Practical Asymptotics

Erscheinungsjahr 2026
ISBN: 978-1-009-69728-6
Verlag: Cambridge University Press

Buch, Englisch, Band 64, 320 Seiten

Reihe: Cambridge Texts in Applied Mathematics

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.

Autoren/Hrsg.

Kozyreff, Gregory

Inhaltsverzeichnis

1. Asymptotic generalities; 2. Matched asymptotic expansions (MAE); 3. The WKB method; 4. The method of multiple scales (MMS); 5. Approximations of integrals; 6. Discrete asymptotics; 7. Divergent series and exponentially small phenomena; 8. Solutions to exercises; Appendix. Inhomogeneous linear ODEs; References; Index.

Über Autor(innen)

Kozyreff, Gregory
Gregory Kozyreff is Senior Research Associate of the Fonds de la Recherche Scientifique – FNRS in the Physics Department at Université Libre de Bruxelles. His research centres on applying asymptotic techniques in nonlinear optics, elasticity, photonics (including photovoltaics), fluid mechanics, and pattern formation. He received the De Donder prize in mathematical physics from the Belgian Royal Academy and co-authored the book 'Applied Solid Mechanics' (2008).