Since you probably don't use partial derivatives everyday and may feel a bit rusty with them, it is probably good for us to review their use.

If *B* is a function of *x*, we denote it as
*B*(*x*) and its
derivative (slope) at *x* by . It is clear what is
going on because *B* is a function of a single variable.

However if *B* is a function of more than one variable, say both
*x* and *t*, then then we denote it
as *B*(*x*,*t*) and we can take derivatives (slopes) in more than one
way. The easiest way to make things clear is to use a partial
derivative where we take the derivative with respect to one
variable while holding the other variable constant.

Hence, is
the partial derivative of *B*(*x*,*t*)
with respect to *x* while holding *t* constant. Similarly
is the partial
derivative of *B*(*x*,*t*) with respect
to *t* while holding *x* constant.

As you can see on the previous page, the wave equation involves taking
two partial derivatives each for both variables of interest.
For example is the second
derivative of *p*(*x*,*t*) with respect to *t*, holding *x* constant,
and is the second derivative
of *p*(*x*,*t*) with respect to *x*, holding *t* constant.

Tue Feb 25 21:24:33 EST 1997