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Methods of Mathematical Modelling

Methods of Mathematical Modelling

Wydawnictwo Springer Nature Customer Service Center GmbH
Data wydania 01/09/2015
Wydanie Pierwsze
Liczba stron 305
Forma publikacji książka w miękkiej oprawie
Poziom zaawansowania Dla profesjonalistów, specjalistów i badaczy naukowych
Język angielski
ISBN 9783319230412
Kategorie Rachunek różniczkowy i formuły, Rachunek wariacyjny, modelowanie matematyczne
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Opis książki

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. "The text is well written. The authors have provided a clear and concise presentation of many important topics in a way that should be accessible to students following a first course in differential equations. ... More advanced students could easily learn a significant amount of useful mathematics reading the text independently. ... Methods of Mathematical Modelling is a welcome addition to the SUMS series and should prove to be useful for many instructors and students." (Jason M. Graham, MAA Reviews, maa.org, February, 2016) "The purpose of this text is to introduce the reader to the art of mathematical modeling ... . The book provides an account of a number of useful for mathematical modelling techniques which are illustrated with examples and complemented with problems for self study." (Yuriy V. Rogovchenko, zbMATH 1333.00025, 2016)

Methods of Mathematical Modelling

Spis treści

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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