This book evolved from a one-year sequence of courses offered by the authors at Iowa State University. The audience for this book typically included theoreti­ cally oriented first- or second-year graduate students in various engineering or science disciplines. Subsequently, while serving as Chair of the Department of Electrical Engineering, and later, as Dean of the College of Engineering at the University of Notre Dame, the first author continued using this book in courses aimed primarily at graduate students in control systems. Since administrative demands precluded the possibility of regularly scheduled classes, the Socratic method was used in guiding students in self study. This method of course deliv­ ery turned out to be very effective and satisfying to student and teacher alike. Feedback from colleagues and students suggests that this book has been used in a similar manner elsewhere. The original objectives in writing this book were to provide the reader with appropriate mathematical background for graduate study in engineering or science; to provide the reader with appropriate prerequisites for more advanced subjects in mathematics; to allow the student in engineering or science to become famil­ iar with a great deal of pertinent mathematics in a rapid and efficient manner without sacrificing rigor; to give the reader a unified overview of applicable mathematics, thus enabling him or her to choose additional courses in mathematics more intelligently; and to make it possible for the student to understand