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Methods of Mathematical Modelling : Continuous Systems and Differential Equations

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概要 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.
目次 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.
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本文を見る Full text available from SpringerLINK ebooks - Mathematics and Statistics (2015)

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登録日 2016.01.13
更新日 2017.11.26