Mathematical Models in the Applied Sciences [Paperback]

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.In mathematical modelling 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 and proceeds to explore a range of classical and continuum models.In mathematical modelling 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 and proceeds to explore a range of classical and continuum models.This book presents a thorough grounding in the techniques of modeling, and proceeds to explore a range of 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. This is a beautiful book...provides an excellent source of insights, techniques, examples, models, open questions and literature for anyone interested in advanced (physicalló²