 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 predatorprey 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 LotkaVolterra predatorprey 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 BoundaryValue Problems  7th Edition
ISBN: 9780495108368
Solutions for Chapter 10.4: Autonomous Systems as Mathematical Models
Get Full SolutionsChapter 10.4: Autonomous Systems as Mathematical Models includes 22 full stepbystep solutions. Since 22 problems in chapter 10.4: Autonomous Systems as Mathematical Models have been answered, more than 15924 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Differential Equations with BoundaryValue Problems, edition: 7. Differential Equations with BoundaryValue Problems was written by and is associated to the ISBN: 9780495108368.

Backtoback stemplot
A stemplot with leaves on either side used to compare two distributions.

Bounded
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

Equation
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.

Imaginary axis
See Complex plane.

Implicitly defined function
A function that is a subset of a relation defined by an equation in x and y.

Interquartile range
The difference between the third quartile and the first quartile.

Leading coefficient
See Polynomial function in x

Lefthand 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

Mathematical induction
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

Opposite
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.

Pointslope form (of a line)
y  y1 = m1x  x 12.

Rational numbers
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 stemandleaf plot)
An arrangement of a numerical data set into a specific tabular format.

Vertical translation
A shift of a graph up or down.