Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 19
... known ( perhaps due to precise experiments ) , then mathemat- ical models are desirable in order to discover which mechanisms best account for the known data , i.e. , which quantities are important and which can be ignored . In complex ...
... known ( perhaps due to precise experiments ) , then mathemat- ical models are desirable in order to discover which mechanisms best account for the known data , i.e. , which quantities are important and which can be ignored . In complex ...
Page 135
... known way on the temperature of its environment . If the temperature is known as a function of time , derive an expression for the future popula- tion ( which is initially No ) . Show that the population grows or decays with an ...
... known way on the temperature of its environment . If the temperature is known as a function of time , derive an expression for the future popula- tion ( which is initially No ) . Show that the population grows or decays with an ...
Page 137
... known ( No Na ( to ) ) , determine the best estimate of the = growth rate using this criteria . ( c ) Redo part ( b ) assuming that a best estimate of the initial population is also desired ( i.e. , minimize the mean - square deviation ...
... known ( No Na ( to ) ) , determine the best estimate of the = growth rate using this criteria . ( c ) Redo part ( b ) assuming that a best estimate of the initial population is also desired ( i.e. , minimize the mean - square deviation ...
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