Practical Applied Mathematics: Modelling, Analysis, Approximation
Cambridge University Press, Mar 24, 2005 - Mathematics - 326 pages
Drawing from a wide variety of mathematical subjects, this book aims to show how mathematics is realised in practice in the everyday world. Dozens of applications are used to show that applied mathematics is much more than a series of academic calculations. Mathematical topics covered include distributions, ordinary and partial differential equations, and asymptotic methods as well as basics of modelling. The range of applications is similarly varied, from the modelling of hair to piano tuning, egg incubation and traffic flow. The style is informal but not superficial. In addition, the text is supplemented by a large number of exercises and sideline discussions, assisting the reader's grasp of the material. Used either in the classroom by upper-undergraduate students, or as extra reading for any applied mathematician, this book illustrates how the reader's knowledge can be used to describe the world around them.
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Units dimensions and dimensional analysis
hair modelling and cable laying
the thermistor 1
Partial differential equations
Theory of distributions
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analysis approximation assume asymptotic expansion balance beam boundary conditions boundary layer cable calculate Chapter characteristic projections coefficient conformal maps conservation Consider constant curve cylinder Deduce delta function density derivative dimensional dimensionless dimensionless parameter dimensions displacement distribution eigenvalue electric field example Exercise exponential Figure first-order Fredholm Alternative frequency gives gradient Green's function harmonics heat equation heat flow heat flux inner expansion integral kinematic kinematic wave Laplace's equation leading order leading-order linear look mass matching mathematical nonlinear normal Note ordinary differential equation oscillations outer expansion pantograph partial differential equation particles physical point force potential pressure radius Rankine-Hugoniot rays region regular expansion Reynolds number right-hand side satisfies scale shock solution solve speed string Suppose surface Taylor series temperature test functions theorem theory thermistor thin timescale traffic unit value problem variables vector velocity viscous fluid wave equation write yolk zero