Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
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Page xi
... applied , this text attempts to introduce to the reader some of the fundamental concepts and techniques of applied mathematics . In each area , relevant observations and experiments are discussed . In this way a mathematical model is ...
... applied , this text attempts to introduce to the reader some of the fundamental concepts and techniques of applied mathematics . In each area , relevant observations and experiments are discussed . In this way a mathematical model is ...
Page xiii
... applied mathematics . For others , a second semester of applied mathematics could consist of , for example , the heat , wave and Laplace's equation ( and the mathematics of Fourier series as motivated by separation of variables of these ...
... applied mathematics . For others , a second semester of applied mathematics could consist of , for example , the heat , wave and Laplace's equation ( and the mathematics of Fourier series as motivated by separation of variables of these ...
Page 6
... applied to m1 , and Ĝ2 to m2 . By applying Newton's second law to each mass , show the law can be applied to the rigid body consisting of both masses , if x is replaced by the center of mass xem [ i.e. , show m ( d2xcm / dt2 ) F , where ...
... applied to m1 , and Ĝ2 to m2 . By applying Newton's second law to each mass , show the law can be applied to the rigid body consisting of both masses , if x is replaced by the center of mass xem [ i.e. , show m ( d2xcm / dt2 ) F , where ...
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