Methods of Mathematical Modelling Continuous Systems and Differential Equations - Witelski, Thomas; Bowen, Mark.; SpringerLink (Online service) (Cham : Springer International Publishing : Imprint: Springer, 2015)
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.
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.
Keywords: Differential equations; Partial differential equations; Mathematical physics; Mathematical models; Calculus of variations; Ordinary Differential Equations; Partial Differential Equations; Mathematical Applications in the Physical Sciences; Mathematical Modeling and Industrial Mathematics; Calculus of Variations and Optimal Control; Optimization