 5.6.1: Assume a discretetime population whose size at generation t + 1 is...
 5.6.2: Suppose a discretetime population evolves according to Nt+1 = (0.9...
 5.6.3: Assume the discretetime population model Nt+1 = bNt , t = 0, 1, 2 ...
 5.6.4: Assume the discretetime population model Nt+1 = bNt , t = 0, 1, 2,...
 5.6.5: Assume the discretetime population model Nt+1 = bNt , t = 0, 1, 2,...
 5.6.6: (a) Find all equilibria of Nt+1 = 1.3Nt , t = 0, 1, 2, . . . (b) Us...
 5.6.7: (a) Find all equilibria of Nt+1 = 0.9Nt , t = 0, 1, 2, . . . (b) Us...
 5.6.8: (a) Find all equilibria of Nt+1 = Nt , t = 0, 1, 2, . . . (b) How w...
 5.6.9: Use the stability criterion to characterize the stability of the eq...
 5.6.10: Use the stability criterion to characterize the stability of the eq...
 5.6.11: Use the stability criterion to characterize the stability of the eq...
 5.6.12: Use the stability criterion to characterize the stability of the eq...
 5.6.13: (a) Use the stability criterion to characterize the stability of th...
 5.6.14: (a) Use the stability criterion to characterize the stability of th...
 5.6.15: Rickers curve is given by R(P) = Pe P for P 0, where P denotes the ...
 5.6.16: Suppose that the size of a fish population at generation t is given...
 5.6.17: Suppose that the size of a fish population at generation t is given...
 5.6.18: (a) Find all equilibria when R = 0.5. (b) Investigate the system wh...
 5.6.19: (a) Find all equilibria when R = 1.5. (b) Investigate the system wh...
 5.6.20: (a) Find all equilibria when R = 2.5. (b) Investigate the system wh...
 5.6.21: Show that for r > 1, there are two fixed points. For which values o...
 5.6.22: Use a calculator or a spreadsheet to simulate the canonical discret...
 5.6.23: In 2325, we consider densitydependent population growth models of ...
 5.6.24: In 2325, we consider densitydependent population growth models of ...
 5.6.25: In 2325, we consider densitydependent population growth models of ...
Solutions for Chapter 5.6: Difference Equations: Stability (Optional)
Full solutions for Calculus For Biology and Medicine (Calculus for Life Sciences Series)  3rd Edition
ISBN: 9780321644688
Solutions for Chapter 5.6: Difference Equations: Stability (Optional)
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus For Biology and Medicine (Calculus for Life Sciences Series), edition: 3. Since 25 problems in chapter 5.6: Difference Equations: Stability (Optional) have been answered, more than 19899 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Calculus For Biology and Medicine (Calculus for Life Sciences Series) was written by and is associated to the ISBN: 9780321644688. Chapter 5.6: Difference Equations: Stability (Optional) includes 25 full stepbystep solutions.

Addition principle of probability.
P(A or B) = P(A) + P(B)  P(A and B). If A and B are mutually exclusive events, then P(A or B) = P(A) + P(B)

Arctangent function
See Inverse tangent function.

Associative properties
a + (b + c) = (a + b) + c, a(bc) = (ab)c.

Binomial theorem
A theorem that gives an expansion formula for (a + b)n

Bounded interval
An interval that has finite length (does not extend to ? or ?)

Combinatorics
A branch of mathematics related to determining the number of elements of a set or the number of ways objects can be arranged or combined

Components of a vector
See Component form of a vector.

Composition of functions
(f ? g) (x) = f (g(x))

Cubic
A degree 3 polynomial function

Dihedral angle
An angle formed by two intersecting planes,

NDER ƒ(a)
See Numerical derivative of ƒ at x = a.

Nonsingular matrix
A square matrix with nonzero determinant

Parametric curve
The graph of parametric equations.

Product rule of logarithms
ogb 1RS2 = logb R + logb S, R > 0, S > 0,

Row echelon form
A matrix in which rows consisting of all 0’s occur only at the bottom of the matrix, the first nonzero entry in any row with nonzero entries is 1, and the leading 1’s move to the right as we move down the rows.

Scalar
A real number.

Sequence
See Finite sequence, Infinite sequence.

Symmetric about the origin
A graph in which (x, y) is on the the graph whenever (x, y) is; or a graph in which (r, ?) or (r, ? + ?) is on the graph whenever (r, ?) is

Transverse axis
The line segment whose endpoints are the vertices of a hyperbola.

Vector
An ordered pair <a, b> of real numbers in the plane, or an ordered triple <a, b, c> of real numbers in space. A vector has both magnitude and direction.