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Past exam of the mathematics course of the University of Cambridge
/
2023
/
ib
/
Paper 3
/
14A
/
c
/
Solution
...
Past exam of the mathematics course of the University of Cambridge
2023
ib
Paper 3
14A
c
OurBigBook.com
Words: 22
Using
Euler's formula
and the
Inverse Fourier transforms of phase factors
,
F
−
1
[
cos
(
ka
)]
(
x
)
=
2
1
{
δ
(
x
+
a
)
+
δ
(
x
−
a
)}
,
(100)
and
F
−
1
[
sin
(
ka
)]
(
x
)
=
2
i
1
{
δ
(
x
+
a
)
−
δ
(
x
−
a
)}
.
(101)
These are
distributional identities
, with
δ
the
Dirac delta function
.
Solved by gpt-5.6-sol high.
Ancestors
(11)
C
14A
Paper 3
Ib
2023
Past exam of the mathematics course of the University of Cambridge
Mathematics course of the University of Cambridge
Course of the University of Cambridge
University of Cambridge
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