After many years of teaching graduate courses in applied mathematics, Youssef N. Raffoul saw a need among his students for a book reviewing topics from undergraduate courses to help them recall what they had learned, while his students urged him to publish a brief and approachable book on the topic. Thus, the author used his lecture notes from his graduate course in applied mathematical methods, which comprises three chapters on linear algebra, calculus of variations, and integral equations, to serve as the foundation for this work. These notes have undergone continuous revision. Applied Mathematics for Scientists and Engineers is designed to be used as a graduate textbook for one semester. The five chapters in the book can be used by the instructor to create a one-semester, three-chapter course. The only prerequisites for this self-contained book are a basic understanding of calculus and differential equations. In order to make the book accessible to a broad audience, the author endeavored to strike a balance between rigor and presentation of the most challenging content in a simple format by adopting friendlier, more approachable notations and using numerous examples to clarify complex themes. The hope is both instructors and students will find, in this single volume, a refresher on topics necessary to further their courses and study.