附註:Includes bibliographical references (pages 318-320) and index.
The basics of modelling -- Units, dimensions and dimensional analysis -- Nondimensionalisation -- Case studies: hair modelling and cable laying -- Case study: the thermistor (1) -- Case study: electrostatic painting (1) -- Partial differential equations -- Case study: traffic modelling -- The delta function and other distributions -- Theory of distributions -- Case study: the pantograph -- Asymptotic expansions -- Regular perturbation expansions -- Case study: electrostatic painting (2) -- Case study: piano tuning -- Boundary layers -- Case study: the thermistor (2) -- 'Lubrication theory' analysis in long thin domains -- Case study: continuous casting of steel -- Lubrication theory for fluids -- Case study: turning of eggs during incubation -- Multiple scales and other methods for nonlinear oscillators -- Ray theory and the WKB method.
摘要:Used either 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. Topics include distributions, asymptotic methods and the basics of modelling. Applications range from piano tuning to egg incubation and traffic flow.
