Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 51
... continuous in the interval and the derivatives of f ( x ) through the Nth derivative are also continuous . where is such that 0 < Ō < 0 , 51 Sec . 15 How Small is Small ? A PENDULUM 42 15 HOW SMALL IS SMALL?
... continuous in the interval and the derivatives of f ( x ) through the Nth derivative are also continuous . where is such that 0 < Ō < 0 , 51 Sec . 15 How Small is Small ? A PENDULUM 42 15 HOW SMALL IS SMALL?
Page 120
... continuous functions of time to represent popula- tions . The previous population data were observed continuously in ... continuous function of time ( by again fitting a smooth curve through the data points ) , the limitations of the ...
... continuous functions of time to represent popula- tions . The previous population data were observed continuously in ... continuous function of time ( by again fitting a smooth curve through the data points ) , the limitations of the ...
Page 170
... continuous and dis- crete logistic equations . How small must △ t be such that solutions of the discrete logistic equation have a behavior similar to solutions of the continuous logistic model ? 40.4 . Leslie proposed the following ...
... continuous and dis- crete logistic equations . How small must △ t be such that solutions of the discrete logistic equation have a behavior similar to solutions of the continuous logistic model ? 40.4 . Leslie proposed the following ...
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