Maple (software) - Revision history

en>Grubbiv: fix nonsense sentence

2015-01-03T20:57:31Z

fix nonsense sentence

← Older revision		Revision as of 22:57, 3 January 2015
Line 1:		Line 1:
	~~{{Unreferenced\|date=December 2009}}~~		Got nothing to tell about myself at all.<br>Great to be a part of wmflabs.org.<br>I really hope I am useful at all<br><br>Feel free to surf to my web page ... [http://hemorrhoidtreatmentfix.com/thrombosed-hemorrhoid-treatment thrombosed hemorrhoids treatment]
	In [[mathematics]], a '''constant term''' is a [[term (mathematics)\|term]] in an [[Expression (mathematics)\|algebraic expression]] that has a value that is [[constant function\|constant]] or cannot change, because it does not contain any modifiable [[Variable (mathematics)\|variables]]. For example, in the [[quadratic polynomial]]
	~~:<math>x^2 + 2x + 3,\ </math>~~
	~~the 3 is a constant term.~~

	~~After [[like terms]] are combined, an algebraic expression will have~~ at ~~most one constant term~~. ~~Thus, it is common to speak of the quadratic polynomial~~
	:<~~math~~>~~ax^2+bx+c,\ </math>~~
	~~where ''x'' is the variable, and has a constant term of ''c''. If ''c'' = 0, then the constant term will not actually appear when the quadratic is written.~~

	~~It is notable that a term that is constant, with a constant as a multiplicative coefficient added~~ to it (although this expression could be more simply written as their product), still constitutes a constant term as a variable is still not present in the new term. Although the expression is modified, the term (and coefficient) itself classifies as constant. However, should this introduced coefficient contain a variable, while the original number has a constant meaning, this has no bearing if the new term stays constant as the introduced coefficient will always override the constant expression - for example, in <math>(x+1)(x-2)</math> when x is multiplied by 2, the result, 2x, is not constant; while 1 * -2 is -2 and still a constant.

	~~Any [[polynomial]] written in standard form has a unique constant term, which can be considered a [[coefficient]] of ''x''<sup>0</sup>. In particular, the constant term will always~~ be ~~the lowest [[Degree of~~ a ~~polynomial\|degree]] term~~ of ~~the polynomial~~. ~~This also applies to multivariate polynomials~~. ~~For example, the polynomial~~
	:<~~math~~>~~x^2+2xy+y^2-2x+2y-4\ </math>~~
	~~has a constant term of −4, which can be considered to be the coefficient of ''x''~~<~~sup~~>0<~~/sup~~>~~''y''<sup>0</sup>, where the variables are become eliminated by exponentiated~~ to ~~0 (any number exponentiated~~ to ~~0 becomes 1)~~. ~~For any polynomial, the constant term can be obtained by substituting in 0 instead of each variable; thus, eliminating each variable~~. ~~The concept of exponentiation to 0 can be extended to~~ [~~[power series]] and other types of series, for example in this power series:~~
	:~~<math>a_0 + a_1 x + a_2 x^2 + a_3 x^3 + \cdots,<~~/~~math>~~
	~~''a''<sub>0<~~/~~sub> is the constant term~~. In general a constant term is one that does not involve any variables at all. However in expressions that involve terms with other types of factors than constants and powers of variables, the notion of constant term cannot be used in this sense, since that would lead to calling "4" the constant term of <math>(x-~~3)^2+4</math>, whereas substituting 0 for ''x'' in this polynomial makes it evaluate to 13.~~

	~~==See also==~~
	* [[Constant (mathematics)]]

	~~{{DEFAULTSORT:Constant Term}}~~
	~~[[Category:Polynomials]]~~
	~~[[Category:Elementary algebra]~~]

86.52.237.238: /* Laplace transform */

2014-01-31T15:15:28Z

Laplace transform

← Older revision		Revision as of 17:15, 31 January 2014
Line 1:		Line 1:
	~~Some consumers of laptop or computer are aware that their computer become slower or have several errors after using for~~ a ~~while. But most individuals don~~'~~t recognize how to speed up their computer and~~ a ~~few of them don't dare to operate~~ it. ~~They always find some experts to keep~~ the ~~computer in wise condition yet they have to invest some income on it. Actually~~, ~~we can do it by yourself~~. ~~There~~ are ~~numerous registry cleaner software which we can get 1 of them online. Some of them are free and we only require to download them. After installing it~~, ~~this registry cleaner software can scan the registry~~. ~~If it found these mistakes~~, it ~~might report we plus you are able to delete them to keep a registry clean. It~~ is ~~easy~~ to ~~operate and it is very~~ the ~~most effective method to repair registry.~~<br><br>~~Document files allow~~ the ~~consumer to input data~~, ~~images~~, ~~tables plus additional elements to enhance~~ the ~~presentation~~. ~~The just problem~~ with ~~this format compared to alternative file kinds like .pdf for example is its ability~~ to ~~be easily editable. This means which anybody watching the file will change~~ it ~~by accident. Additionally,~~ this ~~file structure will~~ be ~~opened by alternative programs yet it refuses to guarantee that what you see~~ in the ~~Microsoft Word application can nonetheless be~~ the ~~same when you see it using another program~~. However, ~~it is nevertheless preferred by many computer consumers for its ease of use and attributes.<br><br>H/w connected error handling - whenever hardware causes BSOD installing newest fixes for~~ the ~~hardware and/ or motherboard may aid. We may furthermore add~~ new ~~hardware which is compatible with all~~ the ~~system.~~<br><br>It is ~~usual which~~ the ~~imm32.dll error is caused as a~~ result ~~of a mis-deletion activity. If you cannot find the imm32.dll anywhere on your computer~~, ~~there~~ is not ~~any question which it must be mis~~-~~deleted when uninstalling programs or alternative unneeded files~~. ~~Hence~~, ~~you are able to directly cope it from different programs or download it from~~ a ~~safe internet and then place it on a computer.~~<br><br>~~Many~~ [~~http://bestregistrycleanerfix.com/fix-it-utilities fix it utilities~~] ~~s allow you to download their product for free, so you can scan~~ the ~~computer oneself~~. ~~That method you can see how various mistakes it finds, where it finds them, and how it can fix them~~. ~~A amazing registry cleaner usually remove your registry difficulties~~, ~~plus optimize plus speed up~~ a PC, ~~with small effort on your part.~~<br><br>~~Turn It Off: Chances~~ are in ~~the event you are like me~~; ~~then we spend a lot~~ of ~~time on the computer on a daily basis. Try providing the computer certain time~~ to ~~do completely nothing; this~~ can ~~sound funny nevertheless~~ in ~~the event you have an older computer you are asking it to do too much.~~<br><br>~~Your registry~~ is the ~~place~~ all ~~the significant configurations for hardware, software plus user profile configurations plus preferences are stored~~. ~~Every time one~~ of ~~these things is changed~~, the ~~database then begins~~ to ~~expand. Over time,~~ the ~~registry can become bloated with unwanted files. This causes a general slow down yet in extreme situations could cause important tasks and programs to stop functioning all together.~~<br><br>~~There are numerous firms that provide the service of troubleshooting a PC each time we call them~~, ~~all you have~~ to ~~do is sign up with them plus for a small fee, you have the machine always functioning effectively plus serve we better~~.		{{Unreferenced\|date=December 2009}}
			In [[mathematics]], a '''constant term''' is a [[term (mathematics)\|term]] in an [[Expression (mathematics)\|algebraic expression]] that has a value that is [[constant function\|constant]] or cannot change, because it does not contain any modifiable [[Variable (mathematics)\|variables]]. For example, in the [[quadratic polynomial]]
			:<math>x^2 + 2x + 3,\ </math>
			the 3 is a constant term.

			After [[like terms]] are combined, an algebraic expression will have at most one constant term. Thus, it is common to speak of the quadratic polynomial
			:<math>ax^2+bx+c,\ </math>
			where ''x'' is the variable, and has a constant term of ''c''. If ''c'' = 0, then the constant term will not actually appear when the quadratic is written.

			It is notable that a term that is constant, with a constant as a multiplicative coefficient added to it (although this expression could be more simply written as their product), still constitutes a constant term as a variable is still not present in the new term. Although the expression is modified, the term (and coefficient) itself classifies as constant. However, should this introduced coefficient contain a variable, while the original number has a constant meaning, this has no bearing if the new term stays constant as the introduced coefficient will always override the constant expression - for example, in <math>(x+1)(x-2)</math> when x is multiplied by 2, the result, 2x, is not constant; while 1 * -2 is -2 and still a constant.

			Any [[polynomial]] written in standard form has a unique constant term, which can be considered a [[coefficient]] of ''x''<sup>0</sup>. In particular, the constant term will always be the lowest [[Degree of a polynomial\|degree]] term of the polynomial. This also applies to multivariate polynomials. For example, the polynomial
			:<math>x^2+2xy+y^2-2x+2y-4\ </math>
			has a constant term of −4, which can be considered to be the coefficient of ''x''<sup>0</sup>''y''<sup>0</sup>, where the variables are become eliminated by exponentiated to 0 (any number exponentiated to 0 becomes 1). For any polynomial, the constant term can be obtained by substituting in 0 instead of each variable; thus, eliminating each variable. The concept of exponentiation to 0 can be extended to [[power series]] and other types of series, for example in this power series:
			:<math>a_0 + a_1 x + a_2 x^2 + a_3 x^3 + \cdots,</math>
			''a''<sub>0</sub> is the constant term. In general a constant term is one that does not involve any variables at all. However in expressions that involve terms with other types of factors than constants and powers of variables, the notion of constant term cannot be used in this sense, since that would lead to calling "4" the constant term of <math>(x-3)^2+4</math>, whereas substituting 0 for ''x'' in this polynomial makes it evaluate to 13.

			==See also==
			* [[Constant (mathematics)]]

			{{DEFAULTSORT:Constant Term}}
			[[Category:Polynomials]]
			[[Category:Elementary algebra]]

en>Gisling: /* Series expansion */

2012-09-01T17:25:09Z

Series expansion

New page

Some consumers of laptop or computer are aware that their computer become slower or have several errors after using for a while. But most individuals don't recognize how to speed up their computer and a few of them don't dare to operate it. They always find some experts to keep the computer in wise condition yet they have to invest some income on it. Actually, we can do it by yourself. There are numerous registry cleaner software which we can get 1 of them online. Some of them are free and we only require to download them. After installing it, this registry cleaner software can scan the registry. If it found these mistakes, it might report we plus you are able to delete them to keep a registry clean. It is easy to operate and it is very the most effective method to repair registry. Document files allow the consumer to input data, images, tables plus additional elements to enhance the presentation. The just problem with this format compared to alternative file kinds like .pdf for example is its ability to be easily editable. This means which anybody watching the file will change it by accident. Additionally, this file structure will be opened by alternative programs yet it refuses to guarantee that what you see in the Microsoft Word application can nonetheless be the same when you see it using another program. However, it is nevertheless preferred by many computer consumers for its ease of use and attributes. H/w connected error handling - whenever hardware causes BSOD installing newest fixes for the hardware and/ or motherboard may aid. We may furthermore add new hardware which is compatible with all the system. It is usual which the imm32.dll error is caused as a result of a mis-deletion activity. If you cannot find the imm32.dll anywhere on your computer, there is not any question which it must be mis-deleted when uninstalling programs or alternative unneeded files. Hence, you are able to directly cope it from different programs or download it from a safe internet and then place it on a computer. Many [http://bestregistrycleanerfix.com/fix-it-utilities fix it utilities] s allow you to download their product for free, so you can scan the computer oneself. That method you can see how various mistakes it finds, where it finds them, and how it can fix them. A amazing registry cleaner usually remove your registry difficulties, plus optimize plus speed up a PC, with small effort on your part. Turn It Off: Chances are in the event you are like me; then we spend a lot of time on the computer on a daily basis. Try providing the computer certain time to do completely nothing; this can sound funny nevertheless in the event you have an older computer you are asking it to do too much. Your registry is the place all the significant configurations for hardware, software plus user profile configurations plus preferences are stored. Every time one of these things is changed, the database then begins to expand. Over time, the registry can become bloated with unwanted files. This causes a general slow down yet in extreme situations could cause important tasks and programs to stop functioning all together. There are numerous firms that provide the service of troubleshooting a PC each time we call them, all you have to do is sign up with them plus for a small fee, you have the machine always functioning effectively plus serve we better.