Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow : an Introduction to Applied Mathematics |
From inside the book
Results 1-3 of 24
Page 51
... continuous in the interval and the derivatives of f ( x ) through the Nth derivative are also continuous . where is such that 0 < Ō < 0 , 51 Sec . 15 How Small is Small ? A PENDULUM 42 15 HOW SMALL IS SMALL?
... continuous in the interval and the derivatives of f ( x ) through the Nth derivative are also continuous . where is such that 0 < Ō < 0 , 51 Sec . 15 How Small is Small ? A PENDULUM 42 15 HOW SMALL IS SMALL?
Page 120
... continuous functions of time to represent popula- tions . The previous population data were observed continuously in ... continuous function of time ( by again fitting a smooth curve through the data points ) , the limitations of the ...
... continuous functions of time to represent popula- tions . The previous population data were observed continuously in ... continuous function of time ( by again fitting a smooth curve through the data points ) , the limitations of the ...
Page 170
... continuous and dis- crete logistic equations . How small must △ t be such that solutions of the discrete logistic equation have a behavior similar to solutions of the continuous logistic model ? 40.4 . Leslie proposed the following ...
... continuous and dis- crete logistic equations . How small must △ t be such that solutions of the discrete logistic equation have a behavior similar to solutions of the continuous logistic model ? 40.4 . Leslie proposed the following ...
Contents
NEWTONS | 6 |
OSCILLATION OF A SPRINGMASS SYSTEM | 12 |
QUALITATIVE AND QUANTITATIVE BEHAVIOR | 18 |
Copyright | |
72 other sections not shown
Other editions - View all
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