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Titlebook: Methods of Mathematical Modelling; Continuous Systems a Thomas Witelski,Mark Bowen Textbook 2015 Springer Nature Switzerland AG 2015 Asympt

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書目名稱Methods of Mathematical Modelling
副標(biāo)題Continuous Systems a
編輯Thomas Witelski,Mark Bowen
視頻videohttp://file.papertrans.cn/633/632394/632394.mp4
概述Provides a self-contained and accessible introduction to mathematical modelling using ordinary and partial differential equations.Presents key approaches for formulating models and solution techniques
叢書名稱Springer Undergraduate Mathematics Series
圖書封面Titlebook: Methods of Mathematical Modelling; Continuous Systems a Thomas Witelski,Mark Bowen Textbook 2015 Springer Nature Switzerland AG 2015 Asympt
描述.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..
出版日期Textbook 2015
關(guān)鍵詞Asymptotic Analysis; Calculus of Variations; Mathematical Modelling; Multiple Scale Analysis; Nonlinear
版次1
doihttps://doi.org/10.1007/978-3-319-23042-9
isbn_softcover978-3-319-23041-2
isbn_ebook978-3-319-23042-9Series ISSN 1615-2085 Series E-ISSN 2197-4144
issn_series 1615-2085
copyrightSpringer Nature Switzerland AG 2015
The information of publication is updating

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Transport Equationss evolution can be described by a partial differential equation (PDE). In the context of properties depending on space and time, such PDEs are called transport equations, and they are generally written as first order evolution equations. We overview the formulation of transport equations and their r
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Variational Principlestimise some property of interest. The derivation of Euler–Lagrange equations from variational principles will be given in detail. Applications to problems in mechanics will be discussed. The elementary analytical framework will be extended to more advanced problems with free boundaries and constrain
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Fast/slow Dynamical Systems asymptotic expansions with phase plane analysis. The . limit yields a separation of time-scales that reduces the overall system to different forms for the fast and slow dynamics over different intervals of time. Asymptotic matching is used to connect the fast and slow solutions and can be interpret
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