I just got a copy of the Simon and Blume math for economists book and I'm disappointed. I looked up "continuously differentiable". The book defines it fine. But what I was looking for was an explanation for what possible use the definition might have. Any math book should say *why* a definition is introduced, not just what it is. That's important for motivation, and also for explanation. Otherwise, the definition is just an arbitrary set of conditions. I can define things too, any way I want. And when you see a zillion definitions in a math book, how are you to know which ones matter and which ones are hardly ever used?