Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page 12
... Equation 5.1 is a second - order linear differential equation with constant coefficients . As you should recall from a course in differential equations , the general solution of this differential equation is where x = c1 cos at + c2 sin ...
... Equation 5.1 is a second - order linear differential equation with constant coefficients . As you should recall from a course in differential equations , the general solution of this differential equation is where x = c1 cos at + c2 sin ...
Page 299
... equation is an initial condition . With an nth order ordinary differential equation , n initial conditions are needed . The number of conditions are correspondingly the same for partial differential equations . Thus for equation 65.3 ...
... equation is an initial condition . With an nth order ordinary differential equation , n initial conditions are needed . The number of conditions are correspondingly the same for partial differential equations . Thus for equation 65.3 ...
Page 303
... differential equation governs the perturbed traffic density . However , equation 66.3 is a linear partial differential equation while the exact traffic equation 66.1 is a nonlinear partial differential equation . The coefficient that ...
... differential equation governs the perturbed traffic density . However , equation 66.3 is a linear partial differential equation while the exact traffic equation 66.1 is a nonlinear partial differential equation . The coefficient that ...
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 |
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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