Mathematical Modelling

Abstract

Chapter 1 is a condensed overview of a raft of techniques which are used in applied mathematics in studying natural phenomena. The chapter focusses on phenomena which occur in continuous systems, modelled by differential equations. Non-dimensionalisation and scaling are treated. For ordinary differential equations, oscillations, hysteresis and resonance are discussed; for partial differential equations, topics covered are waves, nonlinear diffusion, blow-up and reaction–diffusion equations.