2. If z = g(w) is the local inverse of a conformal map w = f (z) at z0 , then there is a nbd U of z0
such that f U : U f (U ) is bijective and f (z0 ) = 0. Since f is continuous, so there is a nbd
N of z0 such that f (z) = 0 on N U . Then g : f (N ) N is
THE DERIVATION OF FOURIER SERIES
sin (a + b) = sin (a) cos (b) + cos (a) sin (b)
(1)
sin (a b) = sin (a) cos (b) cos (a) sin (b)
(2)
cos (a + b) = cos (a) cos(b) sin (a) sin (b)
(3)
cos (a b) = cos (a) cos (b) + sin (a) sin (b)
(4)
1
2
[ (1) + (2) ] :
sin
Homework 1 (Outline Solutions)
Math 424/724
Complex Analysis
1. For example, the function
z2
z 2
f (z) :=
if
if
(z) Q
(z) Q
is dierentiable at z = 0 but not analytic.
2. Note that
1
1
z n = e n log z
1
= e n cfw_ln z+i arg(z)
1
= e n cfw_ln r+i(+2k) ,
=
Review on Chapter 4 and 5
Math 424
Complex Variable
Chapter 4: The SchwarzChristoel Transformation
The SchwarzChristoel Transformation
z
(s x1 )k1 (s x2 )k2 (s xn1 )kn1 ds + B
w=A
(1)
z0
is continuous on the half plane y 0 and is conformal there except
+2+
Ledure ilute
tcfw_ArH
Ol*pfur One =
t.t
Tnr*g* )s
, Ser^.s
z= d+,bie C
7 * Abi
En
r a.buR
lz\' =
b'
onrq
i
d
O
)oc"
t.t
v.2. = d+
Le C*,=Cr[03,
_f]
l=cfw_*e'"
Y=!=r\ > o
e$[z)
A
o< O < sr[
o.^d

AtAtZ)
O
:
O
+
be
o
r)
ALZ'Z') =
*\* f.".f J
li
NORTH VANCOUVER SCHOOL DISTRICT NO. 44  DIRECTORY OF SCHOOLS
CNV
DNV
X
X
X
X
X
X
X
X
X
X
X
Secondary Schools
Argyle Secondary
Carson Graham Secondary
Continuing Education
North Vancouver Distributed Learning
Handsworth Secondary
Mountainside Secondary
Se