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TL;DR As engineers, Sedra/Smith make one more assumption than the OP does. Engineers also make one more assumption than do mathematicians.

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 engineers tend to use, as it allows a time-varying system gain, which can generate output harmonics under certain conditions. So time-independent gain implies superposition, but superposition does not imply time-independent gain.

Engineers tend to be lazy and say linear when they mean LTI - Linear Time-Invariant.

An LTI system can still have a frequency response. 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.

Now for the important difference in assumptions. 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), and the amplifier also has linear phase - that is constant signal delay, then the output will look like a scaled version of the input, and finally we can write Vout/Vin = constant.

Plenty of amplifiers and filters exist where phase is not linear even though the gain may be, and the output of those does not look like the input. The output is usually referred to as suffering from phase distortion.

An ideal amplifier will have infinite bandwidth and zero noise, and not suffer clipping up to any arbitrary signal level.

The response of inductors or capacitors is linear, they obey superposition. They do not obey Vout/Vin = k, there is a differential or integral operator involved.

Engineers do also use time-varying systems, although they call them mixers. A diode ring pumped with a strong local oscillator drive changes its gain cyclically. When a low level signal is passed through, it does obey superposition, and engineers do talk about 'linear' mixers. A good mixer obeys superposition up to higher signal levels than a bad mixer. In a good mixer, the signal passing through does not suffer any intermodulation distortion between its frequency components. There is intermodulation between the local oscillator and the signal components, that's how you get the sum and difference frequencies!

TL;DR As engineers, Sedra/Smith make one more assumption than the OP does. Engineers also make one more assumption than do mathematicians.

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 engineers tend to use, as it allows a time-varying system gain, which can generate output harmonics under certain conditions. So time-independent gain implies superposition, but superposition does not imply time-independent gain.

Engineers tend to be lazy and say linear when they mean LTI - Linear Time-Invariant.

An LTI system can still have a frequency response. 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.

Now for the important difference in assumptions. 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), and the amplifier also has linear phase - that is constant signal delay, then the output will look like a scaled version of the input, and finally we can write Vout/Vin = constant.

Plenty of amplifiers and filters exist where phase is not linear even though the gain may be, and the output of those does not look like the input. The output is usually referred to as suffering from phase distortion.

An ideal amplifier will have infinite bandwidth and zero noise, and not suffer clipping up to any arbitrary signal level.

The response of inductors or capacitors is linear, they obey superposition. Networks involving those do not obey Vout/Vin = k, there is a differential or integral operator involved.

Engineers do also use time-varying systems, although they call them mixers. A diode ring pumped with a strong local oscillator (LO) drive changes its gain with the LO period. When a low level signal is passed through, it does obey superposition, and engineers do talk about 'linear' mixers. A good mixer obeys superposition up to higher signal levels than a bad mixer. In a good mixer, the signal passing through does not suffer any intermodulation distortion between its frequency components. There is intermodulation between the LO and the signal components, that's how you get the sum and difference frequencies!

TL;DR As engineers, Sedra/Smith make one more assumption than the OP does. Engineers also make one more assumption than do mathematicians.

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 engineers tend to use, as it allows a time-varying system gain, which can generate output harmonics under certain conditions. So time-independent gain implies superposition, but superposition does not imply time-independent gain.

Engineers tend to be lazy and say linear when they mean LTI - Linear Time-Invariant.

An LTI system can still have a frequency response. 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.

Now for the important difference in assumptions. 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), and the amplifier also has linear phase - that is constant signal delay, then the output will look like a scaled version of the input, and finally we can write Vout/Vin = constant.

Plenty of amplifiers and filters exist where phase is not linear even though the gain may be, and the output of those does not look like the input. The output is usually referred to as suffering from phase distortion.

An ideal amplifier will have infinite bandwidth and zero noise, and not suffer clipping up to any arbitrary signal level.

The response of inductors or capacitors is linear, they obey superposition. They do not obey Vout/Vin = k, there is a differential or integral operator involved.

Engineers do also use time-varying systems, although they call them mixers. A diode ring pumped with a strong local oscillator drive changes its gain cyclically. When a low level signal is passed through, it does obey superposition, and engineers do talk about 'linear' mixers. A good mixer obeys superposition up to higher signal levels than a bad mixer. In a good mixer, the signal passing through does not suffer any intermodulation distortion between its components. It does suffer intermodulation between the local oscillator and the signal.

TL;DR As engineers, Sedra/Smith make one more assumption than the OP does. Engineers also make one more assumption than do mathematicians.

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 engineers tend to use, as it allows a time-varying system gain, which can generate output harmonics under certain conditions. So time-independent gain implies superposition, but superposition does not imply time-independent gain.

Engineers tend to be lazy and say linear when they mean LTI - Linear Time-Invariant.

An LTI system can still have a frequency response. 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.

Now for the important difference in assumptions. 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), and the amplifier also has linear phase - that is constant signal delay, then the output will look like a scaled version of the input, and finally we can write Vout/Vin = constant.

Plenty of amplifiers and filters exist where phase is not linear even though the gain may be, and the output of those does not look like the input. The output is usually referred to as suffering from phase distortion.

An ideal amplifier will have infinite bandwidth and zero noise, and not suffer clipping up to any arbitrary signal level.

The response of inductors or capacitors is linear, they obey superposition. They do not obey Vout/Vin = k, there is a differential or integral operator involved.

Engineers do also use time-varying systems, although they call them mixers. A diode ring pumped with a strong local oscillator drive changes its gain cyclically. When a low level signal is passed through, it does obey superposition, and engineers do talk about 'linear' mixers. A good mixer obeys superposition up to higher signal levels than a bad mixer. In a good mixer, the signal passing through does not suffer any intermodulation distortion between its frequency components. There is intermodulation between the local oscillator and the signal components, that's how you get the sum and difference frequencies!

TL;DR There are many different assumptions going into subtly different definitions of the word linearity, and what you, I, Sedra/Smith and mathematicians mean when they talk about linearity

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), and the amplifier also has linear phase - that is constant signal delay, then the output will look like a scaled version of the input. Plenty of amplifiers and filters exist where phase is not linear even though the gain may be, and the output of those does not look like the input. The output is usually referred to as suffering from phase distortion.

An ideal amplifier will have infinite bandwidth and zero noise, and not suffer clipping up to any arbitrary signal level.

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.

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

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, but they do obey superposition.

Engineers do recognise time invariant systems, although they call them mixers. A diode ring pumped with a local oscillator changes its gain cyclically. When a signal is passed through, it does obey superposition, and engineers do talk about linear mixers. A good mixer obeys superposition up to higher signal levels than a bad mixer. In a good mixer, the signal passing through does not suffer any intermodulation distortion between its signal components. It does though suffer intermodulation between the local oscillator and the signal.

TL;DR As engineers, Sedra/Smith make one more assumption than the OP does. Engineers also make one more assumption than do mathematicians.

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 engineers tend to use, as it allows a time-varying system gain, which can generate output harmonics under certain conditions. So time-independent gain implies superposition, but superposition does not imply time-independent gain.

Engineers tend to be lazy and say linear when they mean LTI - Linear Time-Invariant.

An LTI system can still have a frequency response. 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.

Now for the important difference in assumptions. 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), and the amplifier also has linear phase - that is constant signal delay, then the output will look like a scaled version of the input, and finally we can write Vout/Vin = constant. 

Plenty of amplifiers and filters exist where phase is not linear even though the gain may be, and the output of those does not look like the input. The output is usually referred to as suffering from phase distortion.

An ideal amplifier will have infinite bandwidth and zero noise, and not suffer clipping up to any arbitrary signal level.

The response of inductors or capacitors is linear, they obey superposition. They do not obey Vout/Vin = k, there is a differential or integral operator involved.

Engineers do also use time-varying systems, although they call them mixers. A diode ring pumped with a strong local oscillator drive changes its gain cyclically. When a low level signal is passed through, it does obey superposition, and engineers do talk about 'linear' mixers. A good mixer obeys superposition up to higher signal levels than a bad mixer. In a good mixer, the signal passing through does not suffer any intermodulation distortion between its components. It does suffer intermodulation between the local oscillator and the signal.