Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 35
... exponential . Thus we first sketch the exponential Ae - ct / 2m and its negative —Ae ̄ct / 2m in dashed lines . Periodically at the “ x's ” the solution lies on the two exponential curves drawn in Fig . 12-2 ( exactly where depends on ...
... exponential . Thus we first sketch the exponential Ae - ct / 2m and its negative —Ae ̄ct / 2m in dashed lines . Periodically at the “ x's ” the solution lies on the two exponential curves drawn in Fig . 12-2 ( exactly where depends on ...
Page 131
... exponential ( Nm 33.3 . Consider a species of animal which only breeds during the spring . Suppose that all adults die before the next breeding season . However , assume that every female produces ... Exponential Growth EXPONENTIAL GROWTH.
... exponential ( Nm 33.3 . Consider a species of animal which only breeds during the spring . Suppose that all adults die before the next breeding season . However , assume that every female produces ... Exponential Growth EXPONENTIAL GROWTH.
Page 132
... exponential behavior N ( t ) = NoeRotto ) , ( 34.3 ) as sketched in Fig . 34-1 for Ro > 0. A population grows exponentially if the growth rate is a positive constant . Similarly , a population decays exponentially if its growth rate is ...
... exponential behavior N ( t ) = NoeRotto ) , ( 34.3 ) as sketched in Fig . 34-1 for Ro > 0. A population grows exponentially if the growth rate is a positive constant . Similarly , a population decays exponentially if its growth rate is ...
Contents
NEWTONS | 6 |
OSCILLATION OF A SPRINGMASS SYSTEM | 12 |
QUALITATIVE AND QUANTITATIVE BEHAVIOR | 18 |
Copyright | |
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Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic ... Richard Haberman No preview available - 1998 |
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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