I've taken up self-study of math and i start using the book called :
Mathematical Analysis I Authors: Canuto, Claudio, Tabacco, Anita
I would like to start from zero to understand taylor expansion and i'm looking about some textbook with homework problems with step-by-step math answers if possible and cover specialy those subjects:
- Local comparison of functions.
- Taylor expansions and applications
I would appreciate any book recommendations.
Thanks in advance.
Best Answer
It is strangely difficult to find good introductory analysis books that are also good "calculus" books.
I have the first edition of the book: It is very rigorous, and many points that are usually glossed over are explained very well. For example, the variable substitution method of calculating limits (which is usually not explained at all) is given a theoretical justification, and the subsequent calculation examples are explicitly related to the relevant theorem. The only problem with my edition is that the English translation is ludicrously awful. (On the other hand the ridiculous grammar and idiosyncratic expressions provide a few laughs.) The translator is obviously not a native-speaker of English. But who cares? It's mathematics!
The book is very helpful, if we must find her only flaw is precisely the translation. (I hope that the second edition has improved)