This book presents mathematical modelling and the integrated process of formulating sets of
equations to describe real-world problems. It describes methods for obtaining solutions of
challenging differential equations stemming from problems in areas such as chemical reactions
population dynamics mechanical systems and fluid mechanics. Chapters 1 to 4 cover essential
topics in ordinary differential equations transport equations and the calculus of variations
that are important for formulating models. Chapters 5 to 11 then develop more advanced
techniques including similarity solutions matched asymptotic expansions multiple scale
analysis long-wave models and fast slow dynamical systems. Methods of Mathematical Modelling
will be useful for advanced undergraduate or beginning graduate students in applied mathematics
engineering and other applied sciences.
