Description: This introduction to the mathematics of incompressible fluid mechanics and its applications keeps prerequisites to a minimum - only a background knowledge in multivariable calculus and differential equations is required. Part One covers inviscid fluid mechanics, guiding readers from the very basics of how to represent fluid flows through to the incompressible Euler equations and many real-world applications. Part Two covers viscous fluid mechanics, from the stress/rate of strain relation to deriving the incompressible Navier-Stokes equations, through to Beltrami flows, the Reynolds number, Stokes flows, lubrication theory and boundary layers. Also included is a self-contained guide on the global existence of solutions to the incompressible Navier-Stokes equations. Students can test their understanding on 100 progressively structured exercises and look beyond the scope of the text with carefully selected mini-projects. Based on the authors' extensive teaching experience, this is a valuable resource for undergraduate and graduate students across mathematics, science, and engineering.
Brief description: Frank H. Berkshire is currently Principal Teaching Fellow in Dynamics in the Department of Mathematics at Imperial College London, where he has been a member of the Academic Staff since 1970-latterly for twenty-five years as Director of Undergraduate Studies until formal 'retirement' in 2011. He has long-term experience of delivering lecture courses and projects, and has received awards for teaching excellence. He has promoted Mathematics extensively in the UK and overseas, and is co-author with Tom Kibble of the textbook Classical Mechanics (1996 and 2004). His research interests are in theoretical and practical dynamics, with wide application in e.g. waves, vortices, planetary motion, chaos, sport and gambling.