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Science Forum Index » Math - Symbolic Forum » Partiel integration
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| es335 |
 Posted: Thu Feb 15, 2007 3:10 am |
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Guest
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Hi
I cannot remember how to integrate a partiel eq. In the next the "d"
is e soft d.
I have the following equation: 0 = d/dr * (1/r * d/dr * (r*v)). Here
is v=v(r) and the one I am looking for. I can see in the book that the
result is: v =1/2 * C1 * r + C2/r
but I cannot get to the result myself.
Can anyone please help me with the integration? |
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| Helmut Jarausch |
| Posted: Thu Feb 15, 2007 4:50 am |
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Guest
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es335 wrote:
Quote: Hi
I cannot remember how to integrate a partiel eq. In the next the "d"
is e soft d.
I have the following equation: 0 = d/dr * (1/r * d/dr * (r*v)). Here
is v=v(r) and the one I am looking for. I can see in the book that the
result is: v =1/2 * C1 * r + C2/r
but I cannot get to the result myself.
Can anyone please help me with the integration?
Sounds like homework?
Just a hint: if the derivate of a function is zero, the
function must be a constant.
--
Helmut Jarausch
Lehrstuhl fuer Numerische Mathematik
RWTH - Aachen University
D 52056 Aachen, Germany |
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| es335 |
| Posted: Thu Feb 15, 2007 5:18 am |
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Guest
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On 15 Feb., 09:50, Helmut Jarausch <jarau...@igpm.rwth-aachen.de>
wrote:
Quote: es335 wrote:
Hi
I cannot remember how to integrate a partiel eq. In the next the "d"
is e soft d.
I have the following equation: 0 = d/dr * (1/r * d/dr * (r*v)). Here
is v=v(r) and the one I am looking for. I can see in the book that the
result is: v =1/2 * C1 * r + C2/r
but I cannot get to the result myself.
Can anyone please help me with the integration?
Sounds like homework?
Just a hint: if the derivate of a function is zero, the
function must be a constant.
No homework unless you count selfstudy for homework. If it was
homework I would have a teacher to ask, but I don't.
I know that the derivative of a constant is zero.
But i don't know how to evaluate the expression above. I have tried
several approches, but I have realised that there must be some rules
regarding the approach I have forgotten or never learned.
Anyway, some help would come in handy. |
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| Alois Steindl |
| Posted: Thu Feb 15, 2007 5:59 am |
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Guest
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"es335" <allettidersigen@hotmail.com> writes:
Quote: On 15 Feb., 09:50, Helmut Jarausch <jarau...@igpm.rwth-aachen.de
wrote:
es335 wrote:
Hi
I cannot remember how to integrate a partiel eq. In the next the "d"
is e soft d.
I have the following equation: 0 = d/dr * (1/r * d/dr * (r*v)). Here
is v=v(r) and the one I am looking for. I can see in the book that the
result is: v =1/2 * C1 * r + C2/r
but I cannot get to the result myself.
Can anyone please help me with the integration?
Sounds like homework?
Just a hint: if the derivate of a function is zero, the
function must be a constant.
No homework unless you count selfstudy for homework. If it was
homework I would have a teacher to ask, but I don't.
I know that the derivative of a constant is zero.
But i don't know how to evaluate the expression above. I have tried
several approches, but I have realised that there must be some rules
regarding the approach I have forgotten or never learned.
Anyway, some help would come in handy.
Hello,
from your posting it is quite hard to guess how much about
differentiation and integration you know at all.
In your case you can answer this question yourself by simply checking
the proposed solution by insertin it into the differential equation.
If you know how to do that, you could just reverse your procedure step
by step.
Alois |
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| es335 |
| Posted: Thu Feb 15, 2007 7:31 am |
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Guest
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On 15 Feb., 10:59, Alois Steindl <Alois.Stei...@tuwien.ac.at> wrote:
Quote: "es335" <allettidersi...@hotmail.com> writes:
On 15 Feb., 09:50, Helmut Jarausch <jarau...@igpm.rwth-aachen.de
wrote:
es335 wrote:
Hi
I cannot remember how to integrate a partiel eq. In the next the "d"
is e soft d.
I have the following equation: 0 = d/dr * (1/r * d/dr * (r*v)). Here
is v=v(r) and the one I am looking for. I can see in the book that the
result is: v =1/2 * C1 * r + C2/r
but I cannot get to the result myself.
Can anyone please help me with the integration?
Sounds like homework?
Just a hint: if the derivate of a function is zero, the
function must be a constant.
No homework unless you count selfstudy for homework. If it was
homework I would have a teacher to ask, but I don't.
I know that the derivative of a constant is zero.
But i don't know how to evaluate the expression above. I have tried
several approches, but I have realised that there must be some rules
regarding the approach I have forgotten or never learned.
Anyway, some help would come in handy.
Hello,
from your posting it is quite hard to guess how much about
differentiation and integration you know at all.
In your case you can answer this question yourself by simply checking
the proposed solution by insertin it into the differential equation.
If you know how to do that, you could just reverse your procedure step
by step.
Alois- Skjul tekst i anførselstegn -
- Vis tekst i anførselstegn -
Hi
Yes, good suggestion. I'll try, but to my embarrassment I also fail at
this. Maybe you can help med get the hang of it.
The "d" is the partial d
The equation is: 0 = d/dr (1/r * d/dr (r*v(r))), EQ1
The result according to my book is:
v(r) = ½*C1*r + C2/r
Rearranging:
0 = v(r) - ½*C1*r - C2/r
Multiplying with r
0 = v(r)*r - ½*C1*r^2 - C2
Differentiating with r, 1. time
0 = d/dr (v(r)*r) - C1*r
Differentiating with r, 2. time
0 = d^2/dr^2 (v(r)*r) - C1
I don't think that I can rearrange this into EQ1. The C1 is in the way
and I cannot see how I can assume it to be zero at this point. And I
am missing the 1/r.
I think that my differentiation is ok (I hope), but certainly
something is wrong or missing - or I have overlooked a way to
rearrange.
When integrating EQ1, I shall start with integrating the outermost d/
dr, right? What will d/dr(d/dr (r*v(r))) be when integrated with
respect to r?
Help is much needed and appreciated. |
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| Alois Steindl |
| Posted: Thu Feb 15, 2007 8:11 am |
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Guest
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Hello,
it's much worse than I thought!
Before you proceed with this example, you should definitely consult an
introductory book about analysis and learn the difference between
differentiation and integration!
As the first two steps in testing the proposed method you have to
multiply the given expression by r and differentiate the product
w.r.t. r.
Alois |
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