<s>
In	O
mathematics	O
,	O
the	O
study	O
of	O
interchange	B-Algorithm
of	I-Algorithm
limiting	I-Algorithm
operations	I-Algorithm
is	O
one	O
of	O
the	O
major	O
concerns	O
of	O
mathematical	O
analysis	O
,	O
in	O
that	O
two	O
given	O
limiting	O
operations	O
,	O
say	O
L	O
and	O
M	O
,	O
cannot	O
be	O
assumed	O
to	O
give	O
the	O
same	O
result	O
when	O
applied	O
in	O
either	O
order	O
.	O
</s>
<s>
This	O
approach	O
justifies	O
,	O
for	O
example	O
,	O
the	O
notion	O
of	O
uniform	B-Algorithm
convergence	I-Algorithm
.	O
</s>
<s>
An	O
opinion	O
apparently	O
not	O
in	O
favour	O
of	O
the	O
piece-wise	O
approach	O
,	O
but	O
of	O
leaving	O
analysis	O
at	O
the	O
level	O
of	O
heuristic	B-Algorithm
,	O
was	O
that	O
of	O
Richard	O
Courant	O
.	O
</s>
<s>
Many	O
of	O
the	O
fundamental	O
results	O
of	O
infinitesimal	O
calculus	O
also	O
fall	O
into	O
this	O
category	O
:	O
the	O
symmetry	O
of	O
partial	O
derivatives	B-Algorithm
,	O
differentiation	B-Algorithm
under	O
the	O
integral	O
sign	O
,	O
and	O
Fubini	O
's	O
theorem	O
deal	O
with	O
the	O
interchange	O
of	O
differentiation	B-Algorithm
and	O
integration	O
operators	O
.	O
</s>
<s>
Interchange	O
of	O
partial	O
derivatives	B-Algorithm
:	O
</s>
<s>
Interchange	O
of	O
derivative	B-Algorithm
and	O
integral	O
:	O
</s>
