**TL;DR Sedra/Smith is not using the word 'linear' to describe amplifiers in exactly the same way that mathematicians define the word. ** 

Engineers tend to say that an amplifier is linear when it has a gain Vout/Vin = k(f), where k can vary with frequency. When excited by any single sinuosoid, the output will look like a perfect scaled copy of the input. 

If k varies with frequency, then when excited by multiple sinusoids, the output will not look like the input, but there will be no intermodulation distortion, the only output frequencies will be those present in the input.

If the input range of frequencies is limited to the flat frequency response part of the spectrum (a condition that is often assumed but not stated), then the output **may** look like a scaled version of the input. It will only actually look like a scaled version if the phase response of the amplifier is linear as well, in other words the delay through the amplifier is equal at all frequencies.

When Sedra/Smith want to describe an amplifier with frequency-independent gain (infinite bandwidth) they call it *ideal*.

Mathematicians say a system H is linear iff (if and only if) it obeys the superposition principle, that H(x+y) = H(x) + H(y). This is weaker than the amplifier sense in that it allows a time-varying system gain, which can generated output harmonics under certain conditions. So time-independent gain implies superposition, but superposition does not imply time-independent gain.

Both engineers and mathematicians regard things like the response of inductors or capacitors as linear. They do not obey Vout/Vin = k, there is a differential or integral operator involved, they do obey superposition.

Many engineering texts talk about 'LTI' systems, meaning Linear Time-Invariant. Engineers tend to use 'linear' casually when they mean LTI.

The mathematician's view is not totally foreign to engineers. I have used frequency mixers. Good ones are 'linear', bad ones are less linear. This is in being used in the distortion/intermodulation/superposition sense. However, looking at just the signal path through a mixer, the local oscillator is causing the mixer's gain to vary cyclically, and intermodulation does occur between the local oscillator and the signal.