This book offers advanced undergraduates and graduate students in physics, engineering, and other natural sciences a solid foundation in several fields of mathematics. Clear and well-written, it assumes a previous knowledge of the theory of functions of real and complex variables, and is ideal for classroom use, self-study, or as a supplementary text.Starting with vector spaces and matrices, the text proceeds to orthogonal functions; the roots of polynomial equations; asymptotic expansions; ordinary differential equations; conformal mapping; and extremum problems. Each chapter goes straight to the heart of the matter, developing subjects just far enough so that students can easily make the appropriate applications. Exercises at the end of each chapter, along with solutions at the back of the book, afford further opportunities for reinforcement. Discussions of numerical methods are oriented toward computer use, and they bridge the gap between the "there exists" perspective of pure mathematicians and the "find it to three decimal places" mentality of engineers. Each chapter features a separate bibliography.