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Fundamental theorem of calculus

2007-09-05T15:32:47Z

111Notavandal: okay seriously, it says theory in the title

:''This page is over '''Calculus'''. Calculus is theory, '''not a fact'''. Information presented in this article should be critically interpreted and taken with an open mind. There are true challenges to this debated theory including the [[God dun maths]] theory''.
'''The Fundamental Theorem of Calculus''' is the rather remarkable result that the two fundamental operations of [[calculus]] are just inverses of each other. Those two operations are performed on [[functions]] from the [[real numbers]] to the real numbers, and are most easily visualized when the functions are expressed in terms of graphs. The operations are:
*Differentiation -- find the slope of a function's graph at a given point.
*Integration -- find the area under a graph between two given limits.
The Fundamental Theorem of Calculus says that the two operations are inverses -- to find the area under the graph of f(x) between a and b, find the function g(x) whose derivative is f(x) (that is, find the ''antiderivative'' of f.) The area under the graph of f is just g(b)-g(a).

The antiderivative of a function is often called the ''indefinite integral''. (Indefinite because the limits a and b haven't been specified.) So, for example, the derivative of <math>\frac{x^3}{3}+7</math> is <math>x^2</math>. From this it follows that the antiderivative of
<math>x^2</math> could be <math>\frac{x^3}{3}+7</math>. But note that the "7" in that formula was a red herring. Adding any constant to a function doesn't change its derivative, so the antiderivative of <math>x^2</math> could have any constant added to it. This arbitrary constant is usually written '''C''' and is called the "constant of integration. The indefinite integral could be written:

:<math>\int x^2\ \mathrm{d}x = \frac{x^3}{3} + C\,</math>,

The Fundamental Theorem of Calculus says that the area under the graph of <math>x^2</math> between a and b is the difference in the values of <math>\frac{x^3}{3}+C</math> between a and b. Note that the constant of integration cancels out.

This kind of integral is called a ''definite integral'', written with the limits:

:<math>\int_a^b x^2\ \mathrm{d}x = \frac{b^3}{3} - \frac{a^3}{3}\,</math>,

The above is a simplified "intuitive" treatment of calculus and of this theorem. The actual "rigorous" proof, "rigorous" definitions of derivative and integral, and statement of the conditions under which the theorem is true, are beyond the scope of this article.

[[Category:Mathematics]]

LOD score

2007-09-05T15:31:07Z

111Notavandal:

:''This page is over '''DNA'''. DNA is theory, '''not a fact'''. Information presented in this article should be critically interpreted and taken with an open mind. There are true challenges to this debated theory including the [[God made de way I am]] theory''.

An '''LOD score''' is a statistical estimate of whether two [[locus|loci]] are likely to lie near each other on a [[chromosome]] and are therefore likely to be inherited together. A LOD score of three or more is generally taken to indicate that the two loci are close.

== Sources ==
http://www.genome.gov/glossary.cfm?key=LOD%20score

[[Category:Genetics]]

Bible Belt

2007-09-05T15:30:00Z

111Notavandal:

The '''Bible Belt''' is a geographical region including part of the South and midsection of the [[United States]]. Social conservatism is the dominant paradigm in these parts.

The Bible Belt includes all of the southern states and some of the surrounding. It has a notoriously high teen pregnancy and STD transmission rates. No reason is known why.

==Bible Belt States==
* [[Alabama]]
* [[Arkansas]]
* [[Florida]]
* [[Georgia]]
* [[Kentucky]]
* [[Louisiana]]
* [[Mississippi]]
* [[Missouri]]
* [[North Carolina]]
* [[Oklahoma]]
* [[South Carolina]]
* [[Tennessee]]
* [[Texas]]
* [[Virginia]]
* [[West Virginia]]
[[category:United States]]