Articles:
Comparing Newton's flawed calculus to the New Calculus:
https://drive.google.com/open?id=0B-mOEooW03iLS2ZmdnUweUN5bUU
Cauchy's Kludge:
https://drive.google.com/open?id=0B-mOEooW03iLS2ZmdnUweUN5bUU
Quick start explanation of auxiliary equation:
https://drive.google.com/open?id=0B-mOEooW03iLS2ZmdnUweUN5bUU
Divisibility identities:
https://drive.google.com/open?id=0B-mOEooW03iLS2ZmdnUweUN5bUU
Proof using Gabriel polynomial that m+n is a factor of every term in the numerator:
https://drive.google.com/open?id=0B-mOEooW03iLS2ZmdnUweUN5bUU
Applets:
Cauchy's Flawed Definition:
https://drive.google.com/open?id=0B-mOEooW03iLS2ZmdnUweUN5bUU
Auxiliary equation:
https://drive.google.com/open?id=0B-mOEooW03iLMHZkUGxIQ0k5ZjQ
Cauchy's Kludge:
https://drive.google.com/open?id=0B-mOEooW03iLeWpvQzZGSWRxUjg
...
https://www.youtube.com/watch?v=4kdRhnY-SNM
Tangent line: a line such that no other straight line can fall between it and the curve - Apollonius.
Neither of those bumbling morons Newton and Leibniz could prove their claims about derivatives and integrals:
https://www.academia.edu/88991847/Neither_Newton_nor_Leibniz_actually_proved_their_claims_about_integrals_and_area
The idiots Cauchy, Weierstrass and others who came after did NOTHING to rigorise calculus. In fact, they did the opposite - they polluted it so much that none of them understand it any longer:
https://www.academia.edu/81300370/Mainstream_mathematics_academics_are_arrogant_and_incorrigible_ignoramuses_The_mean_value_theorem_IS_the_fundamental_theorem_of_calculus
The Britannica is WRONG about the mean value theorem:
https://www.academia.edu/108640381/The_Britannica_entry_for_Mean_Value_Theorem_is_WRONG
A great math channel for kids!
https://www.youtube.com/@TheMathPath-tn7px
Download the free eBook on the Single Variable New Calculus:
https://www.academia.edu/41616655/An_Introduction_to_the_Single_Variable_New_Calculus
Learn about the Holy Grail of Calculus:
https://www.academia.edu/105576431/The_Holy_Grail_of_Calculus
Learn about the Gabriel Polynomial (GP) which is a very advanced concept not possible using mainstream derivative or integral definitions. The GP is always a closed form polynomial and has no Error term:
https://www.academia.edu/45229087/The_Gabriel_Polynomial
Download the best book ever written on the number concept:
https://www.academia.edu/105399167/The_Ultimate_Book_of_Numbers
Get the true Origins and History of Calculus:
https://www.academia.edu/106488069/The_Non_fictional_Origins_and_History_of_Calculus
Discover closed -form trigonometric functions never realised before:
https://www.academia.edu/109334669/Ancient_Greek_trigonometric_formulas_better_than_anything_ever_known
Follow me on Academia.edu:
https://independent.academia.edu/JohnGabriel30
Donate here:
https://gofund.me/af8a5312
or here:
https://wise.com/pay/me/johng3933
All my YouTube videos are backed up here:
https://odysee.com/@NewCalculus:1
The scum of YouTube are constantly threatening and looking for excuses to shut down my channel.
Want to get instant updates for the newest math around? Join our discord server! https://discord.gg/CJ9Ks3WerR
Merchandise Store:
https://new-calculus.printify.me/products
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https://www.youtube.com/watch?v=ApiKVGFTwZc
The theorem is an interesting and very useful result realised in the New Calculus. You can verify it using your bogus mainstream calculus.
The link to the applet here:
https://drive.google.com/open?id=1rgU-OrtZ48arNLe5rt15Xa-M7qM3B530
What this theorem tells you in simple words is this:
You can pick any point on a curve and calculate the area using equal horizontal distances from the point. IF the arithmetic mean (or average value as known in mainstream nose picking circles) remains unchanged and equal to the y ordinate at the same point, then that point is an inflection point!
This theorem was not realised in your bogus mainstream calculus because you've never understood what it means to be a definite integral which is well defined in the New Calculus. It's also an example of the importance of the arithmetic mean with respect to the core of calculus. You can't understand area, volume, etc without understanding the arithmetic mean. Some cranks like Dennis Muller of logical phalluses seems to think the arithmetic mean is entirely unremarkable.
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https://www.youtube.com/watch?v=bgFTB66SlnE
In this video I show you how multiplication can be done using only magnitudes as in Book V (proposition 12) of Euclid's Elements. There is no use of numbers. I only use the fact that a line segment can be extended or diminished as per Requirement 2 of Euclid's five requirements.
I am a genius and I am offering this knowledge to you free of charge. Please support me by contributing money or credits.
Late Edit: I was asked how we can know that the new consequent is a multiple of both. Well, we know that from a circle we can find the product of any two line segments as explained in this video:
https://youtu.be/DG2pgnRFa8g
The third and final part in a three part series on THE BIG DECEPTION.
See also Academic Ignorance and Stupidity - PART21 and PART22.
For the first and only rigorous formulation of calculus in human history:
http://thenewcalculus.weebly.com
Questions and answers:
https://sites.google.com/site/thenewcalculus/questions-and-answers
Applet used in this video available for download at:
https://drive.google.com/open?id=0B-mOEooW03iLTTRwazFyXzNVd2M
Epsilon and delta are functions of each other. To understand this, read my article explaining the inverse method:
https://drive.google.com/open?id=0B-mOEooW03iLMDAtai1rcE9jV1E
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https://www.youtube.com/watch?v=6roMXD4w3RY
I got a question about my trigonometric functions which are superior to Newton's sine and cosine series: "But your functions are not periodic".
As if this is a problem because periodicity can be accomplished by letting each quadrant be one cycle, so that a complete 360 angle has a period of 4 x radius.
The nice thing about my functions is that the sign can be incorporated in the formulas for each quadrant and all that is necessary is to reduce the angle to an acute angle and specify the quadrant. My functions are closed-form and exact unlike Newton's "infinite" series which are mere approximations.
Link to original article:
https://www.academia.edu/109334669/Ancient_Greek_trigonometric_formulas_better_than_anything_ever_known
Follow me on Academia.edu:
https://independent.academia.edu/JohnGabriel30
Donate here:
https://gofund.me/af8a5312
All my YouTube videos are backed up here:
https://odysee.com/@NewCalculus:1
The scum of YouTube are constantly threatening and looking for excuses to shut down my channel.
Want to get instant updates for the newest math around? Join our discord server! https://discord.gg/CJ9Ks3WerR
Merchandise Store:
https://new-calculus.printify.me/products
...
https://www.youtube.com/watch?v=SoGCNLz6RB0
A differential is simply a difference. A derivative is a fraction of differences.
Given that fractions can be equivalent, we call dy and dx symbolic differentials meaning they can take on any value as long as dy/dx is an equivalent fraction so obtained.
There is no such thing as an infinitesimal or infinity - both are junk concepts.
To claim as do the ignorant fools of mainstream mathematics academia that dy = f'(x) dx is a definition for a differential is CIRCULAR, but this should not surprise because in their sewer brains there is a lot of circularity! :-)
If Newton and Leibniz used angle for slope, then all smooth functions would have derivative functions whose ranges fall into the interval (-π/2, π/2) and vertical lines would have a slope.
The New Calculus:
https://www.academia.edu/41616655/An_Introduction_to_the_Single_Variable_New_Calculus
https://www.academia.edu/video/joX821
My historic geometric theorem which exposes Newton's and Leibniz's fraudulent formulation:
https://www.academia.edu/62358358/My_historic_geometric_theorem_of_January_2020
What exactly are differentials?
https://www.academia.edu/75882879/What_exactly_are_differentials_in_calculus
Six simple reasons why mainstream calculus formulation is flawed:
https://www.academia.edu/79881709/Six_simple_reasons_why_the_mainstream_derivative_definition_of_calculus_is_flawed
Theory of number, fractions and arithmetic:
https://www.academia.edu/44820487/Discovering_the_concept_of_number_a_personal_journey
Find many interesting articles here:
https://independent.academia.edu/JohnGabriel30
Thank me for enlightening you by contributing money here:
https://gofund.me/af8a5312
I am hated by mainstream math academics because I expose their ignorance, incompetence, unbelievable stupidity and arrogance. The more I reveal new knowledge and publish truth, the more I am persecuted and hated.
The truth is that I do know better than anyone else. Don't believe me! Prove that my claims are indeed true.
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https://www.youtube.com/watch?v=MeTUrXSfYk8
There are still some numbskulls who think that division by zero takes place in the New Calculus. It never happens because no secant line has the pair (0,0). The form f'(x)= [ f(c+n)-f(c-m) ]/ (m+n) is used for parallel secant lines exclusively. The form
f'(x)=k + Q(x,m,n) or f'(x)=f'(x) + Q(x,m,n) can be used for both the tangent line and the parallel secant lines.
Even in this form, that is, f'(x)=f'(x) + Q(x,m,n), there are innumerably many (m,n) pairs which will satisfy it.
...
https://www.youtube.com/watch?v=07xr7Wn58q4