Chapters 1-7 are targeted to undergraduates, while Chapters 8-12 are more focused on graduate level presentation. Chapters 1-7 provide an elementary approach so students can apply their mathematical knowledge and Chapters 8-12 strengthen students' analysis skills. Topics chosen are of fundamental importance, accessible, and related to current research. Provides accessible and rigorous treatment of most important subjects that leads to current research. A review of the subjects covered in an Elementary Differential Equations course Appears in Chapter 1. Describes for students some qualitative properties of differential equations that will be covered in the rest of the book. End-of-section exercises. Gives students ample opportunity to practice the material just learned.

Open-ended exercises. Provides direction toward graduation theses and research in qualitative theory of differential equations.