Legendre transform: Difference between revisions

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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

Revision as of 08:29, 15 December 2011

The Legendre transform is used to perform a change Term Paper of variables (see, for example, Ref. [1] Chapter 4 section 11 Eq. 11.20 - 11.25).

If one has the function one can write

Let , and , thus

If one subtracts from , one has

or

Defining the function then

The partial derivatives of are

.

See also

References

  1. Mary L. Boas "Mathematical methods in the Physical Sciences" John Wiley & Sons, Second Edition ISBN 0471044091
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