Author’s note: During the final production process a number of unfortunate errors were
introduced into the text. Those that affect the readability of the text, as well as some
“honest errors” by me in the writing of the text, are corrected here. A number of more
minor “stylistic errors” should be corrected in a second printing of the text. Please feel
free to contact the author with any more errors that are found.
Page 19: There is a LaTeX coding error in Exercise 7 on this page. The displayed
formula in the problem should be

S   e k
k 0
Page 21: The line immediately after the third (unnumbered) displayed equation has a
typo in it. The line should read:
"In practice, most architectures assume that the fraction is normalized to be
between -1 and 1;"
Page 66: Much of this page below the horizontal line which separates the algorithm from
the text is garbled. It should read as follows:
Consider the integral with hi  xi  xi 1 and h  maxi hi . Then
ba 2
I ( f )  Tn ( f ) 
h max f 
12
x[ a ,b ]
The student should perhaps think about how to prove this result.
Note that most of this is a continuation of the theorem begun on the previous page.
Page 79: There is a math notation problem in Exercise 6. The primes should be smaller
and more elevated, as in
 u  64u  u  1
Page 94: The four-line displayed equation should be changed to the following:
  xn 

f ( )  f ( x x )
f (c n )
f ( xn )
f (c n )
 f ( x n )  f ( x n ) 


  
 f ( x n )  f (c n ) 
 f ( x n ) 

 ( x n 1  x n )
 f (c n ) 
Page 140: The reference to "Table ??" should be "Table 3.10."
Page 142: The two references to "Table ??" should be "Table 3.10."
Page 143: Table 3.10 should be labeled “Table 3.11;” there is another Table 3.10 on
page 141.
Page 146: Table 3.11 should be Table 3.12; this applies to labeling the table, and to the
reference in the text just above the table.
Page 173: Part of the line styles in Figure 4.5 are wrong. The short dotted segment
which reaches down from the legend box to the solid curve should be in the dash-dot
style. It is a continuation of the "sideways parabola" which is shown in the dash-dot
style.
Page 186: Figure 4.11 is missing some notation. The caption refers to some points
("knots") being marked with a "+" sign, but none of them are. The points at x = 1/3 and x
= 2/3 are knots, and should have been marked with a "+" sign.
Page 189: There is an error in the URL given in the footnote. The complete URL should
be http://www.cs.wisc.edu/~deboor/bib/bib.html.
Page 211: “Exercises 1-??” should be “Exercises 1-4”.
Page 216: In Definition 4.2, "xthree" should obviously be "three".
Page 227: In Table 4.25, "Exercise ??" should be "Exercise 4."
Page 230: In the footnote, it should be "Carl Runge" not "Carle Runge".
Page 296: In Example 5.17, the second displayed equation is missing a factor of (1/2) in
some of the terms. It should read as
 4
11
I 4 ( f )    exp 
2
2  
 1  t1

1
 log 
x1 

1/ 2
 4
11
   exp 
2
2 
 1  t2

1 
 log 
x2 

1/ 2
 4
11
   exp 
2
2 
 1  t3

1
 log 
x3 

Page 309: The "prime" symbol at the end of the long unnumbered equation is rendered
incorrectly. The equation should be
b
b
1
1
I ( f )  T1 ( f )   (a  t )(b  t ) f (t )dt   (t  c) f (t )dt
2a
2a
Page 367: There is some text missing in the large paragraph about two-thirds of the way
down the page. What it should say is:
(To be precise, we have to take h small enough so that 200h is in the stability region for second order AdamsBashforth.) A complete development of how this comes
about is deferred to Appendix A.
Page 372: The title for Algorithm 6.4 is wrong. It should be "Simple Adaptive Solver for
Initial Value Problems."
Page 434: The equation in Exercise 14 is poorly formatted. It should look like this:
max
 ( A) 
x0
min
x0
Ax
x
Ax
x
1/ 2
Page 442 (and beyond): It appears that I used an incorrect right side vector in Examples
7.12 – 7.14. The correct right side vector for the given exact solution is
b = [1, 7, 16, 14]T
When this is used as the right side vector a slightly different sequence of iterates is
produced for each iteration (Jacobi, Gauss-Seidel, SOR), of course. This will be fixed in
subsequent printings of the text. So that students can check their own work, the correct
iterates for the three methods are as follows.
Jacobi:
x(1) = [0.2500, 1.4000, 2.6667, 3.5000]T
x(2) = [-0.1000, 0.8167, 1.8500, 2.7708]T
x(3) = [0.0458, 1.0500, 2.0688, 3.0625]T
Gauss-Seidel: x(1) = [0.2500, 1.3500, 2.4417, 2.8271]T
x(2) = [-0.0875, 0.9292, 2.0406, 3.0117]T
x(3) = [0.0177, 0.9883, 2.0000, 2.9956]T
SOR:
x(1) = [0.2625, 1.4149, 2.5524, 2.9361]T
x(2) = [-0.1220, 0.8889, 2.0030, 3.0344]T
x(3) = [0.0353, 0.9975, 1.9943, 2.9905]T
Page 500: In the footnote, the first citation should be to "Journal of the Institute of
Mathematics and its Applications."
Page 503: The phrase "page XX" should be "page 505."
Page 508: The phrase "page XX" should be "page 510."
Page 524: There is an error in the pseudo-code for Algorithm 9.4. In the second pair of
nested “for” loops, the statement u(i,j) = uo(i,j) occurs. This is backwards; it
should be uo(i,j) = u(i,j).