 6.1: Draw two typical curves y fsxd and y tsxd, where fsxd > tsxd for a ...
 6.2: Suppose that Sue runs faster than Kathy throughout a 1500meter rac...
 6.3: a) What is the average value of a function f on an interval fa, bg?...
 6.4: If we have survival and renewal functions for a population, how do ...
 6.5: (a) What is the cardiac output of the heart? (b) Explain how the ca...
 6.6: (a) Suppose S is a solid with known crosssectional areas. Explain ...
 6.7: Find the average value of the function fstd t sinst 2 d on the inte...
 6.8: Find the average value of the function f sxd x 2 s1 1 x 3 on the in...
 6.9: Antibiotic pharmacokinetics When an antibiotic tablet is taken, the...
 6.10: Salicylic acid pharmacokinetics In a study of the effects of aspiri...
 6.11: Survival and renewal Suppose a citys population is currently 75,000...
 6.12: Animal survival and renewal The fish population in a lake is curren...
 6.13: Cardiac output After a 6mg injection of dye into a heart, the read...
 6.14: Find the volume of the solid obtained by rotating about the xaxis ...
 6.15: Let 5 be the region bounded by the curves y tansx 2 d, x 1, and y 0...
 6.16: Let 5 be the region in the first quadrant bounded by the curves y x...
 6.17: Find the volumes of the solids obtained by rotating the region boun...
 6.18: Let 5 be the region bounded by the curves y 1 2 x 2 and y x 6 2 x 1...
 6.19: The base of a solid is a circular disk with radius 3. Find the volu...
 6.20: The height of a monument is 20 m. A horizontal crosssection at a di...
Solutions for Chapter 6: Applications of Integrals
Full solutions for Biocalculus: Calculus for Life Sciences  1st Edition
ISBN: 9781133109631
Solutions for Chapter 6: Applications of Integrals
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter 6: Applications of Integrals includes 20 full stepbystep solutions. Biocalculus: Calculus for Life Sciences was written by and is associated to the ISBN: 9781133109631. Since 20 problems in chapter 6: Applications of Integrals have been answered, more than 26285 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Biocalculus: Calculus for Life Sciences , edition: 1.

Block matrix.
A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

Complete solution x = x p + Xn to Ax = b.
(Particular x p) + (x n in nullspace).

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

Full row rank r = m.
Independent rows, at least one solution to Ax = b, column space is all of Rm. Full rank means full column rank or full row rank.

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

Hessenberg matrix H.
Triangular matrix with one extra nonzero adjacent diagonal.

Krylov subspace Kj(A, b).
The subspace spanned by b, Ab, ... , AjIb. Numerical methods approximate A I b by x j with residual b  Ax j in this subspace. A good basis for K j requires only multiplication by A at each step.

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

Nullspace N (A)
= All solutions to Ax = O. Dimension n  r = (# columns)  rank.

Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

Random matrix rand(n) or randn(n).
MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

Row picture of Ax = b.
Each equation gives a plane in Rn; the planes intersect at x.

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

Simplex method for linear programming.
The minimum cost vector x * is found by moving from comer to lower cost comer along the edges of the feasible set (where the constraints Ax = b and x > 0 are satisfied). Minimum cost at a comer!

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).