Mathematical Models in Applied Sci: 17 (Cambridge Texts in Applied Mathematics, Series Number 17)
Cambridge University Press, 8/21/2008
EAN 9780521467032, ISBN10: 0521467039
Paperback, 424 pages, 24.6 x 18.9 x 2.4 cm
Language: English
Originally published in English
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.