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Maybe the most prominent (and the first, I think) example of this is the treatment of Dirac's delta function in the Mathematical introduction, pages 60-63 (Second Edition). Does anyone else find it extremely counter-intuitive to define delta as delta(x-x') integrated over x' (!) to give unit value? Of course, delta is even, so it really doesn't matter if it's defined this way, or delta(x'-x), but still... Every textbook I've _ever_ seen defines this as delta(x-T), where T is simple delay, and integration is always done over t, which is completely intuitive (at least to me). BTW, while we're at these pages, I was also a little uncomfortable with his asking for a "proof" in 1.10.2 (altogether with the Taylor's series expansion hint) - what _I_ have learned in school is pretty well summarized in http://en.wikipedia.org/wiki/Dirac's_delta_function#Composition_with_a_function

My question is: did anyone else have these subtle discomforts while reading this book, or is it just my inability to adapt to a different (Yale?) teaching style?