Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 13
... derived in exercise 5.6 using the Taylor series of sines , cosines , and exponentials . A similar expression for e - it , can be derived from equation 5.4a by replacing ∞ by w . This results in iot = cos wt - i sin wt — ( 5.4b ) where ...
... derived in exercise 5.6 using the Taylor series of sines , cosines , and exponentials . A similar expression for e - it , can be derived from equation 5.4a by replacing ∞ by w . This results in iot = cos wt - i sin wt — ( 5.4b ) where ...
Page 280
... derived by assuming that the number of cars is conserved , that is , cars are not created nor destroyed . It is valid everywhere ( all x ) and for all time . It is called the equation of conservation of cars . ( 2 ) The equation of ...
... derived by assuming that the number of cars is conserved , that is , cars are not created nor destroyed . It is valid everywhere ( all x ) and for all time . It is called the equation of conservation of cars . ( 2 ) The equation of ...
Page 389
... derived in the exercises . The shock condition is the same as that which occurs without exits and entrances . EXERCISES 84.1 . From the integral conservation of cars , derive the shock condition when cars are constantly entering a ...
... derived in the exercises . The shock condition is the same as that which occurs without exits and entrances . EXERCISES 84.1 . From the integral conservation of cars , derive the shock condition when cars are constantly entering a ...
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