Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 103
... analyze this situation , the solution can be discussed in the phase plane . 27.1 . Suppose that EXERCISES d2z dt2 dz ... Analyze the linear stability of the equilibrium solution x = 0 . 27.3 . Where in the phase plane is 27.4 . Analyze ...
... analyze this situation , the solution can be discussed in the phase plane . 27.1 . Suppose that EXERCISES d2z dt2 dz ... Analyze the linear stability of the equilibrium solution x = 0 . 27.3 . Where in the phase plane is 27.4 . Analyze ...
Page 121
... analyze data with inaccuracies , a field of study in itself . In formulating a model of the population growth of a species , we must decide what factors affect that population . Clearly in some cases it depends on many quantities . For ...
... analyze data with inaccuracies , a field of study in itself . In formulating a model of the population growth of a species , we must decide what factors affect that population . Clearly in some cases it depends on many quantities . For ...
Page 143
... 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 . Collect human population data in the United States , including the present ...
... 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 . Collect human population data in the United States , including the present ...
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