
Mathematical Modelling with Case Studies
A Differential Equation Approach Using Maple
Glenn R. Fulford, Belinda Barnes
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 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 |
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