This updated edition of its popular predecessor strikes a balance between the mathematical aspects of the subject and its origin in empirics. Applied Mathematics offers, at an elementary level, some of the current topics in applied mathematics such as singular perturbation, nonlinear waves, bifurcation, and the numerical solution of partial differential equations. New material includes a discussion on discrete models, more references to mathematical biology in the text and exercises, and a new chapter on stochastic models including sections on probability, stochastic processes, and stochastic differential equations and difference equations.