Mathematical Models in the Applied Sciences

Presents a thorough grounding in the techniques of mathematical modelling, and proceeds to explore a range of classical and continuum models from an array of disciplines.

A. C. Fowler (Author)

9780521467032, Cambridge University Press

Paperback, published 28 November 1997

424 pages, 106 b/w illus. 1 colour illus. 121 exercises
24.6 x 17.3 x 2.4 cm, 0.7 kg

'Fowler's book is an outstanding contribution to the graduate textbook literature. Reading portions of Fowler's book will give a student a good idea about what applied mathematics really is …' Society for Industrial and Applied mathematics

Mathematical modelling is the basis of almost all applied mathematics. A 'real-world' problem is dissected and phrased in a mathematical setting, allowing it to be simplified and ultimately solved. This book presents a thorough grounding in the techniques of modelling, and proceeds to explore a range of classical and continuum models from an impressive array of disciplines, including: biology, chemical engineering, fluid and solid mechanics, geophysics, medicine, and physics. It assumes only a basic mathematical grounding in calculus and analysis and will provide a wealth of examples for students of mathematics, engineering, and the range of applied sciences.

Part I. Introduction: 1. Mathematical modelling
Part II. Methods: 2. Non-dimensionalisation
3. Asymptotics
4. Perturbation methods
Part III. Classical Models: 5. Heat transfer
6. Viscous flow
7. Solid mechanics
8. Electromagnetism
Part IV. Continuum Models: 9. Enzyme kinetics
10. The Belousov-Zhabotinskii reaction
11. Spruce budworm infestations
12. Chemical reactors
13. Groundwater flow
14. Convection in a porous medium
15. River flow
16. One-dimensional two-phase flow
Part V. Advanced Models: 17. Alloy solidification
18. Ice sheet dynamics
19. Chemosensory respiratory control
20. Frost heave in freezing soils
References.

Subject Areas: Mathematical modelling [PBWH]