DocumentCode :
856162
Title :
The operational matrices of integration and differentiation for the Fourier sine-cosine and exponential series
Author :
Paraskevopoulos, P.N.
Author_Institution :
National Technical University of Athens, Zographou, Greece
Volume :
32
Issue :
7
fYear :
1987
fDate :
7/1/1987 12:00:00 AM
Firstpage :
648
Lastpage :
651
Abstract :
For the Fourier sine-cosine series basis vector 
and the Fourier exponential series basis vector 
, a linear nonsingular transfor-marion 
is determined such that 
. This result is then used to show that the operational matrices of integration 
and 
for and , respectively, are related by the expression 
. Analogous results are derived for the corresponding operational matrices of differentiation 
and 
. General expressions are derived for 
and .
and the Fourier exponential series basis vector , a linear nonsingular transfor-marion is determined such that . This result is then used to show that the operational matrices of integration and for and , respectively, are related by the expression . Analogous results are derived for the corresponding operational matrices of differentiation and . General expressions are derived for and .Keywords :
Fourier series; Integration (mathematics); Matrices; Chebyshev approximation; Computer science; Genetic expression; Jacobian matrices; Optimal control; Sensitivity analysis; Vectors;
fLanguage :
English
Journal_Title :
Automatic Control, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9286
Type :
jour
DOI :
10.1109/TAC.1987.1104663
Filename :
1104663
Link To Document :
