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＜電子ブック＞
Methods of Mathematical Modelling : Continuous Systems and Differential Equations / by Thomas Witelski, Mark Bowen
(Springer Undergraduate Mathematics Series. ISSN:21974144)

版	1st ed. 2015.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2015
大きさ	XVIII, 305 p. 50 illus., 45 illus. in color : online resource
著者標目	*Witelski, Thomas author Bowen, Mark author SpringerLink (Online service)
件　名	LCSH:Differential equations LCSH:Mathematical physics LCSH:Mathematical models LCSH:Mathematical optimization LCSH:Calculus of variations FREE:Differential Equations FREE:Mathematical Physics FREE:Mathematical Modeling and Industrial Mathematics FREE:Calculus of Variations and Optimization
一般注記	Rate equations -- Transport equations -- Variational principles -- Dimensional scaling analysis -- Self-similar scaling solutions of differential equations -- Perturbation methods -- Boundary layer theory -- Long-wave asymptotics for PDE problems -- Weakly-nonlinear oscillators -- Fast/slow dynamical systems -- Reduced models for PDE problems -- Modelling in applied fluid dynamics This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow dynamical systems. Methods of Mathematical Modelling will be useful for advanced undergraduate or beginning graduate students in applied mathematics, engineering and other applied sciences HTTP:URL=https://doi.org/10.1007/978-3-319-23042-9

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