Books on Perturbation Methods I am having problems finding descent books on perturbation methods. I am looking for a book which covers; asymptotic expansions, matched Asymptotic expansions, Laplace's Method, Method of steepest Descent and the WKB method. Due to my style of learning I also need a book with lots of problems which either have solutions or are of the format 'show that ...' so you can check your answer. Does anyone have any suggestions?
 A: I was suggested to start with the following books
$1$. A. H. Nayfeh, Introduction to Perturbation Techniques, Wiley, 1993.
$2$. A. H. Nayfeh, Pertubation Methods, Wiley, 2004.
They contain many examples in mathematical physics and specially in mechanics. However, they don't explain the mathematical theory well. Another recent development which has a nice structure and explanation is
$3$. W. Paulsen, Asymptotic Analysis and Perturbation Theory, CRC Press, 2013.
Also, a classic one is
$4.$ E. J. Hinch, Perturbation Methods, Cambridge University Press, 1991.
The above books are fine; however, I prefer the following that emphasizes the theory by mentioning important theorems and citing pertinent references for their proof. It also contains lots of examples and applications. The material covered in the book is satisfactory. I think it is a gem!

$5.$ M. H. Holmes, Introduction to Perturbation Methods, 2nd Edition, Springer, 2013.

A: Perhaps Advanced Mathematical Methods for Scientists and Engineers: Asymptotic Methods and Perturbation Theory by Bender & Orszag?
A: I can recommend Asymptotics and Special Functions by Frank W. J. Olver. It covers everything you mentioned except matched asymptotic expansions. The book contains several exercises and is written in a rigorous manner.
