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Lee Rudolph
science forum Guru

Joined: 28 Apr 2005
Posts: 566

Posted: Fri Jul 07, 2006 5:26 pm    Post subject: Re: What is the relation between differential equations and differential forms?

israel@math.ubc.ca (Robert Israel) writes:

 Quote: In article , Lee Rudolph wrote: "andrzej" writes: I will be gratefully for any references which are related to relation between nonlinear differential equations and differential forms. Will you be, indeed? Under your previous name, "andrzej" , you seemed ungrateful indeed for all attempts to inform your willful ignorance; why should we believe you are not engaged in the same kind of trolling once again? Andrzej is a very common name in Poland.

And is the "Google Groups" posting account
0VIq4g0AAAALIdXtcD0twijLWH3jqv1L (as found
in the "Injection-Info:" headers both of this
latest post and of "andrzej"'s posts throughout
the thread "How to define a vector without coordinate
system?") also very common in Poland?

 Quote: I don't think you should assume this is the same one.

Reverend Bayes made me do it.

Lee Rudolph
Robert B. Israel
science forum Guru

Joined: 24 Mar 2005
Posts: 2151

Posted: Fri Jul 07, 2006 4:39 pm    Post subject: Re: What is the relation between differential equations and differential forms?

andrzej <question2006a@hotmail.com> wrote:
 Quote: Solution of differential equation y'=f(x,y) Is equivalent to the solution of the equation f(x,y)dx-dy=0 which is actually a differential form. ----------------------------------- Let us consider nonlinear equation (y')^2=f(x,y) the expression f(x,y)dx^2-dy^2=0 isn't a differential form. Then what is it?

Try the two differential forms sqrt(f(x,y)) dx - dy and
-sqrt(f(x,y)) dx - dy (when f(x,y) > 0)

 Quote: ----------------------------------- Let us consider an equation Sin(y')+y'=0 Is it possible to create equivalent differential form in this case?

This DE is equivalent to y' = 0 (if you're working over the reals).

Robert Israel israel@math.ubc.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
Robert B. Israel
science forum Guru

Joined: 24 Mar 2005
Posts: 2151

Posted: Fri Jul 07, 2006 4:32 pm    Post subject: Re: What is the relation between differential equations and differential forms?

In article <e8liut\$4n1\$1@panix2.panix.com>,
Lee Rudolph <lrudolph@panix.com> wrote:
 Quote: "andrzej" writes: I will be gratefully for any references which are related to relation between nonlinear differential equations and differential forms. Will you be, indeed? Under your previous name, "andrzej" , you seemed ungrateful indeed for all attempts to inform your willful ignorance; why should we believe you are not engaged in the same kind of trolling once again?

Andrzej is a very common name in Poland. I don't
think you should assume this is the same one.

Robert Israel israel@math.ubc.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
Lee Rudolph
science forum Guru

Joined: 28 Apr 2005
Posts: 566

Posted: Fri Jul 07, 2006 12:10 pm    Post subject: Re: What is the relation between differential equations and differential forms?

"andrzej" <question2006a@hotmail.com> writes:

 Quote: I will be gratefully for any references which are related to relation between nonlinear differential equations and differential forms.

Will you be, indeed? Under your previous name,
"andrzej" <jedrek_2004@hotmail.com>, you seemed
ungrateful indeed for all attempts to inform your
willful ignorance; why should we believe you are
not engaged in the same kind of trolling once again?

Lee Rudolph
andrzej1167
science forum beginner

Joined: 16 Jan 2006
Posts: 30

 Posted: Fri Jul 07, 2006 11:38 am    Post subject: What is the relation between differential equations and differential forms? Solution of differential equation y'=f(x,y) Is equivalent to the solution of the equation f(x,y)dx-dy=0 which is actually a differential form. ----------------------------------- Let us consider nonlinear equation (y')^2=f(x,y) the expression f(x,y)dx^2-dy^2=0 isn't a differential form. Then what is it? ----------------------------------- Let us consider an equation Sin(y')+y'=0 Is it possible to create equivalent differential form in this case? What about PDE? ----------------------------------- I will be gratefully for any references which are related to relation between nonlinear differential equations and differential forms. Regards, Andrzej

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