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Mathematical Models in the Applied Sciences (Cambridge Texts in 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.
Contents:
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.
Brief Description:
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.
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