Remark 8.1.  If a repeated root occurs, then the process is similar, and it is easy to show that if P(z) has degree of at most 2, then



Example 8.9.  Express  [Graphics:Images/ResidueCalcMod_gr_204.gif]  in partial fractions.  

Explore Solution 8.9.

Enter the function  [Graphics:../Images/ResidueCalcMod_gr_212.gif] and find the partial fraction expansion.  






Compare this with Mathematica's Apart  procedure for the partial fraction expansion.





In the next example we will see that our subroutine will work for complex factors and "Apart" does not.








































(c) 2006 John H. Mathews, Russell W. Howell