A Theorem About Differenciation

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In summary, the method discussed in this conversation is called differenciation and it allows for the verification of expressions of any finite polynomial. The speaker has put a lot of effort into explaining the method and has provided a word document for reference. The method is similar to the Newton series and can be used to check the formula for any function with rational inputs and outputs. The speaker was hoping to be the first to discover this method, but it turns out that Newton had already done so. The speaker finds differenciation to be fun and interesting, and believes it can be useful in discrete math.
  • #1
Eynbanoiqvs
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The above is not a spelling mistake as I am referring to differenciation rather than differentiation. As to the best of my knowledge, no one else has used the same term nor developed a similar method; and so I claim it as my own till challenged.
Using differenciation, one can verify the expression of any finite polynomial.

I put a lot of work in trying to write up an explanation for my method...so it's best seen in the word document attached. But I still don't think it's perfect.
Please post your views and understanding of this. I would like any feedback.
 

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  • Differenciation Method of Deriving Polynomial Expressions.zip
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  • #2
Using differenciation, one can verify the expression of any finite polynomial.
I can't figure out what this sentence is supposed to mean.
I haven't tried downloading your zip file. I'm guessing you're reproducing the theory of difference equations, or possibly have rediscovered some form of Newton series.
 
  • #3
Yes; it is the Newton series...but in a primitive form. Thanks for telling me. I didn't know how to search for it or identify it.

That sentence means that you can use the Newton series method to check the formula for any function; assuming it is a finite polynomial and has rational inputs and outputs.
For example, the sum of natural numbers. If one didn't know any theory behind the derivation; this method could yield n^2 /2 +n/2 by calculation with minimum logic involved.
So simple that a computer could derive the formula.

Thanks again for identifying it! I was hoping I was the first...but I guess Newton bet me! :)
 
  • #4
I've looked at the article, I'll say it's much better written than I expected from a *.doc file posted on the internet!

There's no better way to understand (and to eventually further) a subject than to derive it for yourself, so hopefully you'll continue your study / research, and a lead on existing knowledge will surely help. Sometimes just having good notation makes all the difference!

If nothing else, I think differences are fun -- and the fact of analogies with differentials is interesting -- although I've only spent a little bit of time with them. And they certainly can be very useful in discrete math.
 
  • #5
Thanks! I actually used the latest Word 2007 to design the document, and then converted it into the old format for uploading.
 

Related to A Theorem About Differenciation

1. What is a theorem about differentiation?

A theorem about differentiation is a mathematical statement that provides a rule or formula for finding the derivative of a function. It is used to calculate the rate of change of a function at a specific point.

2. Why is differentiation important in science?

Differentiation is important in science because it allows us to measure and understand the rate of change in various processes. It is used in physics, engineering, economics, and other fields to analyze and model real-world phenomena.

3. What is the difference between differentiation and integration?

Differentiation is the process of finding the derivative of a function, while integration is the process of finding the antiderivative of a function. Differentiation measures the rate of change, while integration measures the accumulated change over an interval.

4. How is the theorem about differentiation used in real-world applications?

The theorem about differentiation is used in many real-world applications, such as calculating velocity and acceleration in physics, predicting stock market trends in economics, and optimizing production processes in engineering. It is also used in machine learning algorithms and data analysis.

5. Are there any limitations to the theorem about differentiation?

While the theorem about differentiation is a powerful tool, it does have some limitations. It cannot be used to find derivatives of discontinuous or non-differentiable functions. It also cannot be used to find the derivatives of functions with multiple inputs. Additionally, it is important to consider the context and assumptions of a problem when using the theorem to ensure accurate results.

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