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
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 |
Common terms and phrases
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