Analysis by its history
by Ernst Hairer, G. Wanner · first published 1996
33% recommend67% neutral
This book presents first-year calculus roughly in the order in which it first was discovered. The first two chapters show how the ancient calculations of practical problems led to infinite series, differential and integral calculus and to differential equations. The establishment of mathematical rigour for these subjects in the 19th century for one and several variables is treated in chapters III and IV. The text is complemented by a large number of examples, calculations and mathematical pictures and will provide stimulating and enjoyable reading for students, teachers, as well as researchers
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Not sure if mentioned, another good book: Analysis by its History
on “Mathematics for the Adventurous Self-Learner” ↗…incomprehensible, unless you're already on the other side. When it comes to analysis in particular, one approach is to start studying it in the order it was discovered. There's a well-regarded book called Analysis by Its History, but I haven't read it. There's another called Understanding Analysis by Stephen Abbott that I recommend if you want to regroup before attacking baby Rudin again.
on “Noted mathematician Rudin dies at 89” ↗An interesting supplementary book is "Analysis by Its History" that gives insight into how classical analysis was actually developed. Not so great to learn from initially, but gives some background on the intuitions from which the modern definitions are based.
on “Ask HN: Resources to learn real analysis?” ↗