HP 49g+ - Manual (Page 151)

Page 14-6
and you will notice that the CAS default variable X in the equation writer
screen replaces the variable s in this definition. Therefore, when using the
function LAP you get back a function of X, which is the Laplace transform of
f(X).
Example 2 – Determine the inverse Laplace transform of F(s) = sin(s). Use:
‘1/(X+1)^2’ ` ILAP
The calculator returns the result: ‘X/EXP(X)’, meaning that L
-1 {1/(s+1) 2 } = x ⋅ e -x .
Fourier series
A complex Fourier series is defined by the following expression
∑
+∞
−∞ =
⋅ =
n
n
T
t in
c t f ),
2
exp( ) (
π
where
∫ ∞ − − −∞ = ⋅ ⋅
⋅ ⋅ ⋅
⋅ = T
n
n dt t
T
n i
t f
T
c
0
. ,... 2 , 1 , 0 , 1 , 2 ,..., , )
2
exp( ) (
1
π
Function FOURIER
Function FOURIER provides the coefficient c
n
of the complex-form of the
Fourier series given the function f(t) and the value of n. The function FOURIER
requires you to store the value of the period (T) of a T-periodic function into
the CAS variable PERIOD before calling the function. The function FOURIER is
available in the DERIV sub-menu within the CALC menu (
„Ö).
Fourier series for a quadratic function
Determine the coefficients c
0
, c
1
, and c
2
for the function g(t) = (t-1) 2 +(t-1), with
period T = 2.