The current version always lives here.
In 2016 I wrote some lecture notes for the Part II course Asymptotic Methods. The long-awaited update has now happened, and the second edition is linked above.
These are intended to cover the Part II course precisely, but also include more examples and some minor extensions that the course might not have time to discuss. Of course for exams what the lecturer actually covers is the important part!
Please send corrections, comments, suggestions, &c to my email address (which may be found on the back page of the PDF, but you should be able to guess it from my web address!). These will be dealt with as soon as I get a chance.
Thank you to everyone who has sent me comments and corrections already, a full list is at the end of the document.
Previous significant versions are linked below in case you’d still like to reference them.
This is a list of articles and books that you might like to look at for context.
Jackson, J.D. (1999), From Alexander of Aphrodisias to Young and Airy. Physics Reports, Volume 320, Issues 1–6, pp. 27-36, DOI:10.1016/S0370-1573(99)00088-5.
Nice short article discussing the optics of rainbows, including the Descartes geometric optics that gives the primary, secondary, etc, and the Young theory using Airy functions to explain the supernumerary arcs.
Berry, M.V. and Howls, C.J., (1990), “Hyperasymptotics” Proc. R. Soc. Lond. A, Volume 430(1880). DOI:10.1098/rspa.1990.0111 Web link.
Short introduction to hyperasymptotics.
Boyd, John P., (1999) “The Devil's Invention: Asymptotic, Superasymptotic and Hyperasymptotic Series” Acta Applicandae Mathematicae, Volume 56(1), pp. 1-98. DOI:10.1023/A:1006145903624
Long introduction to asymptotics, superasymptotics and hyperasymptotics, focusing on the Stieltjes integral example.