Elementary Differential Equations integrates the underlying theory, the solution procedures, and the numerical/computational aspects of differential equations in a seamless way. For example, whenever a new type of problem is introduced (such as first-order equations, higher-order equations, systems of differential equations, etc.) the text begins with the basic existence-uniqueness theory. This provides the student the necessary framework to understand and solve differential equations. Theory is presented as simply as possible with an emphasis on how to use it. The Table of Contents is comprehensive and allows flexibility for instructors.
This is by far my favorite and most referred to text. I got through a good chunk of it but moved on to completing other math texts as it became a little overwhelming to complete it for now. Now I'm going through other differential equation texts as well (finizio/ladas mainly and others). This book covers topics for the most part very clearly but it has sections devoted to problem questions referred to in other texts which is why I keep going back to it for reference over Zill's or Tenenbaums text). This text has a permanent place on my math book shelf at home. I'll get through it eventually but I'm keeping it next to me because I know If I get stumped, there is something in this text to help me. -I wrote this review after referring to this text while reading other texts, several times. The ladas text had a problem about collisions that I had been trying to solve for about a week. After looking for similar problems everywhere else, sure enough, I looked through this and found under First Order Non-linear Differentials a section on One Dimensional Dynamics with distance as the Independent variable which is exactly what I needed explained to me.