Calculus Books, preferably Soviet.

Question

I would like some book recommendations on calculus books for novices. I love old Russian texts and if you you suggest such books(no issue if they are rigorous), I would be very grateful. If the text is quite challenging, I have no problem. But it should be interesting with proper exposition of topics.

The book should be good for self-study, preferably a textbook(again, for beginners). And it's not necessary for it to be Soviet. Just anything good. I merely like Soviet/Slavic books and so, the title.

Thanks to you all.

Edit again:Please try to abstain from suggesting analysis books. All I want is a nice, rigorous Book on Integral and Differential Calculus. Doesn't matter which origin(at this point), but should be translated into English. Thanks.

Answer 1

A (possibly the) standard classic is: Г. Фихтенгольц. Курс дифференциального и интегрального исчисления. (G. Fichtenholtz. The course of differential and integral calculus.)

I personally like very much the following two courses:

Л. Кудрявцев. Курс математического анализа (L. Kudryavtsev. Mathematical Analysis Course) (there are several editions of, in fact, two related courses - a shorter one of two books, and a longer one of three books);

V. Zorich: Mathematical Analysis (the best existing MA course in opinion of V. Arnold).

Answer 2

I would like to recommend "Problems in Mathematical Analysis Hardcover" – 1989 by Boris Demidovich (Editor), G. Yankovsky (Translator). This is a wonderful problem book which has lots of challenging problems. Another wonderful book is "Differential and integral calculus" by Grigorii Mikhailovich Fichtenholz.

Answer 3

I'd like to suggest 'Introductory real Analysis' and 'Elements of the Theory of Functions and Functional Analysis ' both by A.N.Kolmogorov

Answer 4

By Grigorii Mikhailovich Fichtenholz there is also " TheFundamentals of Mathematical Analysis"

Answer 5

L.V. Tarasov has written a book entitled Calculus: Basic Concepts for High Schools. Its first Russian edition was published in 1979 and its English translation in 1982.

This is not a recommendation. I mention the book here merely because it is the only Russian calculus textbook I know of. Someone has put the book on archive.org and its XeLaTeX source in a Gitlab repo, but I am not sure whether they are legal (hence no hyperlinks here).

Answer 6

I remember reading the Chinese translation of Vladimir I. Smirnov's multi-volume "Course of Higher Mathematics" in the summer before freshman year, and liking its balance of rigor and richness. However, the English edition seems too expensive. For a more rigorous treatment, Sergey M. Nikolsky's two-volume "Course in Mathematical Analysis" is hard to beat.

Answer 7

I like to recommend the both parts of the calculus books by Balmohan Limaye here is the link https://g.co/kgs/iexgM8

Answer 8

The book Concepts, Problems and Solutions in School Calculus : A Dialogue Approach by Lev Tarasov and Chandra Shekhar Kumar ( ISBN-13 : 978-9354372926 ) can be a good starting point for beginners because it doesn't assume any previous knowledge on calculus.