manipulating differential operator

shreddinglicks

How does the top of part B become the bottom of part B?

Attachments

• 21.2 KB Views: 21

skipjack

Forum Staff
It's long division, bearing in mind that further terms can be ignored (as they wouldn't affect the final expression).

topsquark

Math Team
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

1 person

shreddinglicks

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.