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 |
AS APPLIED TO A SPRINGMASS SYSTEM | 6 |
Copyright | |
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Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic ... Richard Haberman No preview available - 1998 |
Common terms and phrases
amplitude applied approximation Assume calculated called cars characteristics conservation Consider constant continuous corresponding curve decreases density wave depends derived described determine differential equation discussed distance dx dt dx/dt energy equal equilibrium population equilibrium position equivalent example exercise expression Figure force formula friction function given growth rate hence highway illustrated increases indicate initial conditions integral intersect isoclines known length light limit linear manner mass mathematical model maximum measured method motion moving nonlinear number of cars observer obtained occurs oscillation partial differential equation pendulum period phase plane Pmax possible problem region result road satisfies shock Show shown in Fig simple sketched sketched in Fig slope solution solve species spring spring-mass system stable straight line Suppose tion traffic density traffic flow trajectories Umax unstable valid variables yields zero