Second Printing Typos

7/31/2019 Second Printing Typos

1/10

(x 1)2 + y2 (x 1)2 + y2

Arg(z1z2) = Arg(4i) = Arg(z1) + Arg(z2) = 23 + 56 = 32

z = ei z = ei ei

R R

h(z) = f(g(z)) h(z) = g(f(z))


2/10

D1(1) = {w : |w 1| < 1}C1(1) = {w : |w 1| = 1}

2i 2

{(u, v) : 1 < v < 8} uvv = 1 v = 8

eiei : > 8, 34 < <

ei : > 64, 32

< < 2

.

limz0

z = 0

f f

z D(0) z D(z0)

f2(z)

z = ei : > 0 < 2

|z|eiArg(z) = z


3/10

D1( i2) ={

(u, v) : u2 +(

v + 12)2

> 1}

C1(

i

2

) {(u, v) : u2 + (v + 12)2 > 1}

12

[ux vy + i(yx + uy)] = 0 12 [ux vy + i(vx + uy)] = 0

u2 = x3 3xy2 u2(x, y) = x3 3xy2

f (z) = 2x f (z) = f (x, 0) = 2x

uy = cosh x sin y = vx. uy = cosh x cos y = vx

f x y

f(z) = 1x+iy

= xx2+y2

+ i yx2+y2


4/10

D

0f(z) = 0 z D

f

|f||f|

|f||f| D1(0)

f D1(0)

k=0

zk

z2k+1

k=0

z2k

zk+1

|z0 a| = r |z0 | = r a

g(z) f(z) h(z) f(z)

z2 + 10z + 0 z2 + 10z + 9


7/10

z = 2n z = 2ni

(x2 + 4)3 (x2 + 4)2

f(z) = exp(z2) f(z) = exp(iz2)

[g, n] = limzn

(z n)f(z)cot z = f(z)cos(z) znsin(z)n lim

zncos(z) zn

sin(z)= 1

f n

2

a = 54 a =45

54

y[n] + 1 45

y[n] + 1


8/10

Argf (1+ i) = 3

2

Argf (1+ i) =

2

f (

2+ i

)= i sinh1 = Argf

(2

+ i)

= 2

f (2

+ i) = sinh 1

T(0, y) = 10 y < 1 T(0, y) = 10 y > 1

T(x, y) = 0 2

< x < 2

T(x, 0) = 0 2

< x < 2

4u2

(r+1r )2 +

4v2

(r1r )2 = 1

u2

(r+1r )2 +

v2

(r1r )2 = 1

u2

cos2 v2

sin2 = 1 u

2

4cos2 v2

4sin2 = 1

F(z) = lima0

log(z)log(za)2a

F(z) = lima0

log(z+a)log(za)2a

(x, y) = y2 ln(x1)2+y2

(x+1)2+y2+ x

Arctan y

x1 x

Arctany

x


9/10

f (z) = A(z + 1)1

2 (z 1) 12 f (z) = A(z + 1) 12 (z 1)12

x2 = x2 = 0

F(eiw0tU(t)) F(eiw0tU(t))

F(

ea|t|)

= a(a2+w2)

a > 0

F(i sint1t2

)F(sintt21

)

1|w|4

1|w|4

1|w|4

1|w|4

t 1 + et t 1 + et

1 cos t 1 + cos t

ln s2

s2+112 ln s

2

s2+1


10/10

F (ea|t|) = a(a

2

+w2

)

a > 0

1|w|4

1|w|4

(0 + 0i) = 1+i

= 1s

(0 + 0i) 1+i

= 1+i

= 1s

L(et

)L(cos t) L(et

)L(cos t)

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