Paper:

 

 

 

Author [Jordan Micah Bennett] (myself):

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...

 

I am new here.

Please express your thoughts.

Edited February 27, 20178 yr by Phi for All
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Please express your thoughts.

 

 

In what language is "a soft warping of an amply modicum variation of Newton's calculus" a meaningful statement?

 

 

In what language is "a soft warping of an amply modicum variation of Newton's calculus" a meaningful statement?

 

Language: English

The sample is an example of a standard method of integration involving square roots. What is the point?

Language: English

I looked at your paper, your website, your Facebook, and your resume. You are a very interesting guy. I love your art. You are using everyday language in unusual ways, making it hard to understand your train of thought. It's interesting to say the least but there does not seem to be any intention to connect with your readers.

 

Can you express your idea in everyday language?

I looked at your paper, your website, your Facebook, and your resume. You are a very interesting guy. I love your art. You are using everyday language in unusual ways, making it hard to understand your train of thought. It's interesting to say the least but there does not seem to be any intention to connect with your readers.

 

Can you express your idea in everyday language?

 

I posted particularly to establish a connection.

Anyway, looking at the image above, specifically the parts in red titled 'Sample' and 'Collapse' , what are your thoughts?

 

 

@Mathematic:

The sample is standard, of course.

The 'collapse' portion is non-standard.

 

The "sample" is there to show the difference between the default way of doing things and my way, as seen in the "collapse" portion.

 

Please comment on the non-standard portion.

Edited February 27, 20178 yr by ProgrammingGodJordan

Anyway, looking at the image above, specifically the parts in red titled 'Sample' and 'Collapse' , what are your thoughts?

My thoughts? Sadly although I can talk about the abstract theory of integration, specific integrals make my eyes glaze over. I couldn't do those problems even when I TA'd that class! I have no opinion about anything involving techniques of integration. Pretty much everyone on this site knows that material better than I do.

 

When mathematic says ...

 

The sample is an example of a standard method of integration involving square roots. What is the point?

... I am in no position to disagree. Sounds about right.

 

(Edit) That said, perhaps I'm being overly modest. I recognize the math you did. It seems like a standard exercise in basic integral calculus. Can you say what it is you find significant about it?

Edited February 27, 20178 yr by wtf

My thoughts? Sadly although I can talk about the abstract theory of integration, specific integrals make my eyes glaze over. I couldn't do those problems even when I TA'd that class! I have no opinion about anything involving techniques of integration. Pretty much everyone on this site knows that material better than I do.When mathematic says ... ... I am in no position to disagree. Sounds about right.(Edit) That said, perhaps I'm being overly modest. I recognize the math you did. It seems like a standard exercise in basic integral calculus. Can you say what it is you find significant about it?

Of course, the sample part is a standard example.

 

The 'collapse' bit in contrast, is my invention/input.

No, the part labeled "collapse" is precisely what would be done in any Calculus text.

No, the part labeled "collapse" is precisely what would be done in any Calculus text.

 

This is the first time hearing such data.

 

I had searched for 4 years, without finding the collapse regime.

 

Could you direct us to where the collapse bit exists, in standard texts?

Edited March 10, 20178 yr by ProgrammingGodJordan

This is the first time hearing such data.

 

I had searched for 4 years, without finding the collapse regime.

 

Could you direct us to where the collapse bit exists, in standard texts?

Standard texts won't use the word 'collapse', that's what was said above. But any calculus text worth the paper its printed on will delve very deeply into 'u-substitutions' quite a lot. Go to your local library and check it out.

Standard texts won't use the word 'collapse', that's what was said above. But any calculus text worth the paper its printed on will delve very deeply into 'u-substitutions' quite a lot. Go to your local library and check it out.

 

The paradigm described is not u-substitution.

 

 

/////DIFFERENCE - i:

 

Fundamentally, u-substitution applies for functions of the form ∫ f(x) f'(x) dx. (that is, when integrals contains some function and its derivative)

 

 

EXPLANATION_EXPERIMENT:

 

(A)

 

INITIAL_FUNCTION(a) = ∫ sinx cosxdx.

 

Let u =sinx, and du=4cosxdx. Here we see that the INITIAL_FUNCTION(a) yields the form ∫ udu.

 

In (A) u-substitution nicely applies.

 

 

 

(B)

 

INITIAL_FUNCTION(b) = ∫ √16 - x^2

 

Let u = 4sinθ, and du = 4cosθdθ. Here we see that the INITIAL_FUNCTION(b) does not yield the form ∫ udu.

 

In (B) u-substitution does not apply, such that "dx/dθ * dx" absorbs the solution.

 

 

 

 

 

 

 

 

 

 

/////DIFFERENCE - ii:

 

EXPLANATION_EXPERIMENT:

 

U-substitution when applied to trig integral forms that don't satisfy the fundamental requirement in DIFFERENCE - i, don't engender via my equation "dx/dθ * dx".

Edited March 12, 20178 yr by ProgrammingGodJordan

(B)

 

INITIAL_FUNCTION(b) = ∫ √16 - x^2[/size]

 

Let u = 4cosθ, and du = 4cosθdθ. Here we see that the INITIAL_FUNCTION(b) does not yield the form ∫ udu.

 

In (B) u-substitution does not apply, such that "dx/dθ * dx" absorbs the solution.

So, you 'prove' that this isn't u-substitution by using something different that what your 'collapse' does.

 

You use [math]x=4\sin\theta[/math]... why not try [math]u=4\sin\theta[/math]? And maybe not make a mistake in forming the du term.... "u = 4cosθ, and du = 4cosθdθ" is obviously wrong.

 

 

Lastly, is there any reason you can't use this forum's LaTeX capabilities? Your post here is very difficult to read and it doesn't have to be...

Edited March 12, 20178 yr by Bignose

So, you 'prove' that this isn't u-substitution by using something different that what your 'collapse' does.

 

You use [math]x=4\sin\theta[/math]... why not try [math]u=4\sin\theta[/math]? And maybe not make a mistake in forming the du term.... "u = 4cosθ, and du = 4cosθdθ" is obviously wrong.

 

 

Lastly, is there any reason you can't use this forum's LaTeX capabilities? Your post here is very difficult to read and it doesn't have to be...

 

Typo purged.

 

What my collapse does was represented by the green segment, in my prior comment: dx/dθ * dx.

Edited March 12, 20178 yr by ProgrammingGodJordan

On 3/11/2017 at 8:52 PM, Bignose said:

So, you 'prove' that this isn't u-substitution by using something different that what your 'collapse' does.

 

You use x=4sinθ ... why not try u=4sinθ ? And maybe not make a mistake in forming the du term.... "u = 4cosθ, and du = 4cosθdθ" is obviously wrong.

 

 

Lastly, is there any reason you can't use this forum's LaTeX capabilities? Your post here is very difficult to read and it doesn't have to be...

Yes, that was a bit confusing.

This should be a better explanation: https://drive.google.com/file/d/0B8H3Ghe4haTWbW1uVGxiZ3ZqbEk/view

On ‎3‎/‎11‎/‎2017 at 8:59 PM, ProgrammingGodJordan said:

 

Typo purged.

 

What my collapse does was represented by the green segment, in my prior comment: dx/dθ * dx.

 "dx/dθ * dx" is meaningless.  Did you intend "dx/dθ * dθ"?

Edited September 6, 20178 yr by Country Boy

31 minutes ago, HallsofIvy said:

 "dx/dθ * dx" is meaningless.  Did you intend "dx/dθ * dθ"?

+1

Does this thread have a point?

21 minutes ago, studiot said:

+1

Does this thread have a point?

!

Moderator Note

I'm going to pretend that's a reported complaint and shut this down. The title makes my teeth ache.