function of time would be as shown in Fig . 31-1 . This curve is discontinuous since changes in the monkey population occur in integral units ( +1 for single births , -1 for ...
... observed ? Perhaps the number of monkeys in a laboratory as a function of time would be as shown in Fig . 31-1 . This curve is discontinuous since changes in the monkey population occur in integral units ( +1 for single births , -1 for ...
Page 121
... observed in a laboratory experiment of well - fed animals . Suppose we perform such an experiment starting with No animals and model population as a continuous function of time N ( t ) . We might observe the graph in Fig . 31-2 . Before ...
... observed in a laboratory experiment of well - fed animals . Suppose we perform such an experiment starting with No animals and model population as a continuous function of time N ( t ) . We might observe the graph in Fig . 31-2 . Before ...
Page 185
... observations that have motivated ecologists to seek models of population growth . The fish population in the upper ... observed to occur from year to year . However , during World War I fishing was suspended . The fishermen's catch of ...
... observations that have motivated ecologists to seek models of population growth . The fish population in the upper ... observed to occur from year to year . However , during World War I fishing was suspended . The fishermen's catch of ...
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 |
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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