This book outlines the philosophy and techniques needed for the application of mathematics to industrial and scientific problems. Taking a practice-oriented approach, the author includes twenty-one problems, all of which illustrate the power of differential equations in industrial applications. The problems presented touch upon a wide range of situations, including smoke dispersion from a high chimney, the hot rolling of steel, resonance in a gear box, submarine detection, and the shape of laser meltpools. Tayler pays particular attention to the formulation of these problems and has carefully ordered them to illustrate the coherent development of partial differential equations.