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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.