Mathematical Modelling with Case Studies

A Differential Equation Approach Using Maple

Glenn R. Fulford, Belinda Barnes

428 pages, parution le 14/10/2002

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Résumé

This book aims to provide students with the essential skills required to apply mathematical models to a wide variety of problems. The focus is on mathematical techniques that are relevant to models involving differential equations.
Models in the following three particular areas are considered and a range of applications are presented, and complemented with case studies, to emphasise the diversity of application and relevance that these differential equation models can offer.

Growth and decay processes are illustrated through drug assimilation, the spread of pollution and the detection of art forgeries.
Interacting populations, such as in predator-prey and competing species systems are considered.
Heating/cooling processes are applied to, for example, home insulation and the detection of land mines.

The main mathematical techniques presented are those of model building and the solution to these differential equation systems. Numerical analysis is encouraged and Maple code for .the graphs and analysis is integrated into the text.
The book can be used as a course text, or as a reference for those in disciplines other than mathematics who require expertise in this area. It requires a basic knowledge of calculus and fundamental computing skills.
Contents

Introduction to mathematical modeling
I. Introduction to Compartmental Models
Compartmental Models
II. Models of Single Populations
Numerical solutions of differential equations
Formulating interacting population models
Phase-plane analysis
Linearisation Analysis
Some improved population models
III. Models of Heating and Cooling
Formulating basic heat models
Solving time dependent heat problems
Solving heat conduction problems
IV. Models with Partial Differential Equations
Introduction to partial differential equations
IV. Appendices
A. Differential Equations
B. Further mathematics
C. Notes on Maple
D. SI Unit

Caractéristiques techniques

	PAPIER
Éditeur(s)	Taylor and Francis Books
Auteur(s)	Glenn R. Fulford, Belinda Barnes
Parution	14/10/2002
Nb. de pages	428
Format	17,5 x 24,5
Couverture	Broché
Poids	780g
Intérieur	Noir et Blanc
EAN13	9780415298049
ISBN13	978-0-415-29804-9