Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 95
... solve it by sketching the solution in the phase plane using the energy integral , we will illustrate the method of ... Solving for v , we see these isoclines are v = ( k / m2 ) x . For this example all the isoclines are straight lines ...
... solve it by sketching the solution in the phase plane using the energy integral , we will illustrate the method of ... Solving for v , we see these isoclines are v = ( k / m2 ) x . For this example all the isoclines are straight lines ...
Page 146
... solve this system , initial conditions are necessary . These are the initial probabilities . The problem we will solve is one in which the initial population ( t = 0 ) is known with certainty , being some value No. In that case all the ...
... solve this system , initial conditions are necessary . These are the initial probabilities . The problem we will solve is one in which the initial population ( t = 0 ) is known with certainty , being some value No. In that case all the ...
Page 301
... solve partial differential equations in the case in which they can be integrated . The arbitrary constants that appear are replaced by arbitrary functions of the " other " independent variable . EXERCISES 65.1 . Determine the solution ...
... solve partial differential equations in the case in which they can be integrated . The arbitrary constants that appear are replaced by arbitrary functions of the " other " independent variable . EXERCISES 65.1 . Determine the solution ...
Contents
Mechanical Vibrations 1 | 3 |
NEWTONS LAW | 4 |
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
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