Results 1 to 11 of 11

Math Help - Inverse Differential Operator ..

  1. #1
    Member
    Joined
    Sep 2010
    Posts
    98

    Inverse Differential Operator ..

    Problem:

    Evaluate e^x \; \dfrac{1}{D(D-1)} \; x


    Solution:

    I have two ways here:

    First Way: integrate x then calculate 1/(D-1) for the result (wich is x^2/2)

    Second Way: evaluate 1/(D-1) for x then integrate the result

    The problem here is that the two ways gives different results!

    first way gives: -e^x (\dfrac{1}{2}x^2+x+1)

    second way gives: -e^x(\dfrac{1}{2}x^2+x)

    What's wrong?
    +
    Anyone know a good site contains practice problems in inverse differential operator??
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    I'm not sure I would view it that way. How about this:

    e^{x}\dfrac{1}{D(D-1)}\left[x\right]=

    e^{x}\dfrac{1}{D(D-1)}\left[\dfrac{1}{1/x}\right]=

    e^{x}\dfrac{1}{D}\left[\dfrac{1}{-x^{-2}-x^{-1}}\right]=\dots

    It depends on how you interpret the operator 1/D. It's a multiplicative inverse, right? How is the original problem stated, exactly?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Sep 2010
    Posts
    98
    \dfrac{1}{D}=\int

    This is exactly the definition for it.

    And the problem is exactly as I wrote it.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    So, what's the definition of 1/(D-1)?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Sep 2010
    Posts
    98
    You are wasting my time.
    Do not reply in this thread If you have no idea about the differential operators and thier inverses. I posted this thread to find someone help to fix my problem.
    I did not post it to explain differential operators and thier inverses.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    You are perilously close to breaking rules 3 and 11. If someone who is helping you asks for clarification, you are supposed to give it.

    Since you bring up wasting time, I could just as easily claim you are wasting my time by being unclear in the OP. I've never seen anyone write the operational inverse of an operator A as 1/A. It is always A^{-1}, for the very reason that it would be confusing otherwise.

    Without knowing more, I'd say it would be safest to apply the (D-1)^{-1} first, because operators don't always commute (in fact, they rarely do). Without knowing how you're defining (D-1)^{-1} relative to D^{-1}, I don't know whether they would commute. However, the expression

    e^{x}D^{-1}(D-1)^{-1}x

    would definitely have you evaluating (D-1)^{-1}x, followed by integrating.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Sep 2010
    Posts
    98
    Sorry for the last reply.
    You know exam's stress -_-
    Thanks for your helping, I asked my prof. and he told me that the differential operators and thier inverses do not commute.
    Thanks again.
    And I will have a good one
    Follow Math Help Forum on Facebook and Google+

  8. #8
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    Apology accepted. You're welcome for whatever help I could provide. See you around!
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Member
    Joined
    Sep 2010
    Posts
    98
    Thanks.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    Here's a thread you might find very interesting.
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Member
    Joined
    Sep 2010
    Posts
    98
    Thanks.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Differential Operator Norm
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: November 29th 2011, 06:13 AM
  2. Finding a particular solution using an inverse operator
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: June 5th 2011, 06:35 PM
  3. Adjoint of a differential operator
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 23rd 2010, 05:16 AM
  4. Inverse of discrete second derivative operator
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: September 11th 2010, 08:46 PM
  5. square of differential operator
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: April 5th 2010, 12:04 PM

Search Tags


/mathhelpforum @mathhelpforum