For courses in differential equations. This book provides a concrete and readable text for the traditional course in elementary differential equations that science, engineering, and mathematics students take following calculus. This is a strongly algebraic-oriented text with some computer enhancements for numerical methods. Matters of definition, classification, and logical structure deserve (and receive here) careful attention for the first time in the mathematical experience of many of the students. While it is neither feasible nor desirable to include proofs of the fundamental existence and uniqueness theorems along the way in an elementary course, students need to see precise and clear-cut statements of these theorems and understand their role in the subject. Appropriate existence and uniqueness proofs in the Appendix are included and referenced where appropriate in the main body of the text.