Customer Reviews

Mathematical Analysis II (Universitext)

5 star:		(4)
4 star:		(1)
3 star:		(0)
2 star:		(0)
1 star:		(0)

 

 

Since I am listed by Amazon (but not by Springer) as one of the authors, you should quite properly be skeptical of my 5-star review. But I really mean it: I think the book is outstanding.

Now the correction. I am IN NO SENSE a co-author of this book, merely its translator. The translation was very enjoyable work, and I enjoyed the interaction with the author that it made possible. That, however, does not make me a co-author. (But if you'd like to see some books that I HAVE authored, please search.)

Roger Cooke

The book besides covering a broad material on classical analysis(with a modern touch), exposes the basic core of analysis expected from a mathematics or physics student without making use of pedantic and unnecessary formalism. The author emphasizes the connection of important ideas via concrete and substancial examples more than insisting in pathological and or trivial examples. It has plenty of examples coming from physics and other sciences(following the tradition of the russian school : of teaching mathematics emphasizing links with other areas). We can't forget to mention the many geometrical insights provided. Moreover the book is "filled" w/ good exercises that really colaborates for a solid mathematical education and has also a detailed appendix where an instructor can find some very interesting and challenging problems for a seminar discussion or final exams. Undoubtly an worthwhile reading!

These two books written by V.A. Zorich represent a great course in analysis, both for people who just started dealing with the subject and for more experienced students. The treatment is thorough and spreads from an entire chapter about real numbers to very advanced problems. It also points out many applications in natural sciences.

A good and rather necessary addition would be the solutions to the problems given in these books. Thus students would have a way to check their work. Nevertheless it's worth more than five stars.

This is a two-volume treatise on Mathematical Analysis at undergraduate level. These two volumes are the most complete that I have seen so far. There is plenty of material here; one could easily spend two academic years (4 semesters of 6 quarters) to cover both volumes completely. Everything needed in undergraduate analysis is here: convergence (pointwise and uniform), differentiation, integration, integrals depending on parameters, interchanging limits, metric spaces, partial derivatives, multiple integrals, Stokes' Theorem, and much, much more. The author is a very good writer, and his proofs are slick, but readable. Exercises range from routine to quite challanging. Anyone studying real analysis (or mathematical analysis) should have these two volumes handy. Highly recommended.

On the section of limit of sequence, there is a proof about number e. it says that (1+1/n)^n is a decreasing sequence and larger than zero. Therefore it has a limit e.
But by intuition, (1+1/n)^n as n tends to limitless is an increasing sequence. The whole process looks odd.
What's wrong?