Theoretical research sometimes resembles panning for gold: the first to 'discover' a given subject can take their pick of any bold simplifying assumptions and mine all the good nuggets before the rest of us join in. Still, some beautiful exact results may lie just below the surface. Every now and then, they are uncovered through mathematical tours de force. Short of extraordinary mathematical skills, there is, fortunately, a third way towards successful analytical investigations: Asymptotics – the craft of treating limiting cases. This book is addressed to scientists and engineers from Masters level up who want to enrich their numerical investigations with analytical results. It provides strategies for obtaining approximate results when parameters become small or large. Built round a large number of examples, it demonstrates how the techniques apply to a variety of problems, by considering applications from areas as diverse as quantum mechanics, elasticity, electromagnetism and population dynamics.

‘Kozyreff’s book is incredibly comprehensive: it provides a wealth of new examples to demonstrate classic techniques (Matched Asymptotic Expansions, Multiple Scales etc.) while also covering more unusual, but increasingly important, topics like Discrete and Exponential Asymptotics. Throughout, Kozyreff keeps the student in mind, from the careful integration of code to facilitate algebraic manipulations to a wealth of exercises with solutions provided in an Appendix.’

Dominic Vella - University of Oxford

‘This is just the book I wish had been available when I was a grad student. I have been a user of various bits of Fasymptotic theory, but there are other quite basic concepts that have remained a mystery to me. Instead of trying to prove theorems or present theory that would apply in all possible cases, Kozyreff quietly takes you through example after example, slowly building up your intuition and giving you the chance to practice with examples and solutions. Not only would I teach using this book if I had the chance, but I would first take the course myself!’

Alan Champneys - University of Bristol