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This has been a question for many, many years. Dodgson (i.e. Lewis Carroll) goes to typically wacky lengths to defend using a two-thousand-year-old text (see a helpful review here). Honestly, it really depends a lot upon the subject matter. Some people are still using Granville's Calculus (apparently), but try to read an algebraic geometry text from 80 ...


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For me, generally, using any book that is easy to use, for a new topic is the ideal strategy. Worrying too much about missing some particular insight is counter-productive versus just moving forward. There will always be a tension of completeness versus ease of first entry. I just think you are better off going forward and then filling in, versus worrying ...


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Although, I do not have any recommendation for trigonometry text and most of the arguments for & against seems valid here. But I do want to point out, SL Loney is widely used as a reference textbook in India for Trignometry & Coordinate geometry. Any student who is serious about qualifying the university entrance exams must solve part 1 of the Loney'...


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My book Calculus from the Ground Up focuses on differentials, and uses it to provide a unification of process and simplification of understanding of a lot of different parts of calculus. To read about the thought process that led to the book you can see this arXiv link; the focus on differentials that you are asking for led naturally to a refactoring of the ...


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