- Problem 11.3:
Keep in mind that before you can apply partial fractions
decomposition, be sure that the ratio of two polynomials
is a proper fraction.
For example, 4/3 is not a proper fraction.
However, 4/3 = 1 + 1/3, and 1/3 is a proper fraction.
Recall that the Mathematica command Apart can perform partial fractions decomposition. Apart tends to reduce the fraction so that the denominators are first-order and second-order. If you want Apart to reduce a second-order polynomial into two first-order polynomials, then you will need to input a factored denominator, e.g.

In[4]:= Apart[ a / ((z - 1 + I)(z - 1 - I)) ] -I I -- a - a 2 2 Out[4]= ---------- + ---------- -1 - I + z -1 + I + z

Last updated 12/03/10. Send comments to bevans@ece.utexas.edu