Methods of Mathematical Modelling

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

Autorentext

Thomas Witelski is a Professor of Mathematics at Duke University specializing in nonlinear partial differential equations and fluid dynamics. He is a long-time participant in many study groups on mathematical modelling and industrial problems. He is the co-Editor-in-Chief of the Journal of Engineering Mathematics and also serves on the editorial board for the European Journal of Applied Mathematics. Witelski received his Ph.D. in Applied Mathematics from the California Institute of Technology in 1995 and was a postdoctoral fellow at the Massachusetts Institute of Technology.

Mark Bowen is an Associate Professor in the International Center for Science and Engineering Programs at Waseda University, where he teaches courses in differential equations and nonlinear dynamics. His expertise is in asymptotic analysis, nonlinear differential equations and fluid dynamics. He received his Ph.D. in Applied Mathematics in 1998 from the University of Nottingham.

Inhalt
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.