What I am doing here is making a rough draft of the Preface and then the Introduction to the textbook True Calculus.
For the first 7 editions of this book, I did not bother with a preface or introduction, but feel it needed here in the 8th edition. Once I get enough clarity and body to the preface and introduction I will stop with this rough draft.
This book True Calculus is actually two textbooks in one. The first textbook is for High School students which was usually called in the USA as PreCalculus. PreCalculus stopped short of the limit concept. The second textbook is for College and University students. And I find this two texts in one text very much advantageous in that it allows those who mastered the High School text of about 10 pages long to read more by reading some of the text for the College students. Likewise, for the College students who are unclear or forgotten prerequisites and go back to the High School text and catch up on what they missed or forgot.
The High School text of this two text book is about 10 pages long and I endeavored to make it as simple as possible for anyone interested to learn for themselves without a teacher, to learn Calculus. With a teacher, each page can be expanded by the teacher to make homework so that 1 page can last for a week in classroom. The same for the College text, which is about 90 or 100 pages long. So the primary text is this book, and the teacher can make up his or her own homework from the given page covered.
I believe in practical drills and pragmatism as the best means of learning. So that actually doing hands on math graphing and computing is the best way to learn math. We have to read, but then to drill and calculate with pencil and paper and graph paper is the best way to learn.
Now the book is fully titled as "TRUE CALCULUS; without the phony limit concept" and the reason for that is because every book on Calculus at present is a phony mathematics and I discuss this phoniness and fakery and liaring in the introduction and in parts of the textbook itself.
The world, at this moment does not have a True Calculus book available other than this textbook and the introduction tells us why.
A few hours ago in sci.physics, I wrote:
Rough draft of 8th ed True Calculus, preface and introduction #-1
This is a rough draft of the preface and introduction of the Textbook: 8th ed.: TRUE CALCULUS; without the phony limit concept
Preface and Introduction
I need a preface and introduction for the 8th edition of this book.
So let me try to frame a preface:
Mathematicians of Old Math never faced up to the responsibility of well defining finite versus infinite. They lacked the logic and intelligence to do so. The core of the problem is that one runs into the other. Finite becomes infinite with a borderline that separates them. Come up close to the borderline and on one side is finite, the other side resides infinite numbers and infinity.
In order to ever, or even discuss finite and infinity, one needs to intercede with the borderline.
Now in Old Math, it was not that they had no clues of where to look for this borderline because several theorems in old ancient mathematics gave clear clues of where to look for this borderline. The theorem that at infinity, the pseudosphere surface area equals exactly that of the associated sphere area. So that with a calculation of where the first time a pseudosphere surface area matches or has crossed over the area of the sphere of equal radius would be a borderline of finite with infinity. As it just happens, the first time that this occurs is Floor pi*10^603 where pi has its first three zero digits in a row. Another place to look for this borderline was the Euler formula for regular polyhedra where the digits of pi are evenly divisibly by 5 factorial which again is 10^603 Floor pi. Another place to look is the Riemann Hypothesis where the Euler encoding of addition of terms crosses over the Riemann encoding of multiplication of terms.
So Old Math ran on lies and liaring and never facing up to real true math of insisting on the border between finite versus infinite. And in that liaring, Calculus was caught in that liaring. Something had to be done to wiggle out from the liaring of a well defined infinity. And the liaring that was glummed upon or was given to Old Math as the excuse, the sweeping under the carpet of lies and liaring was the Limit concept.
The "limit concept" in modern mathematics is no more than Voo-doo mathematics, just as Voo doo and withcraft are fakery science compared to real science of medicine.
So as a real scientists checks for viruses of a disease, a Voo-doo or limit concept mathematician do dances around the problem and invoke all sorts of ghostly nonsense. Performing a limit is no better than performing a Voo Doo witch dance in Africa.
So the aim of this textbook for High School and for College and University is to set the student straight and clear and true calculus, not the nonsense of limit concept fakery.
And the prime means of doing that is the new concept of Cells in Coordinate Grid Systems.