Я не в курсе, можно я уточню? Мне казалось, Рудин (baby) - для математиков-первокурсников:
Rudin in Preface писал(а):
This book is intended to serve as a text for the course in analysis that is usually taken by advanced undergraduates or by first-year students who study mathematics.
Может быть, лет 40-50 назад так и было. Но сейчас ситуация примерно такая:
MAA Reviews писал(а):
Calculus courses in the USA have been transformed from strong mathematical crucibles, in which approximation and geometrical proofs were part and parcel of the subject, into much less rigorous courses taken by all or most incoming freshman science majors. When Rudin wrote this book, calculus courses included epsilon-delta limit arguments and inequalities on the real line alongside related rates, solving differential equations and calculating volumes and areas using standard integral formulas. Looking at the books of the past — such as Lipman Bers’ Calculus and Edwin E. Moise’s Calculus — it’s easy to see why Rudin was the book of choice for analysis courses. It was reasonable to expect that students who did well in such calculus courses would have more then sufficient background to be able to tackle Rudin, despite the effort it would require of even good students.
Today’s students don’t stand a chance — most are simply overwhelmed due to lack of preparation. It’s as simple as that. Unless they’ve had the good fortune and talent to be guided through high school to a good honors calculus course as freshmen — such as those based on Spivak’s Calculus — reading this book is going to be a real struggle, to say nothing of the exercises.
http://www.maa.org/press/maa-reviews/pr ... l-analysisХотя это и правда относится к, как вы их называете, "инженерам", например, к теорфизикам :)
А вот примерно как выглядит undergraduate программа матфака MIT:
https://math.mit.edu/academics/undergra ... 8/pure.phpВот кто ходит на курс анализа 18.100A:
Цитата:
The class usually contains students from years 2,3,4,and G (grad students) -- about equal numbers of each. Sometimes freshmen also take it.
По Рудину преподается более сложный вариант - 18.100B. Боюсь, доля первокурсников там еще меньше :)
И ещё, когда математики "натаскиваются" в calculus? (пределы, неопр. инт-лы, div-grad, и пр.)
Цитата:
The subject 18.100 Real Analysis is basic to the program. Since this subject is strongly proof-oriented, many students find it useful to begin as Freshmen by taking 18.014 and 18.024 Calculus with Theory.
) трудновато.