On Monday, November 18, 2013 1:43:09 PM UTC-6, wrote:
Improvements of the Fourier theory #71 Math-Professor-text 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 Floor-pi*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 no-one 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/EM...E/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.





Now I did this only by eyeball so it must be checked and where I typed into a Google search of cos(.0001x) and up appears a graph where the cosine intersects the x-axis at about 20,000. But that is not our concern. Our concern is where does the cosine form a straightline that is equal to y = 1 in the 10 Grid? Which means the tip of the top of those crests form a straight enough line to be from 0 to 10.

Now at cos(.01x) I am not sure that the cosine forms that straight line so that we have x=0, y=1 and x=10, y =1 in 10 Grid. In 10 Grid, remember we truncate for the only numbers that exist are increments of 0.1.

So the question is, in 10 Grid what is the cosine Fourier equation for the line y = 1? And the answer appears to be that of y = cos(0.001x).

Now I must pause here, because it is likely possible to have a different sine and cosine combination to deliver a y = 1 function, a better one than the above of y = cos(0.001x).

So one may begin to see the entire game plan here. That I want to convert every function of the Cartesian Coordinate System into a equation of only sine and cosine.

What is the function y = x in Fourier theory?

Now most professors of math are very skeptical of any changes in what they learned or memorized learned of mathematics. So right away they raise red flags instead of a desire to "learn and learn something new and better." So right away they will complain why bother with converting functions to that of sine and cosine strings? And the answer is simple and easy. Because once a function is made into a pure sine and cosine string, its general formula for derivative and integral are immediately obtained. And why is that true? Because every function is built from numerous cells and the derivative and integral inside each cell is dependent on the sine and cosine of the right triangle in that cell. So if we know a function by pure sine and cosine string, then we know its general formula for derivative and integral. We no longer have to make up "tricks of the trade" to find the derivative and integral, we just simply write the function and it reveals its derivative and integral because it was a part of the function.

AP