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Methods of Mathematical Modelling: Continuous Systems and Differential Equations

Methods of Mathematical Modelling: Continuous Systems and Differential Equations

Authors
Publisher Springer, Berlin
Year
Pages 305
Version paperback
Language English
ISBN 9783319230412
Categories Differential calculus & equations
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291.90 PLN / €62.58 / £54.33
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Book description

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.

Methods of Mathematical Modelling: Continuous Systems and Differential Equations

Table of contents

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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