Notesale: Turn your study into money

Document Preview

Extracts from the notes are below, to see the PDF you'll receive please use the links above

---

A fractional rational function
(rational fraction) is called a
function in the form of a ratio
of two polynomials:

Pm ( x)
f ( x) 
Qn ( x)

A rational fraction is said to be
irregular if the degree of the
polynomial of the numerator
is equal or greater than the
degree of the polynomial of the
denominator:
m  n
...


Any irregular rational fraction
by dividing the numerator by
the denominator can be
represented as a sum of a
polynomial and a regular
rational fraction:

P( x )
R( x)
 L( x ) 

...



k1
2
Q(x) x  x1 (x  x1 )
( x  x1 )
B1
B2
Bkr

...



kr
2
x  xr ( x  xr )
( x  xr )
Cs1x  Ds1
C1x  D1

...
 2

s1
x  p1 x  q1
( x  p1 x  q1 )
M sm x  Nsm
M 1 x  N1

...
 2
sm
x  pm x  qm
(x  pm x  qm )

To find the coefficients in the
last equation, you can apply,
for example,
method of comparing coefficients
with the same degrees (method of
undetermined coefficients)

---