Prev: Proving Two Statements To Be Equal
Next: An Ultrafinite Set Theory
From: Rob Johnson on 24 Feb 2010 18:46
In article <1639156091.263730.1267038939707.JavaMail.root(a)gallium.mathforum.org>,
"cronusf(a)gmail.com" <cronusf(a)gmail.com> wrote:
>I'm looking at a book that solves a differential equation with integrating factor. In the end that get something like:
>
>L(x) = exp( int_^x()dx )
>
>Note that they omit the lower limit of integration and just keep the upper limit of integration. What does this mean? Is this a shortcut where the lower integration limit is implied somehow (it would be 0 in the context of the problem).

My guess is that

|\x
L(x) = exp( | () dx )
\|

was really intended to use the indefinite integral

|\
L(x) = exp( | () dx )
\|

Unfortunately, the extra limit, perhaps intended to make something
more explicit, is not only non-standard, but also confusing.

Rob Johnson <rob(a)trash.whim.org>
take out the trash before replying
to view any ASCII art, display article in a monospaced font
From: cronusf on 24 Feb 2010 09:24
Here is a link to the document showing the notation:

http://www.cs.cornell.edu/courses/cs667/2005sp/notes/09wang.pdf

It appears on page 2 in solving the ODE: There is an upper limit x but no lower limit.
From: mary on 24 Feb 2010 20:37

<cronusf(a)gmail.com> wrote in message
news:47549557.264970.1267057471464.JavaMail.root(a)gallium.mathforum.org...
> Here is a link to the document showing the notation:
>
> http://www.cs.cornell.edu/courses/cs667/2005sp/notes/09wang.pdf
>
> It appears on page 2 in solving the ODE: There is an upper limit x but no
> lower limit.


I think it may just indicate that both limits are on x, but they are not
specified (yet) ? (see bottom of page 2)
see bottom of page 4, he uses upper and lower



From: Robert Israel on 24 Feb 2010 20:54
"cronusf(a)gmail.com" <cronusf(a)gmail.com> writes:

> Here is a link to the document showing the notation:
>
> http://www.cs.cornell.edu/courses/cs667/2005sp/notes/09wang.pdf
>
> It appears on page 2 in solving the ODE: There is an upper limit x but no
> lower limit.

It just means an indefinite integral, considered as a function of x.
The x is unnecessary in this case.
--
Robert Israel israel(a)math.MyUniversitysInitials.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
From: David C. Ullrich on 25 Feb 2010 05:47
On Wed, 24 Feb 2010 14:15:09 EST, "cronusf(a)gmail.com"
<cronusf(a)gmail.com> wrote:

>I'm looking at a book that solves a differential equation with integrating factor. In the end that get something like:
>
>L(x) = exp( int_^x()dx )
>
>Note that they omit the lower limit of integration and just keep the upper limit of integration.
>What does this mean? Is this a shortcut where the lower integration limit is implied somehow
> (it would be 0 in the context of the problem).

I agree with others that this is a bad notation, and also that having
an "x" in the limit and also the "dx" is simply wrong. But the point
to leaving out the lower limit hasn't been mentioned as far as I can
see:

The point is that the lower limit doesn't matter. Because for example
int_0^x f(t) dt and int_1^x f(t) dt differ by a constant, and that
constant doesn't matter - if x^2 works here then x^2 + 2 also works.



First  |  Prev  |  Next  |  Last
Pages: 1 2 3
Prev: Proving Two Statements To Be Equal
Next: An Ultrafinite Set Theory