This book is an excellent introduction to the mathematics needed by economists. It covers all the background needed to begin in a typical economics Ph.D. program, and presents it understandably. I found that it is rigorous enough that I can apply what I have learned from it confidently. It uses total differentials where more advanced books might use vector calculus. This is a more intuitive approach, and better suited for an introduction. It includes some very good illustrations which clarify the concepts.