Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 128
... result . ( c ) Show that 1 X 1 + x 1 1 + x ( d ) By integrating the result of part ( c ) , show that In ( 1 + x ) = x S x x dx . 1 + x ( e ) Using the result of part ( d 128 Population Dynamics - Mathematical Ecology.
... result . ( c ) Show that 1 X 1 + x 1 1 + x ( d ) By integrating the result of part ( c ) , show that In ( 1 + x ) = x S x x dx . 1 + x ( e ) Using the result of part ( d 128 Population Dynamics - Mathematical Ecology.
Page 184
... result . Describe how Figs . 42-1 and 42-2 are consistent with this result . ( b ) Describe the result that exists which is analagous to part ( a ) , but occurs if ym < 0 . 42.17 . Consider equation 42.1b . If a is a constant , how does ...
... result . Describe how Figs . 42-1 and 42-2 are consistent with this result . ( b ) Describe the result that exists which is analagous to part ( a ) , but occurs if ym < 0 . 42.17 . Consider equation 42.1b . If a is a constant , how does ...
Page 276
... result of cars entering the region at x = a . Assuming that no cars are created or destroyed in between , then the changes in the number of cars result from crossings at x = a and x = b only . If cars are flowing at the rate of 300 cars ...
... result of cars entering the region at x = a . Assuming that no cars are created or destroyed in between , then the changes in the number of cars result from crossings at x = a and x = b only . If cars are flowing at the rate of 300 cars ...
Contents
Mechanical Vibrations 1 | 3 |
NEWTONS LAW | 4 |
NEWTONS LAW AS APPLIED TO A SPRINGMASS SYSTEM | 6 |
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Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic ... Richard Haberman No preview available - 1998 |
Common terms and phrases
analyze approximation Assume c₁ c₂ calculated conservation of cars Consider corresponding d2x dt2 de/dt density wave velocity depends derived determine dq/dp dx dt dx/dt equilibrium population equilibrium position equilibrium solution example exercise exponential Figure flow-density force formula friction function growth rate highway increases initial conditions initial density initial traffic density initial value problem integral intersect isoclines logistic equation mass mathematical model maximum method of characteristics motion moving Newton's nonlinear pendulum number of cars observer occurs ordinary differential equation oscillation P/Pmax P₁ partial differential equation period phase plane Pmax potential energy problem qualitative region result sharks shock velocity Show shown in Fig simple harmonic motion Sketch the solution sketched in Fig slope solve species spring spring-mass system stable straight line Suppose Taylor series tion traffic flow traffic light trajectories Umax Umaxt unstable equilibrium variables velocity-density x₁ yields zero др