Başlık:
Methods of Mathematical Modelling Continuous Systems and Differential Equations
Yazar:
Witelski, Thomas. author.
ISBN:
9783319230429
Ek Yazar:
Edition:
1st ed. 2015.
Fiziksel Tanım:
XVIII, 305 p. 50 illus., 45 illus. in color. online resource.
Series:
Springer Undergraduate Mathematics Series,
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.
Abstract:
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.
Konu Terimleri:
Added Author:
Added Corporate Author:
Electronic Access:
http://dx.doi.org/10.1007/978-3-319-23042-9