Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
Drexel University or The Math Forum.



Improvements of the Fourier theory #71 MathProfessortext 8th ed.: TRUE CALCULUS
Posted:
Nov 18, 2013 2:26 PM


Improvements of the Fourier theory #71 MathProfessortext 8th ed.: TRUE CALCULUS
This subtext is to teach college and university professors of mathematics what the real and true Fourier theory is all about.
Now many people reading my posts realize I scold math professors a lot. And the reason I do that is because they want to ignore their mistakes and ignore a person like me who wants to improve their math and make their math correct. So when you are a college or university professor of mathematics and teaching contradictory garbage like a dy/dx derivative where the limit makes dx go to 0 and division by 0; or when you teach that the integral is the summation of thin rectangles, for which the limit has forced out all the interior area of those rectangles so that the width of integral summations are 0 width, again, you as a college or university math professor is teaching contradictory garbage in your classroom.
When you teach a limit concept that is wholly irrelevant in finding the derivative or integral, then you are wasting the time and time of the life of students.
When you teach math that there is a infinity just beyond finite, yet you never in all your math career ever have the wit to find a **border between finite and where infinity starts** then you failed at logic and math and you failed in every piece of math that involves finite versus infinity.
So math professors have a lot of strikes against them. But I am willing to write this 10 page subtext of True Calculus just for the audience of college and university Math Professors. Even though they are short of wit of logic as per finite versus infinite and who have been "dolts of mathematics" in accepting dy/dx where dx =0 and accepting rectangles without interior area since the limit took away all the interior area.
You see, math professors would rather keep teaching garbage than correct their mistakes and teach the real true math, because they are embarrassed or simply the change is too much for them.
But I will not ignore the math professors and keep on scolding them until they do change for the better.
So I write this Fourier Improvement text. It is meant not for graduate students in college but meant for college math professors.
If you ignore me, I scold you, but if you jump in and participate, I praise you for your wit. That is my motto for writing this Fourier text. College professors of math can improve the Fourier theory, if they jump in and participate, but if they hide away and ignore these posts, well, that leaves me only to scold the entire community of college math professors.
Now this is only going to be 10 pages long and makes the 5th subtext of the whole text called True Calculus.
First off, I need to throw out the miserable terminology given to the Fourier theory. Such miserable and vague terms as that of Fourier series, Fourier analysis, Fourier transform, Fourier synthesis. Making up terms in science is not science itself but a clutter mess to hide the fact that you do not know much about the subject itself. So we dispense with this terminology nonsense and call it just simply Fourier theory.
Now the only reason I can write this subtext is because of the Cell theory which is far more general and universal over the Fourier theory. The Fourier theory is a subset of the Cell theory.
Now what gives rise to the Cell theory is the resolution of the border between finite and infinite. In the 10 Grid system where we pretend that 10 is the last and largest finite number and any number beyond is an infinite number causes a chain reaction in that the smallest nonzero finite number becomes 0.1. This number, 0.1 in 10 Grid is microinfinity whereas 10 is macroinfinity. What that does is tell us that the only numbers of mathematics in 10 Grid are those numbers of 0, .1, .2, .3 on up to 9.9 then finally 10. And any other number is an infinity number for which mathematics has no role for infinity numbers other than recognize that they take up Space between finite numbers.
Mathematics is only about Finite numbers because only finite numbers can be made precise and that is the definition of mathematics is equal to precision. Mathematics breaksdown when it involves itself into infinity numbers.
Now the true border of finite versus infinity is easily found, and in 2011 using the pseudosphere with associated sphere areas it is seen that the areas become exactly equal at Floorpi*10^603. That number is huge and well beyond most every Physics numbers, except for perhaps magnetic monopoles. So the difference between a 10 Grid and a 10^603 Grid is a huge difference. In fact, our TV and computer screens work on just a simple 100 or 1000 Grid system where a circle looks like a perfect circle when it appears on our computer in the 100 Grid system.
So, the Fourier theory was discovered in the early 1800s and it had a large flaw, in that it went to infinity yet noone bothered to fetch an infinity borderline. (An interesting side note is that Fourier is noted for the discovery of the Greenhouse gas effect that warms Earth.)
So what happens with the Fourier theory when you apply a finite to infinity border?
Well, a lot happens, and a lot changes.
What happens is that you can provide a Fourier Coordinate System that overlaps the Cartesian Coordinate System. In the Fourier Coordinate system every finite point is a sine and cosine component.
Now take a look at this website page
http://jwilson.coe.uga.edu/EMT668/EMAT6680.Folders/Dickerson/assignments/assignment%201/COSINE/COSINE~1.HTM y = cos x jwilson.coe.uga.edu/EMT668/.../Dickerson/.../COSINE/COSINE~1.HTM
Laura Dickerson. To examine the graph of y = cos x, I will examine y = A cos (Bx +C) for different values of A, B, and C. ... Let's us first look at the graph y = cos x.
Now, take a look at the bottom of that web page where Laura graphs y = cos (1/3 x).
Can you see a trend there between cos x , cos 1/2 x and then cos 1/3x. That the graph becomes more and more flat almost approaching a line, a straightline.
So, the question is in 10 Grid all in the 1st Quadrant only, what is the function y = cos (.1x)? Is it a straight line or where does it become a straightline so that x=0, y=1 and x=10, y=1? Do I need to have y = cos 0.01x in order to achieve a straightline in 10 Grid by using cosine function?
When you have a border between finite and infinite which causes a Grid System of finite points separated by holes and gaps of microinfinity, causes a major change in the Fourier theory, so that the Fourier theory becomes an alternative Coordinate System to the Cartesian Coordinate System.
 Drexel's Math Forum has done an excellent search engine for author posts as seen here: http://mathforum.org/kb/profile.jspa?userID=499986
Now, the only decent search for AP posts on Google Newsgroups, is a search for plutonium.archimedes@gmail.com 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 hatespam posts due to searchenginebombing 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



