Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 143
... birth rate by 25 percent . ( a ) Analyze the three cases of that exercise . ( b ) How long does it take each to double ? ( c ) Compare the results of this problem to exercise 35.5 . 35.7 ... Birth Processes STOCHASTIC BIRTH PROCESSES 143*
... birth rate by 25 percent . ( a ) Analyze the three cases of that exercise . ( b ) How long does it take each to double ? ( c ) Compare the results of this problem to exercise 35.5 . 35.7 ... Birth Processes STOCHASTIC BIRTH PROCESSES 143*
Page 144
... birth occurs or it does not ; there are no other possibilities . In At time , if the probability of one birth from one hen is △ t , then we " expect " if there are a large number of hens No , then there would be No △ t births . This ...
... birth occurs or it does not ; there are no other possibilities . In At time , if the probability of one birth from one hen is △ t , then we " expect " if there are a large number of hens No , then there would be No △ t births . This ...
Page 145
... birth is approximately the same as the prob- ability of at least one birth . Thus , w - t༤ 1 - - ( 1 − λAt ) N - 1 * For this last expression to be valid At must be extremely small . Let us consider these probabilities if At is that ...
... birth is approximately the same as the prob- ability of at least one birth . Thus , w - t༤ 1 - - ( 1 − λAt ) N - 1 * For this last expression to be valid At must be extremely small . Let us consider these probabilities if At is that ...
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