- 10.4.1: A pendulum is released at u p3 and is given an initial angular velo...
- 10.4.2: (a) If a pendulum is released from rest at u u0, show that the angu...
- 10.4.3: A bead with mass m slides along a thin wire whose shape is describe...
- 10.4.4: A bead with mass m slides along a thin wire whose shape is describe...
- 10.4.5: A bead is released from the position x(0) x0 on the curve z x2 2 wi...
- 10.4.6: Rework with z cosh x.
- 10.4.7: (Refer to Figure 10.4.9.) If xm x1 xM and x x1, show that F(x)G(y) ...
- 10.4.8: From (i) and (iii) on page 391, conclude that the maximum number of...
- 10.4.9: In many fishery science models, the rate at which a species is caug...
- 10.4.10: A predator-prey interaction is described by the LotkaVolterra model...
- 10.4.11: A competitive interaction is described by the LotkaVolterra competi...
- 10.4.12: In (1) show that (0, 0) is always an unstable node.
- 10.4.13: In (1) show that (K1, 0) is a stable node when K1 K2a21 and a saddl...
- 10.4.14: Use 12 and 13 to establish that (0, 0), (K1, 0), and (0, K2) are un...
- 10.4.15: In (1) show that is a saddle point when K1a12 K2 and K2a21 K1.
- 10.4.16: Damped Pendulum If we assume that a damping force acts in the direc...
- 10.4.17: Nonlinear Damping In the analysis of free, damped motion in Section...
- 10.4.18: A bead with mass m slides along a thin wire whose shape may be desc...
- 10.4.19: An undamped oscillation satisfies a nonlinear secondorder different...
- 10.4.20: The Lotka-Volterra predator-prey model assumes that in the absence ...
- 10.4.21: The dynamical system arises in a model for the growth of microorgan...
- 10.4.22: Use the methods of this chapter together with a numerical solver to...
Solutions for Chapter 10.4: Autonomous Systems as Mathematical Models
Full solutions for Differential Equations with Boundary-Value Problems | 7th Edition
A stemplot with leaves on either side used to compare two distributions.
A function is bounded if there are numbers b and B such that b ? ƒ(x) ? B for all x in the domain of f.
Coefficient of determination
The number r2 or R2 that measures how well a regression curve fits the data
A statement of equality between two expressions.
Graph of a polar equation
The set of all points in the polar coordinate system corresponding to the ordered pairs (r,?) that are solutions of the polar equation.
See Complex plane.
Implicitly defined function
A function that is a subset of a relation defined by an equation in x and y.
The difference between the third quartile and the first quartile.
See Polynomial function in x
Left-hand limit of f at x a
The limit of ƒ as x approaches a from the left.
Lower bound for real zeros
A number c is a lower bound for the set of real zeros of ƒ if ƒ(x) Z 0 whenever x < c
A process for proving that a statement is true for all natural numbers n by showing that it is true for n = 1 (the anchor) and that, if it is true for n = k, then it must be true for n = k + 1 (the inductive step)
Mean (of a set of data)
The sum of all the data divided by the total number of items
See Additive inverse of a real number and Additive inverse of a complex number.
Paraboloid of revolution
A surface generated by rotating a parabola about its line of symmetry.
Point-slope form (of a line)
y - y1 = m1x - x 12.
Numbers that can be written as a/b, where a and b are integers, and b ? 0.
Rectangular coordinate system
See Cartesian coordinate system.
Stemplot (or stem-and-leaf plot)
An arrangement of a numerical data set into a specific tabular format.
A shift of a graph up or down.