Methods of Mathematical Modelling
Continuous Systems and Differential Equations
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Beschreibung
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.
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.
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 via asymptotic analysis Includes many challenging exercises and connections to classic models in applied mathematics including the Burgers equation, the Korteweg de Vries equation, Euler-Lagrange equations, pattern formation via Turing instabilities Demonstrates a variety of solution techniques including boundary layer theory, self-similar solutions, fast/slow dynamical systems, and multiple scale analysis Includes supplementary material: sn.pub/extras
Autor*in
Thomas Witelski
Themen in »Methods of Mathematical Modelling«
Asymptotic Analysis Calculus of Variations Mathematical Modelling Multiple Scale Analysis Nonlinear Oscillators Ordinary Differential Equations Partial Differential Equations Perturbation Methods
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“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)
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