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14-18 Computer Algebra System (CAS)
and with period T (T being equal to the contents of the
variable PERIOD).
If f(x) is a discrete series, then:
Example
Determine the Fourier coefficients of a periodic function f
with period 2π and defined over interval [0, 2π] by
f(x)=x
2
.
Typing:
STORE(2π,PERIOD)
FOURIER(X
2
,N)
The calculator does not know that N is a whole number,
so you have to replace EXP(2∗ i∗N∗π) with 1 and then
simplify the expression. We get
So if , then:
Typing:
FOURIER(X
2
,0)
gives:
so if , then:
IBP Partial integration
IBP has two parameters: an expression of the form
and .
f
x() c
N
e
2iNxπ
T
----------------
N ∞–=
∞+
∑
=
2 iNπ 2+⋅⋅ ⋅
N
2
----------------------------------
N 0≠
c
N
2 iNπ 2+⋅⋅ ⋅
N
2
----------------------------------
=
4 π
2
⋅
3
-------------
N 0=
c
0
4 π
2
⋅
3
-------------
=
ux() v' x()⋅ vx()
hp40g+.book Page 18 Friday, December 9, 2005 1:03 AM