major confusion: harmonic waves

StephenPrivitera

"In contrast to the case of a harmonic wave on a string, a harmonic wave in a dispersive medium cannot be regarded as a simple succession of wave pulses because the pulses change their shape, whereas a harmonic wave does not."
Is this self-contradictory or is it just me? A harmonic wave in a dispersive medium has pulses which change shape, but a harmonic wave does not have pulses which change shape. What is the author trying to say?
Next sentence,
"There is then no simple connection between the speed of a wave pulse and the speed of a harmonic wave."
What's the difference?
"We call the speed of the peak of a wave pulse the group velocity."
I looked this up. It is
v=dw/dk where w is the angular frequency and k is the wave number
How would I take this derivative(ie, how do I write w=f(k))?
Why would w and k change?