Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 5
... approximation . We emphasize the word approximation , for although mathematics is frequently treated as a science of exactness , mathematics is applied to models which only approximate the real world . EXERCISES 2.1 . Consider Fig . 2-2 ...
... approximation . We emphasize the word approximation , for although mathematics is frequently treated as a science of exactness , mathematics is applied to models which only approximate the real world . EXERCISES 2.1 . Consider Fig . 2-2 ...
Page 52
... approximation , even for angles that are not too small . However , we must still investigate whether the solution to the linear equation , d20 / dt2 = ( g / L ) , is a good approximation to the solu- tion to the more difficult nonlinear ...
... approximation , even for angles that are not too small . However , we must still investigate whether the solution to the linear equation , d20 / dt2 = ( g / L ) , is a good approximation to the solu- tion to the more difficult nonlinear ...
Page 89
... approximation . The use of the binomial expansion facilitates the above calculation . * Thus T ( E ) = 2√ 1 or ... approximations requiring a Taylor series need only an applica- tion of a binomial expansion , saving the tedious effort ...
... approximation . The use of the binomial expansion facilitates the above calculation . * Thus T ( E ) = 2√ 1 or ... approximations requiring a Taylor series need only an applica- tion of a binomial expansion , saving the tedious effort ...
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