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Diffstat (limited to 'latex/know/concept/partial-fraction-decomposition/source.md')
| -rw-r--r-- | latex/know/concept/partial-fraction-decomposition/source.md | 12 |
1 files changed, 5 insertions, 7 deletions
diff --git a/latex/know/concept/partial-fraction-decomposition/source.md b/latex/know/concept/partial-fraction-decomposition/source.md index aa03f9c..69428e7 100644 --- a/latex/know/concept/partial-fraction-decomposition/source.md +++ b/latex/know/concept/partial-fraction-decomposition/source.md @@ -3,7 +3,7 @@ # Partial fraction decomposition -*Partial fraction decomposition* or *expansion* is a method to rewrite a +**Partial fraction decomposition** or **expansion** is a method to rewrite a quotient of two polynomials $g(x)$ and $h(x)$, where the numerator $g(x)$ is of lower order than $h(x)$, as a sum of fractions with $x$ in the denominator: @@ -21,9 +21,9 @@ $$\begin{aligned} } \end{aligned}$$ -Then the constant coefficients $c_n$ can either be found the hard way, +The constants $c_n$ can either be found the hard way, by multiplying the denominators around and solving a system of $N$ -equations, or the easy way by using the following trick: +equations, or the easy way by using this trick: $$\begin{aligned} \boxed{ @@ -31,8 +31,7 @@ $$\begin{aligned} } \end{aligned}$$ -If $h_1$ is a root with multiplicity $m > 1$, then the sum takes the -form of: +If $h_1$ is a root with multiplicity $m > 1$, then the sum takes the form of: $$\begin{aligned} \boxed{ @@ -41,8 +40,7 @@ $$\begin{aligned} } \end{aligned}$$ -Where $c_{1,j}$ are found by putting the terms on a common denominator, -e.g.: +Where $c_{1,j}$ are found by putting the terms on a common denominator, e.g. $$\begin{aligned} \frac{c_{1,1}}{x - h_1} + \frac{c_{1,2}}{(x - h_1)^2} |