When I first started teaching Calculus many years ago, I checked the textbooks being used at a few colleges and found them too disorganized. I then examined about 50 calculus books, and finally selected one for the following year. I used this book for all three semesters of Calculus, for a total of five years, until I started using rough drafts of my own book for Calculus I. The original book is
indeed one of the best; yet, it has (for the purposes I have in teaching) a number of deficiencies. I wanted to copy the best and yet remedy the flaws in my own book.
One is the overall organization. It was quite good, and yet there are a number of tangential topics the author discusses which seem to detract from the main thrust of the book. For example, there are extensive discussions of applications to Economics in Chapters 4, 5, and 17, or quadric surfaces in three dimensions in a chapter on vectors. I have tried to remedy this in my own textbook, as well as add applications directly related to math and calculus.
Students also complained that the examples worked out in original text are usually quite simple, and do not give much insight into solving the more difficult problems assigned in the exercise sections. Some of the remedies I incorporate are: a number of theorems whose proofs are relegated to future
courses in advanced calculus. At least some of these proofs could be given in appendices. I also included a short table of integrals.
I also took into account the way the book will be used, so I created the book in a way that allows it to lay flat, retain its physical integrity, and keep to one edition so that students will not have to constantly buy a new textbook. While I recognize that the real world rarely has nice solutions, the goal of this textbook is understanding concepts via calculation. It is to my past (and future) students, who will be employed as servants of God's kingdom, that I dedicate this book.
God created all wisdom and knowledge as well as the physical things present
in the universe (Proverbs 8:22-31). Before the Fall, men could communicate
freely with God, and be in His presence. After the Fall, this was not possible.
Furthermore, God placed a curse on the ground (Gen. 3:17-19), symbolic of a
curse over all areas where man labors, including the mental ones. The entire
universe is fallen, and suffers from the corruption of sin (Rom. 8:22).
Never-the-less, there are certain things men can know which tell them that God
is the Creator, and the physical and mental things (even though
distorted and corrupt) do point to a glorious creator (Rom. 1:20), so as
to leave men without excuse. Therefore, all areas of endeavor (including
mathematics) show the glory of God in some manner, be it ever so distorted.