Partial Fraction Decomposition

#Math
Decomposes a fraction of polynomials into a sum of simpler fractions

Topics

• Cover Up Method

Complex Numbers

$\displaystyle F(s)=\frac{b(s)}{a(s)}=\frac{b_{0}+b_{1}s+\ldots +b_{m}s^{m}}{a_{0}+a_{1}s+\ldots +a_{n}s^{n}}=\frac{r_{1}}{s-{\lambda}{1}}+\ldots +\frac{r{n}}{s-\lambda_{n}}$

• $\displaystyle \lambda_{1},\ldots ,\lambda_{n}$ are the poles of $\displaystyle F$
• $\displaystyle r_{1},\ldots ,r_{n}$ are the residues
• $\displaystyle \lambda_{k}=\lambda^{}{l} \leftrightarrow r*{k}=r^{*}_{l}$