3.8 Simplifying Polynomial Expressions


3.8.1 Partial Fractions


• The next is a flowchart for partial fraction expansions.



• The partial fraction expansion for,



• Consider the example below where the order of the numerator is larger than the denominator.



• When the order of the denominator terms is greater than 1 it requires an expanded partial fraction form, as shown below.



• We can solve the previous problem using the algebra technique.





3.8.2 Summation and Series


• The notation is equivalent to assuming and are integers and . The index variable is an index often replaced with j, k, m, and n.


• Operations on summations:







• Some common summations:


for both real and complex .

for both real and complex . For , the summation does not converge.

• In Scilab