This textbook, covering the basic mathematics taught to first-year students of science and engineering, reflects the growing awareness that ancillary mathematics should not be taught in isolation from its applications. Topics covered include calculus, ordinary and partial differential equations and statistics. Each chapter starts with two or three examples setting the new techniques to be studied in the context of the scientific world; the mathematics is then presented, along with worked examples. Numerical methods are integrated with analytical techniques where appropriate. The resulting textbook provides the teacher with a rich and varied source of applications for classroom use and students with a textbook for self-learning, giving insight into the significance and role of mathematics in science and engineering.