Asymptotic Methods in Analysis

To study this book you should be comfortable with:

a) Undergraduate Level Real Analysis. b) Elementary Notions from Complex Variable Theory including Complex Integration, Calculus of Residues, Power Series Expansions and related ideas.


a small tree bearing so many fruits   January 14, 2007
Gilles Benson (Beauvais, France)
4 out of 4 found this review helpful

this book stands apart on my shelves since I used it so often that I had to replace it three times; the subject of asymptotics is both useful and fascinating; this book delves in it through many examples first showing how to deal with them in elementary fashion, then using more advanced tools and finally exhibiting heavy machinery; although a lot of complex analysis tools are present in the text, it is quite possible to get a good grasp of what is done in it since elementary methods are always stated in the first instance e.g. the study of U_n+1 = sin(U_n): using calculus, it is shown that U_n which tends to zero is not far from (3/n)^(1/2) (sorry about that for those who do not speak fluent mathematics...), then 4 terms of the asymptotic development are given followed by a more general method to get an arbitrary number or terms.
This book will prove useful to you in different fashion as the years go on
and your mathematical skill is improving.
Moreover, the price is really affordable.
As a matter of fact, I first bought this book in 1986...and I find it still really pleasurable.


Knuth calls this a beautiful book.   November 27, 1998
7 out of 16 found this review helpful

Asymptotic methods in analysis is great book. I came to know about this book while reading TAOCP vol 1. As Knuth says this is a truly beautiful book on the subject.


A novice review   March 18, 2001
bergvall jonas (Sweden)
3 out of 11 found this review helpful

This will be an alternative review since I lack the complete knowledge foundation required by the book, yet I've purchased it knowing so in advance.

This is simply an elegantly written book in terms of language use. The book is designed with a language use; the way i prefer to write swedish text, no matter the subject at hand.

Also parsing arbitrarly there are some references to other russians work. As far as I can evaluate by glimpse and rudimentary mathematical knowledge there is proof and definition driven reasoning which is a must in mathematics in order to be of great use for the reader at hand.

Also for a novice like myself the extensive and clear, instant writing about necessary mathematical methods, functions and so on to solve the problems developed, functions in use give back great insight value; The art of thinking of how go about solving the issues at hand.

I think one would feel confident in reading this as one go by reading mathematical/Physics courses at University (if you do/did). This mean that for me the reading would be limited to pieces of reading as one grow with required knowledge.

10-20 points in mathematical analysis and additional introduction course in functions of complex variables would suffice (of course this is an estimation).