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Motivation

I agree that sometimes authors present a concept simply because it's a standard example in the subject, but then spend a single page on it and just move on to other things. One example that comes to mind is a particular text on undergraduate real analysis which introduced Fourier Series in a few pages and then had a single sloppy exercise related to applications to PDEs. I'm not saying the book should have dedicated a chapter to PDEs, but one ugly exercise seems like a travesty and makes you scratch your head about why you're wasting your time on this stuff. I don't expect incredibly motivated concepts in graduate texts on the same subject simply because by then I should have already been motivated enough to study onwards.

However, motivation for what you're doing is one of those dangerous phrases in mathematics. For the more difficult and abstract stuff out there, it's not always straightforward to communicate the direct usefulness of an idea. Just because I tell you a result is incredibly useful in say, the sciences, does that make all the difference? When I learned the Radon-Nikodym theorem in real analysis, I could not for the life of me see a genuinely useful application of it, until I came to the formal definition of conditional expectation in probability. In short, the proof of existence and uniqueness of conditional expectation is by the abstract nonsense argument of the Radon-Nikodym theorem. I certainly think it would have been quite nice if somebody told me in my real analysis class why we were learning the Radon-Nikodym theorem, but at the same time I don't think I would have been ready to learn the substantial amount of probability to really understand what the heck the formal definition of conditional expectation is (let alone why it's useful!).

ButPlus, much of the time I don't come to play devils advocate for appreciate a moment, if textbooks get too good textbook until I've read it would put professors out all the way through. If you're curious about "applications" of a job! what you're learning, try going ahead 20-30 pages, and hopefully the author will have started subjects which apply what you have learned.

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Motivation for what you're doing is one of those dangerous phrases in mathematics. For the more difficult and abstract stuff out there, it's not always straightforward to communicate the direct usefulness of an idea. Just because I tell you a result is incredibly useful in say, the sciences, does that make all the difference? When I learned the Radon-Nikodym theorem in real analysis, I could not for the life of me see a genuinely useful application of it, until I came to the formal definition of conditional expectation in probability. In short, the proof of existence and uniqueness of conditional expectation is by the abstract nonsense argument of the Radon-Nikodym theorem. I certainly think it would have been quite nice if somebody told me in my real analysis class why we were learning the Radon-Nikodym theorem, but at the same time I don't think I would have been ready to learn the substantial amount of probability to really understand what the heck the formal definition of conditional expectation is (let alone why it's useful!).

In the end, you're going to need to find a textbook which suites your needs. Each person has their own style for absorbing the material they need. Some people love the straightforward definition - theorem - proof approach while others like to see a section on "applications" after every idea presented (I personally fall into the latter category). If you want to learn the nitty-gritty version of complex analysis, you pick up Complex Analysis by Ahlfors. If you want to learn complex analysis from an engineering point of view, you pick up Complex Analysis For Engineers. It's up to you which applications you want to see, so supplement your knowledge accordingly.

But, to play devils advocate for a moment, if textbooks get too good it would put professors out of a job!