Our point of view, which in on way diminishes the utility of the course's content, is that the differential equations course has two overarching functions: [1] It is where students are introduced to the central subject in all of applied mathematics, a subject whose questions have spawned most of the classecal theory of analysis since the time of Newton and continue to create a rich field of mathematical activity today. [2] It is a place to reinforce and extend the student's [perhaps tenuous] understanding of calculus. It is the next step after calculus on the path that leads to real analysis. Whether the student will follow that path any farther makes little difference.

    Throughout this book, we attempt to emphasize that the primary goal when studying a differential equation is always to understand the behavior of its solutions. Writing down formulas for solution is just one means to that end. Qualitative and numerical methods are equally, if not more, important. Moreover, all of these ''tools'' are manifestations of theory, and we endeavor to emphasize that fact at a level which is appropiate for the course.

1. Introduction
2. Linear First-Order Equations
3. Nonlinear First-Order Equations 1
4. Nonlinear First-Order Equations 2
5. Second-Order Linear Equations 1
6. Second-Order Linear Equations 2
7. The Laplace Transform
8. First-Order Linear Systems
9. Geometry Of Autonomous Systems In The Plane
10. Nonlinear Systems In Applications
etc.