This book shows how mathematics is more than a series of calculations. Mathematical topics include distributions, ordinary and partial differential equations, asymptotic methods and the basics of modelling. Applications range from piano tuning to egg incubation and traffic flow. The text is supplemented by large numbers of exercises and sideline discussions, assisting the readers grasp of the material. Used either in the classroom by upper-undergraduate students, or as extra reading for any applied mathematician, this book illustrates how the readers knowledge can be used to describe the world around them.