Legendre transform - Revision history

Carl McBride: Undo revision 12023 by TermPaperServices (talk)

2011-12-15T09:33:51Z

Undo revision 12023 by TermPaperServices (talk)

← Older revision		Revision as of 11:33, 15 December 2011
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	The '''Legendre transform''' is used to perform a change ~~[http://www.ghostpapers.com Term Paper]~~ of variables (see, for example, Ref. <ref>Mary L. Boas "Mathematical methods in the Physical Sciences" John Wiley & Sons, Second Edition ISBN 0471044091</ref> Chapter 4 section 11 Eq. 11.20 - 11.25).		The '''Legendre transform''' is used to perform a change of variables (see, for example, Ref. <ref>Mary L. Boas "Mathematical methods in the Physical Sciences" John Wiley & Sons, Second Edition ISBN 0471044091</ref> Chapter 4 section 11 Eq. 11.20 - 11.25).

	If one has the function <math>f(x,y);</math> one can write		If one has the function <math>f(x,y);</math> one can write

TermPaperServices at 07:29, 15 December 2011

2011-12-15T07:29:11Z

← Older revision		Revision as of 09:29, 15 December 2011
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	The '''Legendre transform''' is used to perform a change of variables (see, for example, Ref. <ref>Mary L. Boas "Mathematical methods in the Physical Sciences" John Wiley & Sons, Second Edition ISBN 0471044091</ref> Chapter 4 section 11 Eq. 11.20 - 11.25).		The '''Legendre transform''' is used to perform a change [http://www.ghostpapers.com Term Paper] of variables (see, for example, Ref. <ref>Mary L. Boas "Mathematical methods in the Physical Sciences" John Wiley & Sons, Second Edition ISBN 0471044091</ref> Chapter 4 section 11 Eq. 11.20 - 11.25).

	If one has the function <math>f(x,y);</math> one can write		If one has the function <math>f(x,y);</math> one can write

Carl McBride: Slight tidy

2011-02-01T14:46:47Z

Slight tidy

← Older revision		Revision as of 16:46, 1 February 2011
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	The '''Legendre transform''' ~~(Adrien-Marie Legendre)~~		The '''Legendre transform''' is used to perform a change of variables (see, for example, Ref. <ref>Mary L. Boas "Mathematical methods in the Physical Sciences" John Wiley & Sons, Second Edition ISBN 0471044091</ref> Chapter 4 section 11 Eq. 11.20 - 11.25).
	is used to perform a ~~change ''~~change of variables''
	(see, for example, Ref. 1, Chapter 4 section 11 Eq. 11.20 - 11.25):

	If one has the function <math>f(x,y);</math> one can write		If one has the function <math>f(x,y);</math> one can write
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	:<math>\frac{\partial g}{\partial x}= p, ~~~ \frac{\partial g}{\partial q}= -y</math>.		:<math>\frac{\partial g}{\partial x}= p, ~~~ \frac{\partial g}{\partial q}= -y</math>.

	~~==Example==~~
	==See also==		==See also==
	*[[Thermodynamic relations]]		*[[Thermodynamic relations]]
	==References==		==References==
	~~#Mary L. Boas "Mathematical methods in the Physical Sciences" John Wiley & Sons, Second Edition.~~		<references/>
	#[http://www.iupac.org/publications/pac/2001/7308/7308x1349.html Robert A. Alberty "Use of Legendre transforms in chemical thermodynamics", Pure and Applied Chemistry '''73''' pp. 1349-1380 (2001)]		;Related reading
			*[http://www.iupac.org/publications/pac/2001/7308/7308x1349.html Robert A. Alberty "Use of Legendre transforms in chemical thermodynamics", Pure and Applied Chemistry '''73''' pp. 1349-1380 (2001)]
	[[category: mathematics]]		[[category: mathematics]]

163.117.132.133 at 10:01, 15 February 2008

2008-02-15T10:01:10Z

← Older revision		Revision as of 12:01, 15 February 2008
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	then		then

	:<math>dg = p~dx ~~+ q~~~dy</math>		:<math>dg = p~dx - y~dq</math>

	The partial derivatives of <math>g</math> are		The partial derivatives of <math>g</math> are

Carl McBride at 10:34, 28 May 2007

2007-05-28T10:34:02Z

← Older revision		Revision as of 12:34, 28 May 2007
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	#Mary L. Boas "Mathematical methods in the Physical Sciences" John Wiley & Sons, Second Edition.		#Mary L. Boas "Mathematical methods in the Physical Sciences" John Wiley & Sons, Second Edition.
	#[http://www.iupac.org/publications/pac/2001/7308/7308x1349.html Robert A. Alberty "Use of Legendre transforms in chemical thermodynamics", Pure and Applied Chemistry '''73''' pp. 1349-1380 (2001)]		#[http://www.iupac.org/publications/pac/2001/7308/7308x1349.html Robert A. Alberty "Use of Legendre transforms in chemical thermodynamics", Pure and Applied Chemistry '''73''' pp. 1349-1380 (2001)]
			[[category: mathematics]]

Carl McBride: /* References */

2007-05-28T10:17:33Z

References

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	==References==		==References==
	#Mary L. Boas "Mathematical methods in the Physical Sciences" John Wiley & Sons, Second Edition.		#Mary L. Boas "Mathematical methods in the Physical Sciences" John Wiley & Sons, Second Edition.
	#[http://www.iupac.org/publications/pac/2001/7308/7308x1349.html R. A. Alberty "Use of Legendre transforms in chemical thermodynamics", Pure and Applied Chemistry '''73''' pp. 1349-1380 (2001)]		#[http://www.iupac.org/publications/pac/2001/7308/7308x1349.html Robert A. Alberty "Use of Legendre transforms in chemical thermodynamics", Pure and Applied Chemistry '''73''' pp. 1349-1380 (2001)]

Carl McBride at 10:17, 28 May 2007

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← Older revision		Revision as of 12:17, 28 May 2007
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	==Example==		==Example==
			==See also==
			*[[Thermodynamic relations]]
	==References==		==References==
	#Mary L. Boas "Mathematical methods in the Physical Sciences" John Wiley & Sons, Second Edition.		#Mary L. Boas "Mathematical methods in the Physical Sciences" John Wiley & Sons, Second Edition.
			#[http://www.iupac.org/publications/pac/2001/7308/7308x1349.html R. A. Alberty "Use of Legendre transforms in chemical thermodynamics", Pure and Applied Chemistry '''73''' pp. 1349-1380 (2001)]

Carl McBride at 10:07, 28 May 2007

2007-05-28T10:07:37Z

← Older revision		Revision as of 12:07, 28 May 2007
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	~~[[http~~://en.~~wikipedia~~.~~org/wiki/Legendre_transform Legendre transform]]~~		The '''Legendre transform''' (Adrien-Marie Legendre)
			is used to perform a change ''change of variables''
			(see, for example, Ref. 1, Chapter 4 section 11 Eq. 11.20 - 11.25):

			If one has the function <math>f(x,y);</math> one can write

			:<math>df = \frac{\partial f}{\partial x}dx + \frac{\partial f}{\partial y}dy</math>

			Let <math>p= \partial f/ \partial x</math>, and <math>q= \partial f/ \partial y</math>, thus

			:<math>df = p~dx + q~dy</math>

			If one subtracts <math>d(qy)</math> from <math>df</math>, one has

			:<math>df- d(qy) = p~dx + q~dy -q~dy - y~dq</math>
			or
			:<math>d(f-qy)=p~dx - y~dq </math>

			Defining the function <math>g=f-qy</math>
			then

			:<math>dg = p~dx + q~dy</math>

			The partial derivatives of <math>g</math> are

			:<math>\frac{\partial g}{\partial x}= p, ~~~ \frac{\partial g}{\partial q}= -y</math>.

			==Example==
			==References==
			#Mary L. Boas "Mathematical methods in the Physical Sciences" John Wiley & Sons, Second Edition.

Cuesta: New page: http://en.wikipedia.org/wiki/Legendre_transform Legendre transform

2007-05-26T15:36:06Z

New page: http://en.wikipedia.org/wiki/Legendre_transform Legendre transform

New page

[[http://en.wikipedia.org/wiki/Legendre_transform Legendre transform]]