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Mathematical Methods by Pearson
book

Mathematical Methods by Pearson

by E. Rukmangadachari
May 2024
Intermediate to advanced content levelIntermediate to advanced
437 pages
17h 41m
English
Pearson India
Content preview from Mathematical Methods by Pearson
Fourier Series 10-7
2. Multiply-Defined or Piecewise-
Defined Functions
(a) f : [p, p] R defi ned by
0, ( , 0)
()
cos , (
, )
fx
x
p
p
=
0
in
in
(b) g : (2, 2) R defi ned
by
1, (
2, 1
)
0, ( 1,0)
()
1, (0,1)
1, (1,2)
gx
x
x
−−
=
+
in
in
in
in
are multiply-defined or piecewise-defined functions.
While e
valuating integ
rals of multiply- or
piecewise-defined functions we have to split the
interval of integration into sub-intervals and write
the integral as the sum of integrals over the respec-
tive subintervals with the corresponding values of
the function taken as the integrands. Thus,
02
02
10 1 2
210 1
() 0. cos ; ()
1. 0. (1 ) (1 )
f x dx dx x dx g x dx
dx dx x dx x dx
pp ...
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Publisher Resources

ISBN: 9781299446557Publisher Website