Corrections to textbook, Math
311-102, Topics in Applied Mathematics I,
Summer 2005
The book is Multivariable Mathematics, fourth edition,
by Richard E. Williamson and Hale F. Trotter, 2004, ISBN
0-13-067276-9.
- Page 44, problem 17
- The problem is correct, but the answer in the back of the book
on page 748 has a typographical error. The second sentence of
the answer should say "L and N" instead of "L
and M".
- Page 87, problem 19
- The answer in the back of the book on page 751 is wrong.
The correct inverse matrix is
1 -1 1 -3/4
0 1/2 0 -1/8
0 0 1 -1/4
0 0 0 1/4
- Page 98, problem 7
- There are sign errors in the answer in the back of the book on
page 751. Although det A=7 is correct, the other answers
are the negatives of the correct ones: det B=-2,
det AB=det BA=-14.
- Page 126, problem 27
- The authors were trying to illustrate a subtle point, but they
got the answer wrong in the back of the book on page 754. On
the interval [0,1] (which is where the functions live in this
problem), the absolute value function |x| is indistinguishable
from the identity function x, so the function does
have a continuous derivative on the interval [0,1] (namely, the
constant 1). So |x| is in the domain of L. If we
had been working in the space of functions on the interval [-1,1],
then the authors' answer would have been right.
- Page 171, problem 3
- The problem does not say whether the rotations are right-handed
or left-handed. The answer in the back of the book on page 758
corresponds to a right-handed rotation about the x-axis but a
left-handed rotation about the y-axis. If you take both rotations
to be compatible with the right-hand rule, then the matrix S
will be
0 0 1
0 1 0
-1 0 0
and the axis of the composite rotation SR will be (1,1,-1).
- Page 211, problem 9
- In the answer on page 769, the figure is mislabeled. The
third coordinate of the point should be 1/√2 (the reciprocal
of the square root of 2) instead of 1/21/2. The
perspective in the drawing is unclear; the surface is a
sphere.
- Page 244, problem 19
- The answer in the back of the book on page 775 is wrong.
The correct matrix is
1 1
2 4
- Page 244, problem 25
- The answer to part (b) in the back of the book on page 775
is misleading, if not wrong. In T(x,y), the variables x and y ought
to mean the components of the vector written in the statement of
the problem with a boldface letter y. In that case, the second
component of T(x,y) should be 1+x+y instead of x+y.
- Page 274, problem 9
- The answer to part (c) in the back of the book on
page 778 is off by a factor of 2. The determinant of the
Jacobian matrix should be -4(u2+v2).
- Page 346, problem 15
- The answer in the back of the book on page 785 is wrong.
The correct answer is π/2.
- Page 419, problem 27
- The answer to part (c) in the back of the book on page 793
has a typographical error. The letter k in the answer
should be the letter a.
- Page 431, problem 27
- The answer in the back of the book on page 794 belongs to
a different problem. The answer to part (a) is that the
two-dimensional analogue is just the definition of radian measure.
The answer to part (b) is 2π(1-1/√3).
- Page 431, problem 29
- The answer in the back of the book on page 794 is wrong.
The answer should be 2πb3.
- Page 448, problem 19
- The answer in the back of the book on page 796 is wrong.
The answer should be π, not 0.
- Page 449, problem 27
- The answer in the back of the book on page 796 is correct,
but there are other correct answers. Another natural answer is
(-yz,-xz+3x2/2,c). In fact, any gradient field can be
added to the answer.