Methods of Mathematical Modelling : Continuous Systems and Differential Equations (1st ed. 2015.)

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Methods of Mathematical Modelling : Continuous Systems and Differential Equations (1st ed. 2015.)

フォーマット:
電子ブック
責任表示:
by Thomas Witelski, Mark Bowen
本文言語:
英語
出版情報:
Cham, Germany. 2015-. Springer International Publishing,Imprint: Springer
シリーズ:
Springer Undergraduate Mathematics Series
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. 続きを見る
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.
Rate equations
Transport equations
Variational principles
Dimensional scaling analysis
Self-similar scaling solutions of differential equations
Perturbation methods
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