I am studying asymptotic methods right now; things such as mellin transform, inverse mellin transform, saddle point method, laplaces method, etc… and I get very frustrated because I can't get very far through the proofs without getting stuck. It usually involves some approximation of some sort that I fail to see why it works.
I've had graduate level complex and real analysis, but not a whole lot of practice in applying bounding/approximation techniques. I have tried picking up books on asymptotic analysis that begin very basic: big oh, little oh, etc… but the exercises quickly become non-trivial. I just need practice bounding and approximating things, and applying these things to contour integrals and the other methods I've mentioned.
A resource, roadmap, book, etc… any advice you can offer would be great. I just want to be able to have the background assumed in some of these expositions on asymptotic methods…and I don't see how to get it.
Best Answer
Here are some hints which might be useful. Far from being an expert in this field, I by myself depend strongly on accessible information. Fortunately there are some good books from the great providing appropriate information.
A first step:
The next one is much more comprehensive.
Another reference in this book, namely ref. [329] (and also referred to by D.E.Knuth and D.E.Greene above) points to a classic of P. Henrici which is my next hint for you.