The Purpose of Polynomials


by leanne_19
Tags: polynomials, purpose
leanne_19
leanne_19 is offline
#1
Jul15-07, 04:17 PM
P: 1
1. Given the history of polynomials and there application why are they important?







3. When I researched the history all I found on the internet all I found was who was the first to solved certain types of poynomial. It didn't help me figure out why they might be important. I know how to solve them, I am just not sure how to apply them to everyday life and what their purpose is. Any suggestions
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution
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Gib Z
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#2
Jul15-07, 05:36 PM
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A quick search of "polynomials are important" in google finds : http://nostalgia.wikipedia.org/wiki/Polynomial.

Polynomials are important because they are the simplest functions: their definition involves only addition and multiplication (since the powers are just shorthands for repeated multiplications). They are also simple in a different sense: the polynomials of degree ≤ n are precisely those functions whose (n+1)st derivative is identical zero. One can view calculus as the project of analyzing complicated functions by means of approximating them with polynomials. The culmination of these efforts is Taylors theorem, which roughly states that every differentiable function locally looks like a polynomial, and the Weierstrass approximation theorem, which states that every continuous function defined on a compact interval of the real axis can be approximated on the whole interval as closely as desired by a polynomial.
GoldPheonix
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#3
Jul15-07, 08:49 PM
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They are the basis of all other equations, as per Taylor's Theorem iterated to infinity?

weaser
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#4
Jul16-07, 12:53 AM
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The Purpose of Polynomials


Polynomials define simple curves in the language of mathematics so that they may be easily analyzed and modified. Simple curves can be combined to closely approximate more complicated curves. Planets, weather, etc. move in curves. Mechanical forces, chemical and biological processes, etc. are not constant but change over space and time. These changes and other changes like fluctuations in the economy can be approximated by curves. Also, televisions, computers, phones, music players, etc. all receive signals that are sine waves (curves). Does an electrical engineer factor polynomials on a daily basis? No. A novelist doesn't analyze the structure of each sentence, but at some point the novelist needed to learn sentence structure to write books. In the same way, polynomials are the building blocks of all these sciences.


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