What is the DC component?

From a book I am currently reading ("Fundamentals of Pulse and Digital Circuits" 3th Edition by Ronald J. Tocci) it is explained that any periodic waveform with a frequency has three components:
1. A DC component (Also called the average value in the book)
2. A sinusoidal component equal to the fundamental frequency
3. Integer multiples of the fundamental frequency
What exactly is the DC component? Is it another name for the DC offset or is it something else?

 

The DC component would be the constant voltage added to a pure AC waveform. For example, the true average voltage a pure AC waveform would be zero. When the AC waveform has a DC component, the average voltage would be equal to the DC voltage instead, because oposite peaks cancel each other leaving only the DC component.

 

Its pretty much the vertical offset on the AC signal...

So if the AC is flucating vertically around a certain voltage, that voltage will be the DC compononet of the signal

 

For a time-varying sine wave:

x(t) = A + BSin(2ft)

A is the DC component. It shifts the function up or down the y-axis. Note that it is independant of the function variable t.

Dave