Clarification of the term "Linear"

The term "linear" is very clear when applied to a mathematical function. A function F is linear if and only if it obeys homogeneity and superposition:

Homogeneity: F(cx) = cF(x)
Superposition: F(x+y) = F(x) + F(y)

In the context of what we have seen so far, the only elements that are linear as mathematical functions are resistors. An independent voltage source or an independent current source is not a linear element. (There are also linear dependent sources, linear capacitors and linear inductors, but we have not yet introduced them in our class. You will see them later.)

Formally, a circuit composed of only linear elements is a linear circuit. When we add independent sources to a linear circuit as inputs, we get a circuit that is not linear because it has an offset: its v-i characteristic at a pair of exposed terminals may not pass through the origin. However, we can make a Thevenin or Norton equivalent model of such a circuit: the Thevenin resistance summarizes the effect of the linear elements and the Thevenin voltage summarizes the effect of the independent sources.

However the term "linear," when applied to an electrical circuit often takes on an informal meaning. We often say that a circuit containing only linear elements and independent sources is a "linear circuit." So, in the informal sense, a linear circuit is one where we can apply the Thevenin or Norton theorems to summarize the behavior at a pair of exposed terminals.

Sorry for the confusion of words — natural language is like that!