Math 118 : Winter 2009 : Homework 1 Solution
January 18, 2009
1
(a)
+
g (k ) =
+
=
eikx g (x)dx
eikx f (x/a)dx
+
eikay f (y )dy
=a
= af (ak )
(b)
+
g (k ) =
+
=
eikx g (x)dx
eikx f (x)dx
+
eikx f (x)dx
=
= f (k )
contact
Kaiyuan Zhang through kzhang@math
Math 118 : Winter 2009 : Homework 2 Solution
February 13, 2009
1
f (x)dx
(1)
Rn
(1 + r) rn1 drd
=
=Cn1
(1 + r) rn1 dr
(2)
(3)
0
where Cn1 is the measure of (n 1)-dimensional sphere which is nite.
If > n,
0
0
=
0
=
(1 + r) rn1 dr
(4)
(1 + r) (1 + r)n1 dr
(
Math 118 - Winter 2009 - Midterm Exam
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