 17.a: Explain why s(t) should be an increasing function.
 17.b: Can you find a function for Michaels speed at any time t?
 17.c: Michaels acceleration is the rate at which his speed is changing wi...
 17.d: Can you find Michaels speed and acceleration at the time t = 15 min...
 17.e: At what point do you think the hill was steepest? How far had Micha...
 17.1: A particle P moves in a straight line with a displacement function ...
 17.2: A particle P moves in a straight line with a displacement function ...
 17.3: A particle moves in a straight line with velocity function v(t)=2pt...
 17.4: An object moves in a straight line with displacement function s(t) ...
 17.5: A particle moves in a straight line with displacement function s(t)...
 17.6: The position of a particle moving along the xaxis is given by x(t)...
 17.7: A particle P moves in a straight line. Its displacement from the or...
 17.8: A particle P moves along the xaxis with position given by x(t)=1 2...
 17.9: In an experiment, an object is fired vertically from the earths sur...
 17.10: The temperature of a liquid after being placed in a refrigerator is...
 17.11: The height of a certain species of shrub t years after it is plante...
 17.12: In the conversion of sugar solution to alcohol, the chemical reacti...
 17.13: Find exactly the rate of change in the area of triangle PQR as chan...
 17.14: On the Indonesian coast, the depth of water at time t hours after m...
 17.15: The voltage in a circuit is given by V (t) = 340 sin(100t) where t ...
 17.16: A piston is operated by rod [AP] attached to a flywheel of radius 1...
 17.17: A right angled triangular pen is made from 24 m of fencing, all use...
 17.18: A symmetrical gutter is made from a sheet of metal 30 cm wide by be...
 17.19: A sector of radius 10 cm and angle is bent to form a conical cup as...
 17.20: At 1:00 pm a ship A leaves port P. It sails in the direction 030 at...
 17.21: Hieu can row a boat across a circular lake of radius 2 km at 3 km h...
 17.22: In a hospital, two corridors 4 m wide and 3 m wide meet at right an...
Solutions for Chapter 17: Applications of differential calculus
Full solutions for Mathematics for the International Student: Mathematics SL  3rd Edition
ISBN: 9781921972089
Solutions for Chapter 17: Applications of differential calculus
Get Full SolutionsChapter 17: Applications of differential calculus includes 27 full stepbystep solutions. Since 27 problems in chapter 17: Applications of differential calculus have been answered, more than 44527 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: Mathematics for the International Student: Mathematics SL, edition: 3. Mathematics for the International Student: Mathematics SL was written by and is associated to the ISBN: 9781921972089.

Cholesky factorization
A = CTC = (L.J]))(L.J]))T for positive definite A.

Circulant matrix C.
Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn  l . Cx = convolution c * x. Eigenvectors in F.

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax  x Tb over growing Krylov subspaces.

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

Eigenvalue A and eigenvector x.
Ax = AX with x#O so det(A  AI) = o.

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

Identity matrix I (or In).
Diagonal entries = 1, offdiagonal entries = 0.

Incidence matrix of a directed graph.
The m by n edgenode incidence matrix has a row for each edge (node i to node j), with entries 1 and 1 in columns i and j .

Iterative method.
A sequence of steps intended to approach the desired solution.

Multiplier eij.
The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).

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

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

Semidefinite matrix A.
(Positive) semidefinite: all x T Ax > 0, all A > 0; A = any RT R.

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

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.

Symmetric matrix A.
The transpose is AT = A, and aU = a ji. AI is also symmetric.