Methods of Mathematical Modelling: Continuous Systems and Differential Equations

by Thomas Witelski, Mark Bowen

Overview

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.

Product Details

ISBN-13:	9783319230412
Publisher:	Springer International Publishing
Publication date:	09/18/2015
Series:	Springer Undergraduate Mathematics Series
Edition description:	1st ed. 2015
Pages:	305
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

About the Author

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.

Table of 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.

Editorial Reviews

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)

From the Publisher