CHANGES

<li>In Example 1.4.2, explicitly say how the volume is computed.
<li>In first example in 1.9 (1.9.1), mention explicitly that \(\alpha\) is a
constant.
<li>In section 1.9, terms in some equations were ordered with \(u_x\) first
and \(u_t\) second and some vice-versa.  Order them all the same for
consistency's sake, that is, \(u_x\) first.
This includes the exercises 1.9.1, 1.9.2, 1.9.3, 1.9.6, and 1.9.101.
(There is no change in content, it's just how its presented)
<li>In section 2.2, just before Theorem 2.2.1, mention that we are for the moment
supposing that the roots are real.
<li>In exercises 2.3.9, 2.3.10, 2.3.104, 2.3.105 change "find a linear combination that works."
to "find a linear combination that gives 0." as "works" may be a little confusing or unclear.
<li>Add a few words about the quadrant in the explanation of how to get the phase shift.
It is not too important, so we don't want to dwell on it, but it turns out many students here
have not seen polar coordinates yet (or just don't remember them).  Also add the
equations for A and B in terms of C and \(\gamma\) as that makes it easier to see.
<li>In the mass-spring diagram in 2.4 and 2.6, mark the direction of the position \(x.\)
<li>At the end of 2.5, add more detail to computation with variation of
parameters.
<li>At the end of 2.5, add a paragraph recapping of how that procedure (variation of parameters)
would work in general.  Then also remark that if there is a coefficient in front of the \(y'' ,\)
it is necessary to first divide by it.
<li>Make the caption to Figure 4.17 slightly more descriptive, which as
side condition gets rid of a horrible page break.
<li>After Theorem 6.1.1 (linearity of the Laplace transform), demonstrate
its use together with the table with a quick computation, rather than just
saying it.
<li>Right after the second shifting property, do a quick example
where the function is not just a constant.
<li>In Theorem 6.3.1, mention that the convolution is of exponential order.
<li>In first example in 6.5 (6.5.1), mention explicitly that \(\alpha\) is a
constant.