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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.