My Math Forum manipulating differential operator

 Differential Equations Ordinary and Partial Differential Equations Math Forum

May 23rd, 2019, 05:57 AM   #1
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manipulating differential operator

How does the top of part B become the bottom of part B?
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 May 23rd, 2019, 12:07 PM #2 Global Moderator   Joined: Dec 2006 Posts: 21,026 Thanks: 2257 It's long division, bearing in mind that further terms can be ignored (as they wouldn't affect the final expression).
 May 23rd, 2019, 01:59 PM #3 Math Team     Joined: May 2013 From: The Astral plane Posts: 2,301 Thanks: 960 Math Focus: Wibbly wobbly timey-wimey stuff. You can also see this as a Maclaurin series in powers of D: $\displaystyle \dfrac{1}{1 - \dfrac{D}{3} + \dfrac{4D^2}{9}} \approx 1 + \dfrac{D}{3} - \dfrac{D^2}{3}$ To second order in D. -Dan Thanks from shreddinglicks
May 24th, 2019, 04:53 AM   #4
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Quote:
 Originally Posted by skipjack It's long division, bearing in mind that further terms can be ignored (as they wouldn't affect the final expression).
I tried to perform this long division but I am not getting the proper answer. I keep getting a remainder that is my original denominator.

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