This is the finest textbook ever written on Calculus. It is actually two textbooks in one printed textbook for the first 10 pages are for High School students and the remaining 100 or so pages are for the College and University student:
HS-Textbook 8th ed. : TRUE CALCULUS; without the phony limit concept
Uni-textbook 8th ed.: TRUE CALCULUS; without the phony limit concept
The first ten pages of this textbook is devoted to High School (HS) students learning Calculus for the first time. The first ten pages is so well written that it requires no teacher, simply the interest and desire of a student to learn true Calculus, not the fake and phony calculus with its limit concept.
The High School text of this two text all-in-one-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 a classroom. The same for the College text, which is about 100 pages long. So the primary text is this book, and the teacher can make up his or her own homework from the given pages 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 of 2013, 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.
Mathematicians of Old Math, Old Math is math before 2011, 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 finite runs into the infinite. Finite becomes infinite with a borderline that separates them. Without a borderline between the two, they are one and the same, for unless you can distinguish what is a finite number from what is a infinite number, the concept of infinity is meaningless. 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.
Old Math is any math before 2011, where no-one well defined what is finite and what is infinite and Calculus suffered immensely in Old Math.
Now in Old Math, it was not that they had no clues of where to look for this borderline because several theorems in old mathematics gave clear clues of where to look for this borderline.
(A) 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 turns out, the first time that this occurs is Floor pi*10^603 where pi has its first three zero digits in a row.
(B) Another place to look for this borderline was the Euler formula for regular polyhedra where the digits of pi are evenly divisible by 5 factorial (2*3*4*5 = 120) which again is 10^603 Floor pi.
(C) Another place to look is the Riemann Hypothesis where the Riemann zeta encoding of addition of terms crosses over the Euler zeta encoding of multiplication of terms, for the first time.
So Old Math with its ignorance and muddleheadedness of never facing up to its real responsibilities of well-defining all of its terms of math, by insisting on the border between finite versus infinite, by insisting on where is the borderline is nothing more than fakery math. And in that ignorance and laziness and stupidity, Calculus was caught up in that quagmire of having to explain how Calculus works. How can you explain how Calculus works if you cannot well-define what finite is and what infinite is? Something had to be done to wiggle out from the obfuscation of what infinity is. And the avenue of escape, shameful escape, was to dream up a totally irrelevant technique called the "limit concept".
Does it matter if we bang on drums and carry wishbones around for rainfall to come? No, for it is irrelevant that we bang on drums and carry wishbones. Weather is not related to drum beating and wishbones.
The "limit concept" in modern mathematics is no more than Voo-doo mathematics, just as Voo-doo and withcraft are irrelevant to real science of medicine.
So as a real scientists checks for viruses of a disease, or genetics of a disease, a Voo-doo dance or limit concept exercise are irrelevant acts in doing medicine or doing the Calculus.
So the aim of this textbook for High School and for College and University is to set the student straight and clear on true calculus, not the nonsense of limit concept fakery.
And the prime means of doing that as the reader will quickly learn on page 1 of this 8th edition, (page 6 of the 7th edition) is the new concept of Cells in Coordinate Grid Systems.
The prime essential of Calculus is two features: (i) a fixed and rigid Euclidean geometry Coordinate System with its straightline segments connecting the points of all functions, and, (ii) Cells, with the angles made by connecting the points of the function
Calculus exists because of (i) and (ii) and the limit concept was a total silly and stupid concoction that diverted attention of what Calculus is.
Calculus is really easy, if you are shown the true Calculus, not a bunch of entangled irrelevancies. So easy, that I would hazard to guess that the High School student who is really interested, will learn the Green, Stokes, Divergence theorems and even the Maxwell Equations of the last pages of the College text, because of the simplicity that the Cell concept renders all of Calculus.
In Old Math, because the entire subject of Calculus was based on a irrelevancy that none of Calculus was ever seen in the "mind's eye" of anyone. When I say "mind's eye" I mean someone knows a subject so well that they have no reservations of any aspect of the subject. When someone learns something is still troubled all over the place, is because they never truly learned the subject for it is masked in fakery like the Calculus with limit concept, or it is not made comprehensible by the author. Under the cell concept we even see Green, Stokes, Divergence theorems in the mind's eye.