Mistakes and typos that have been found so far:
Chapter 3. On page 54 there is a discussion of how to construct the
Poincaré section of driven pendulum. In the text (5th line from the
top) and in the footnote it is stated that the condition for finding
the times when the driving force is zero are ,
where n is an integer. This is incorrect, as it is missing
a factor of 2 (which is implied by the discussion). The condition should
instead read , and the footnote should read
This error was first noted by James Behrens, and subsequently reported
by several others.
Chapter 5. On page 133, equation 5.25 should read
Note that the correct result (the one given here) was used to
generate the solid curve in Figure 5.16.
Thanks to Bob Delaney for finding this and the next several errors.
Chapter 7. On page 159, the line after equation 7.1 should read
``The arithmetic here is performed modulo m, with m typically
Chapter 7. On page 171, on the fifth line the sentence should read
``Mixing will be roughly complete when is equal ...''
The is omitted in the book.
Chapter 10. On page 285, on the line after equation 10.46, the
sentence should read ``We can thus use (10.46) to obtain ,
that is, the value of the new wave function one
spatial unit in from the `right' boundary.''
Appendix 4. On page 393, the second and third lines of the program
listing should read
! x(i,n), y(i,n) = position of particle n
! i = 1 and 2 correspond to the old and current positions
Appendix 1. This item concerns the Euler-Cromer and Verlet methods,
and thus also is relevant to chapters 3 and 4, where the Euler-Cromer
method is used. It turns out that the Euler-Cromer and Verlet methods
are much more similar than is apparent (at least to me) at first sight.
This can be seen as follows.
The Euler-Cromer method can be written as
where is the second derivative of y at step i. This also implies
The Verlet method can be written as
If one eliminates from (2) one arrives at
precisely (4). Hence, the two methods are equivalent
with regards to y.
However, they are not necessarily the same with regards to the velocity.
For the Verlet method it is best to obtain the velocity as a centered
which is different, and more accurate than, the Euler-Cromer expression.
Thanks to Sam Buss for pointing out the equivalence of the Euler-Cromer
and Verlet methods.
On page 138, 6th line from the bottom, ``appling'' should be
``applying.'' On p. 207, the 8th line from the top
should read ``... and can be reviewed by reading ...''
On page 384, there is a typo in the comments for the waves-on-a-string
program. 18 lines from the bottom it should read
! n = 1 = position two time steps ago
Thanks to Ramin Jamshidi for finding these errors.
Thu Aug 13 11:02:49 EST 1998