This book is written for beginning graduate students in applied mathematics, science, and engineering, and is appropriate as a one-year course in applied mathematical techniques (although I have never been able to cover all of this material in one year). We assume that the students have studied at an introductory undergraduate level material on linear algebra, ordinary and partial differential equations, and complex variables. The emphasis of the book is a working, systematic understanding of classical techniques in a modern context. Along the way, students are exposed to models from a variety of disciplines. It is hoped that this course will prepare students for further study of modern techniques and in-depth modeling in their own specific discipline.