A nice book for people who are taking Calculus IV(Differential Equations) is "Ordinary Differential Equations: An Elementary textbook for Students of Mathematics, Engineering, and the Sciences by Morris Tenenbaum and Harry Pollard." This is a Dover book, but it explains in a very straight forward manner, and also reviews some of the properties of a function and such. A very good book full of Definitions and Exercises. I'de recommend it for anyone taking Differential Equations. It is separted into 12 parts, and each part contains a given amount of Lessons. Parts- 1. Basic Concepts 2. Special Types of Differential Equations of the first order 3. Problems leading to Differential Equations of the first order 4. Linear Differential Equations of Order greater than one 5. Operators and Laplace Transforms 6. Problems leading to Linear Differential Equations of Order two 7. Systems of Differential Equations. Linearization of first order systems 8. Problems giving rise to systems of equations. Special types of second order linear and Non-Linear Equations solvable by reducing to systems 9. Series Methods 10. Numerical Methods 11. Existance and Uniqueness Theorem for the first order differential equation y'=f(x,y). Picard's Method. Envelopes. Clairaut Equations. 12. Existance and Uniqueness Theorems for a system of first order differential equations and for linear and non-linear differential equations of order greater than one. Wronskians. Definitions are contained in the book, so as you move on you learn alot of definitions. As well, there are a given amount of theorems with proof for each theorem in the lessons. I would list the lessons in each part, but due to it that there are 12 parts each with about 4 to 5 lessons, is alot of typing. There are examples all through out the book. There are also Excercises each with about 14 to 20 problems to solve and questions to answer. I do understand that the usual Characteristic of Dover books are complex and go right into the material of it. However this Dover book, out of all the Dover books I own is the most straight forward on the material. The book is about 2 inches thick so there is a lot of material. It's a little book in height, but is two inches thick. Anyways, as a Dover book it does dive into the material quickly however it is very straightforward. Since this book is on Differential Equations it assumes you have a background in Calculus. I'de recommend it for undergraduate students.