Well, I tried to fetch a new technique of Calculus from the Cell theory of its Complimentarity function. In True Calculus, the integral and derivative is always bounded by the border of finite with infinity, so that the coordinate system has an upper bound and so the integral such as in 10-Grid can be no larger than 100 = 10x10 in first quadrant. That gave rise to a complimentarity function, a function that Old Math could never have.

I believe the Chain rule with its composite functions is the apex of the Uni text. I was hoping to find a new technique that would be the apex. Maybe I will find it in the future, if there is such a new technique. What am I looking for? I am looking for a improvement in finding the formula of the derivative and integral without relying so much upon the Power formula. The Cell theory gives me the derivative and integral in any specific cell of a function, but the cell theory does not give me the overall general formula of the derivative and integral that the Power formula provides. So that is what I am looking for in a new technique.

However, the Cell theory does give me a new technique for the Surface Integral which will be immense help in the Green, Stokes and other advanced calculus. The Cell theory provided that new technique in previous editions and is very much brand new to all of Old Calculus. For only in the Cell theory can you offer a residence for two functions simultaneously, such as y = 1/x and y =1 can you plot both functions
and have two functions inside each individual cell that which we can subtract one from the other and capture a surface area. But this is to be discussed in advanced calculus.

Here I want to finish the Uni-text and I finish it with the Chain rule and then the big discovery of the 8th edition, that all the proofs in Old Calculus were invalid since all those proofs had to use the derivative as defined by dy/dx and where the limit concept was used, for which the dx could be and was forced to be equal to 0. When you have a Calculus based on dy/dx and a limit concept, the integral becomes thin rectangles of 0 interior area and the derivative becomes dy/dx so that you end up with dy/0.

Now it is truly amazing that ever since *1821 when Cauchy and Weierstrass invented the limit concept, that all mathematicians were not smart enough to say-- "I am not going to buy into and believe a concept that makes the summing up of rectangles of zero interior area, and that makes the derivative become dy/0." You would be surprised how the education grading system that gives students a A grade if they use the limit concept with its phony rectangles of 0 interior area and its derivative of dy/dx becomes dy/0. Once you reward a student with a A grade by teaching them (propagandizing them) to the limit, that they seem to never henceforth question their having been propagandized of the real truth about Calculus. Which goes to show that most people, even in math and science are run by, and propelled by sentiment, and not by what they should be run by -- logic.

So what I am going to do here is close out the Uni-text and thus it would be only about 30 pages long, making this entire text book half as long as promised, of that of 60 pages and not of 120 pages. I prefer a 60 pages text rather than a 120 page text. And keep in mind that the text spans High School through to Graduate College.

Now before leaving the Chain Rule, I need to discuss its major importance because as I wrote earlier, physics has no need of exponents in power formula of greater than 4. Physics rarely, if ever runs into x^5 or higher.

So, why all this fuss over the Chain Rule for math and physics? And the answer is quite clear and easy, for it is because of the trigonometry functions. As Stewart shows in his textbook Calculus, 5th ed, 2003, page 220 where he differentiates the functions y = sin(x^2) and y = (sin(x))^2. The trigonometry functions are a breeze to differentiate with the aid of the Chain Rule. So, maybe, just maybe, I had embarked upon the wrong class-of-functions to try to find a new technique using complimentarity. Perhaps if I used the trig functions that this new technique becomes apparent.

So, what I am going to do is close out the Uni text and then begin the Advanced Calculus text with its new technique of surface integral using Cell theory.


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Drexel's Math Forum has done an excellent search engine for author posts as seen he
http://mathforum.org/kb/profile.jspa?userID=499986

Now, the only decent search for AP posts on Google Newsgroups, is a search for for it brings up posts that are mostly authored by me and it brings up only about 250 posts. Whereas Drexel brings up nearly 8,000 AP posts. Old Google under Advanced Search
for author, could bring up 20,000 of my authored posts but Google is deteriorating in quality of its searches, likely because AP likes an author search and Google does not want to appear as satisfying to anything that AP likes. If AP likes something, Google is quick to change or alter it.

So the only search engine today doing author searches is Drexel. Spacebanter is starting to do author archive lists. But Google is going in the opposite direction of making author archived posts almost impossible to retrieve.

All the other types of Google searches of AP are just top heavy in hate-spam posts due to search-engine-bombing practices by thousands of hatemongers who have nothing constructive to do in their lives but attack other people.

Now one person claims that Google's deteriorating quality in searches of science newsgroups is all due to "indexing". Well, that is a silly excuse in my opinion, because there is no indexing involved when one simply asks for a author search. No indexing involved if one wants only the pure raw complete list of all posts by a single author. And Google is called the best search engine of our times, yet I have to go to Drexel to see 8,000 of my posts of which I had posted 22,000 to 36,000 posts from 1993 to 2013. It is a shame that Drexel can display 8,000 while Google has a difficult time of displaying 250 of my authored posts. Where the premiere search engine of Google is outclassed by Drexel and even by Spacebanter.

Archimedes Plutonium