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QttoAo94middotAS fi1 =t 4 bull bull

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J~7 [97 ---) j YJ

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1- 1 10

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lufJ t (J v Av L

A L et ItfQC~ Itti 7 f ~~7rJl1 r Ii 6kyv

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• DMath Notes Part1
• DMath Notes Part2pdf

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• DMath Notes Part1
• DMath Notes Part2pdf

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• DMath Notes Part1
• DMath Notes Part2pdf

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• DMath Notes Part1
• DMath Notes Part2pdf

bull

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2 zmiddot

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bull-

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QttoAo94middotAS fi1 =t 4 bull bull

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J~7 [97 ---) j YJ

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B+ shy

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1- 1 10

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-~ t

-1 1-~z

aot 1

LIe 0 A (z)= -shy1-10z 3 n

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• DMath Notes Part1
• DMath Notes Part2pdf

r

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~ - 1u 1gt =amp0

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• DMath Notes Part1
• DMath Notes Part2pdf

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• DMath Notes Part1
• DMath Notes Part2pdf

19 j12 J 320

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• DMath Notes Part1
• DMath Notes Part2pdf

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fn ~av~ ~ fa ~oA0 v9 Cl fA v~ ()UJf~~J bull bull

Clil -I ~(rtlJ olCe~9 f ~ = 11 ~ n-1 o~o -) f2 ftf1 -fl ~ 0 Q 11

bull-

n -fJt ~ f~-lt() On ~ (4t L) tfi bull 1

(f 40 -) f ~J U)S c(( seJtICJ ~fmiddotIpoundgt

--

QZ -2 ~ - =(Alz) -oo-a-t=J-2i[Mz) -J --He) = D Fgt

Z-2[ A(z) ~ i -22) -2

z-1(

II (z) -1) -gt ~ (io) 0 1=)

A(~)-1- ~z (A(2) 1) _~z2 (f+z)) ~ 0 =-gt AIL) (lt1- tl z - ~ z~) 1 of- 22 - 2z =L

bullbull

QttoAo94middotAS fi1 =t 4 bull bull

(11Z ~)

Tof o~tftA ~ ricro oelajAD~ CJnAtJovV Ai- Y~JJ~7IIt__ l 1 p~cS(- (~

[ J 1 0 - ~ ( 1 middotc ~ tl J o middot - ~ ~~

V bull bull middot llaquov )(1 OfJ~+t cP

f fCw on 1c l6ogt tw ---t71 ~t6 7- O J110~rYv ~f9~~~ ~~Ko) rt

Y I 0 tpound) n middot bull

LI ~

J~7 [97 ---) j YJ

t 1 J ~ t1D Q I

1q ~dJ

pound1 [ ACz) -Qo 1 -10 A(z1 = 1 middot 1-~z

A(z~ ~ -4qo ~ ~~ -i(y =

A(z) (1-1OZ) 2 at ~ bull

B+ shy

bullbull

1- 1 10

1 ~ -- - 1- _ 1

-~ t

-1 1-~z

aot 1

LIe 0 A (z)= -shy1-10z 3 n

qn = (~o1l) 1011 shy

1

J (z) = bullbull 1-1 oz

lufJ t (J v Av L

A L et ItfQC~ Itti 7 f ~~7rJl1 r Ii 6kyv

~= A ~ =3 ~(2Y-l )al1t1 =-20 l

Xf~61 fflfv11f~V of ZVJV(Aql-A Tfp3P~7~A) o ~)o bull 0 e-- r tgt~OI4 5~otf~q

UiJ 71-] W U ~ n ~ 71 lIo i Y4fr 14 ~

~ C(I () Z (~)

-

r~o

r

omiddot 0 ~ oj 0

~

lt- Of-dlaquo -

~omiddot~Ct~ middot middot 1s n ifP~~ o (to nf0~ 70 11if)

C ~tl) ~ c (~-41) = t~-4~ (1 +) i () I

• DMath Notes Part1
• DMath Notes Part2pdf

n1 an = 0n- -I- Qn-2 ~ rib QC

lJ 0 Q 1 1

fJill lLf~Cl

lio l (~J )

~ t~ - l eamp(o 020 ~s l 11 IIgt

- PDf (0 7utJ

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1 iTf

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~ep 16f-4 TvJ rl f v1A c) eoJ v

ltlot 1 -t ()(z + t ~- i

G bull (0 ~ )+ 01 2~ + 0 t (n1l1

- omiddot qo + ( 1 r ~ t + (-J))

~ middotn ( n- i) 2

s

J] ~ i ~ 00 middot

--gt- Z V =7 ~ a -shyW 0 oiO

A

0

(~) -) 1w vJ I JO l

~11 V () C ( )

I

1 5151 2

cJ (4) 1 ( 5) 2 ri- + 1 z 2 2 f ~

middot l~ 1~ ~middot t) W1rT~v 1 ~~t 4 en 7 ~ao1 ( ~~ ~2 ) ~ ArzJ f f (3 Cz))r lt

00

~ 7 f 2 0 01 Z m 11 )

K Al2

_p A(z) - _ 1_o fl =i 1 Z

( ~)

O f ~ () +2--Pt ~ Z- 1 1gt 3 lt middot 2 3 A(~) = 3 - -2 ) 2 +- 9 1 - 1- - -J

1 -~2 f - z amp-2)t 1-5 1z

- q 0 - 0 0 1=-CJ 2 i a~ r bull

~ - 1u 1gt =amp0

2 zmiddot

J

~ -1 7 11 B- )btv t ~Ol

1v

2+1 1fQ~~~ 3 A(z)=z_z+2 I Qn

21 bull_ z 1 A A(2) = z~ut - (tr1)(z-2) -oz- i

z-t1 rA - tgt 1~)(2-Z) ~ L7r +shy -z Joz-1 amp

31 - - A-Ishy ~ G - 1) oz- 2 Z-J

~

bull I

- -zbull

~ g(~-L)

~qPf4I~t Av~e li~S rJltt~Us fl 670pound9fPO~gt JJYlf~~l (~ Qrtf i(t-i (tHf -1 + + (0 an ~ n- ~ Ii I f 0 7 7 i- 1

fn ~av~ ~ fa ~oA0 v9 Cl fA v~ ()UJf~~J bull bull

Clil -I ~(rtlJ olCe~9 f ~ = 11 ~ n-1 o~o -) f2 ftf1 -fl ~ 0 Q 11

bull-

n -fJt ~ f~-lt() On ~ (4t L) tfi bull 1

(f 40 -) f ~J U)S c(( seJtICJ ~fmiddotIpoundgt

--

QZ -2 ~ - =(Alz) -oo-a-t=J-2i[Mz) -J --He) = D Fgt

Z-2[ A(z) ~ i -22) -2

z-1(

II (z) -1) -gt ~ (io) 0 1=)

A(~)-1- ~z (A(2) 1) _~z2 (f+z)) ~ 0 =-gt AIL) (lt1- tl z - ~ z~) 1 of- 22 - 2z =L

bullbull

QttoAo94middotAS fi1 =t 4 bull bull

(11Z ~)

Tof o~tftA ~ ricro oelajAD~ CJnAtJovV Ai- Y~JJ~7IIt__ l 1 p~cS(- (~

[ J 1 0 - ~ ( 1 middotc ~ tl J o middot - ~ ~~

V bull bull middot llaquov )(1 OfJ~+t cP

f fCw on 1c l6ogt tw ---t71 ~t6 7- O J110~rYv ~f9~~~ ~~Ko) rt

Y I 0 tpound) n middot bull

LI ~

J~7 [97 ---) j YJ

t 1 J ~ t1D Q I

1q ~dJ

pound1 [ ACz) -Qo 1 -10 A(z1 = 1 middot 1-~z

A(z~ ~ -4qo ~ ~~ -i(y =

A(z) (1-1OZ) 2 at ~ bull

B+ shy

bullbull

1- 1 10

1 ~ -- - 1- _ 1

-~ t

-1 1-~z

aot 1

LIe 0 A (z)= -shy1-10z 3 n

qn = (~o1l) 1011 shy

1

J (z) = bullbull 1-1 oz

lufJ t (J v Av L

A L et ItfQC~ Itti 7 f ~~7rJl1 r Ii 6kyv

~= A ~ =3 ~(2Y-l )al1t1 =-20 l

Xf~61 fflfv11f~V of ZVJV(Aql-A Tfp3P~7~A) o ~)o bull 0 e-- r tgt~OI4 5~otf~q

UiJ 71-] W U ~ n ~ 71 lIo i Y4fr 14 ~

~ C(I () Z (~)

-

r~o

r

omiddot 0 ~ oj 0

~

lt- Of-dlaquo -

~omiddot~Ct~ middot middot 1s n ifP~~ o (to nf0~ 70 11if)

C ~tl) ~ c (~-41) = t~-4~ (1 +) i () I

• DMath Notes Part1
• DMath Notes Part2pdf

s

J] ~ i ~ 00 middot

--gt- Z V =7 ~ a -shyW 0 oiO

A

0

(~) -) 1w vJ I JO l

~11 V () C ( )

I

1 5151 2

cJ (4) 1 ( 5) 2 ri- + 1 z 2 2 f ~

middot l~ 1~ ~middot t) W1rT~v 1 ~~t 4 en 7 ~ao1 ( ~~ ~2 ) ~ ArzJ f f (3 Cz))r lt

00

~ 7 f 2 0 01 Z m 11 )

K Al2

_p A(z) - _ 1_o fl =i 1 Z

( ~)

O f ~ () +2--Pt ~ Z- 1 1gt 3 lt middot 2 3 A(~) = 3 - -2 ) 2 +- 9 1 - 1- - -J

1 -~2 f - z amp-2)t 1-5 1z

- q 0 - 0 0 1=-CJ 2 i a~ r bull

~ - 1u 1gt =amp0

2 zmiddot

J

~ -1 7 11 B- )btv t ~Ol

1v

2+1 1fQ~~~ 3 A(z)=z_z+2 I Qn

21 bull_ z 1 A A(2) = z~ut - (tr1)(z-2) -oz- i

z-t1 rA - tgt 1~)(2-Z) ~ L7r +shy -z Joz-1 amp

31 - - A-Ishy ~ G - 1) oz- 2 Z-J

~

bull I

- -zbull

~ g(~-L)

~qPf4I~t Av~e li~S rJltt~Us fl 670pound9fPO~gt JJYlf~~l (~ Qrtf i(t-i (tHf -1 + + (0 an ~ n- ~ Ii I f 0 7 7 i- 1

fn ~av~ ~ fa ~oA0 v9 Cl fA v~ ()UJf~~J bull bull

Clil -I ~(rtlJ olCe~9 f ~ = 11 ~ n-1 o~o -) f2 ftf1 -fl ~ 0 Q 11

bull-

n -fJt ~ f~-lt() On ~ (4t L) tfi bull 1

(f 40 -) f ~J U)S c(( seJtICJ ~fmiddotIpoundgt

--

QZ -2 ~ - =(Alz) -oo-a-t=J-2i[Mz) -J --He) = D Fgt

Z-2[ A(z) ~ i -22) -2

z-1(

II (z) -1) -gt ~ (io) 0 1=)

A(~)-1- ~z (A(2) 1) _~z2 (f+z)) ~ 0 =-gt AIL) (lt1- tl z - ~ z~) 1 of- 22 - 2z =L

bullbull

QttoAo94middotAS fi1 =t 4 bull bull

(11Z ~)

Tof o~tftA ~ ricro oelajAD~ CJnAtJovV Ai- Y~JJ~7IIt__ l 1 p~cS(- (~

[ J 1 0 - ~ ( 1 middotc ~ tl J o middot - ~ ~~

V bull bull middot llaquov )(1 OfJ~+t cP

f fCw on 1c l6ogt tw ---t71 ~t6 7- O J110~rYv ~f9~~~ ~~Ko) rt

Y I 0 tpound) n middot bull

LI ~

J~7 [97 ---) j YJ

t 1 J ~ t1D Q I

1q ~dJ

pound1 [ ACz) -Qo 1 -10 A(z1 = 1 middot 1-~z

A(z~ ~ -4qo ~ ~~ -i(y =

A(z) (1-1OZ) 2 at ~ bull

B+ shy

bullbull

1- 1 10

1 ~ -- - 1- _ 1

-~ t

-1 1-~z

aot 1

LIe 0 A (z)= -shy1-10z 3 n

qn = (~o1l) 1011 shy

1

J (z) = bullbull 1-1 oz

lufJ t (J v Av L

A L et ItfQC~ Itti 7 f ~~7rJl1 r Ii 6kyv

~= A ~ =3 ~(2Y-l )al1t1 =-20 l

Xf~61 fflfv11f~V of ZVJV(Aql-A Tfp3P~7~A) o ~)o bull 0 e-- r tgt~OI4 5~otf~q

UiJ 71-] W U ~ n ~ 71 lIo i Y4fr 14 ~

~ C(I () Z (~)

-

r~o

r

omiddot 0 ~ oj 0

~

lt- Of-dlaquo -

~omiddot~Ct~ middot middot 1s n ifP~~ o (to nf0~ 70 11if)

C ~tl) ~ c (~-41) = t~-4~ (1 +) i () I

• DMath Notes Part1
• DMath Notes Part2pdf

I

1 5151 2

cJ (4) 1 ( 5) 2 ri- + 1 z 2 2 f ~

middot l~ 1~ ~middot t) W1rT~v 1 ~~t 4 en 7 ~ao1 ( ~~ ~2 ) ~ ArzJ f f (3 Cz))r lt

00

~ 7 f 2 0 01 Z m 11 )

K Al2

_p A(z) - _ 1_o fl =i 1 Z

( ~)

O f ~ () +2--Pt ~ Z- 1 1gt 3 lt middot 2 3 A(~) = 3 - -2 ) 2 +- 9 1 - 1- - -J

1 -~2 f - z amp-2)t 1-5 1z

- q 0 - 0 0 1=-CJ 2 i a~ r bull

~ - 1u 1gt =amp0

2 zmiddot

J

~ -1 7 11 B- )btv t ~Ol

1v

2+1 1fQ~~~ 3 A(z)=z_z+2 I Qn

21 bull_ z 1 A A(2) = z~ut - (tr1)(z-2) -oz- i

z-t1 rA - tgt 1~)(2-Z) ~ L7r +shy -z Joz-1 amp

31 - - A-Ishy ~ G - 1) oz- 2 Z-J

~

bull I

- -zbull

~ g(~-L)

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fn ~av~ ~ fa ~oA0 v9 Cl fA v~ ()UJf~~J bull bull

Clil -I ~(rtlJ olCe~9 f ~ = 11 ~ n-1 o~o -) f2 ftf1 -fl ~ 0 Q 11

bull-

n -fJt ~ f~-lt() On ~ (4t L) tfi bull 1

(f 40 -) f ~J U)S c(( seJtICJ ~fmiddotIpoundgt

--

QZ -2 ~ - =(Alz) -oo-a-t=J-2i[Mz) -J --He) = D Fgt

Z-2[ A(z) ~ i -22) -2

z-1(

II (z) -1) -gt ~ (io) 0 1=)

A(~)-1- ~z (A(2) 1) _~z2 (f+z)) ~ 0 =-gt AIL) (lt1- tl z - ~ z~) 1 of- 22 - 2z =L

bullbull

QttoAo94middotAS fi1 =t 4 bull bull

(11Z ~)

Tof o~tftA ~ ricro oelajAD~ CJnAtJovV Ai- Y~JJ~7IIt__ l 1 p~cS(- (~

[ J 1 0 - ~ ( 1 middotc ~ tl J o middot - ~ ~~

V bull bull middot llaquov )(1 OfJ~+t cP

f fCw on 1c l6ogt tw ---t71 ~t6 7- O J110~rYv ~f9~~~ ~~Ko) rt

Y I 0 tpound) n middot bull

LI ~

J~7 [97 ---) j YJ

t 1 J ~ t1D Q I

1q ~dJ

pound1 [ ACz) -Qo 1 -10 A(z1 = 1 middot 1-~z

A(z~ ~ -4qo ~ ~~ -i(y =

A(z) (1-1OZ) 2 at ~ bull

B+ shy

bullbull

1- 1 10

1 ~ -- - 1- _ 1

-~ t

-1 1-~z

aot 1

LIe 0 A (z)= -shy1-10z 3 n

qn = (~o1l) 1011 shy

1

J (z) = bullbull 1-1 oz

lufJ t (J v Av L

A L et ItfQC~ Itti 7 f ~~7rJl1 r Ii 6kyv

~= A ~ =3 ~(2Y-l )al1t1 =-20 l

Xf~61 fflfv11f~V of ZVJV(Aql-A Tfp3P~7~A) o ~)o bull 0 e-- r tgt~OI4 5~otf~q

UiJ 71-] W U ~ n ~ 71 lIo i Y4fr 14 ~

~ C(I () Z (~)

-

r~o

r

omiddot 0 ~ oj 0

~

lt- Of-dlaquo -

~omiddot~Ct~ middot middot 1s n ifP~~ o (to nf0~ 70 11if)

C ~tl) ~ c (~-41) = t~-4~ (1 +) i () I

• DMath Notes Part1
• DMath Notes Part2pdf

1 5151 2

cJ (4) 1 ( 5) 2 ri- + 1 z 2 2 f ~

middot l~ 1~ ~middot t) W1rT~v 1 ~~t 4 en 7 ~ao1 ( ~~ ~2 ) ~ ArzJ f f (3 Cz))r lt

00

~ 7 f 2 0 01 Z m 11 )

K Al2

_p A(z) - _ 1_o fl =i 1 Z

( ~)

O f ~ () +2--Pt ~ Z- 1 1gt 3 lt middot 2 3 A(~) = 3 - -2 ) 2 +- 9 1 - 1- - -J

1 -~2 f - z amp-2)t 1-5 1z

- q 0 - 0 0 1=-CJ 2 i a~ r bull

~ - 1u 1gt =amp0

2 zmiddot

J

~ -1 7 11 B- )btv t ~Ol

1v

2+1 1fQ~~~ 3 A(z)=z_z+2 I Qn

21 bull_ z 1 A A(2) = z~ut - (tr1)(z-2) -oz- i

z-t1 rA - tgt 1~)(2-Z) ~ L7r +shy -z Joz-1 amp

31 - - A-Ishy ~ G - 1) oz- 2 Z-J

~

bull I

- -zbull

~ g(~-L)

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fn ~av~ ~ fa ~oA0 v9 Cl fA v~ ()UJf~~J bull bull

Clil -I ~(rtlJ olCe~9 f ~ = 11 ~ n-1 o~o -) f2 ftf1 -fl ~ 0 Q 11

bull-

n -fJt ~ f~-lt() On ~ (4t L) tfi bull 1

(f 40 -) f ~J U)S c(( seJtICJ ~fmiddotIpoundgt

--

QZ -2 ~ - =(Alz) -oo-a-t=J-2i[Mz) -J --He) = D Fgt

Z-2[ A(z) ~ i -22) -2

z-1(

II (z) -1) -gt ~ (io) 0 1=)

A(~)-1- ~z (A(2) 1) _~z2 (f+z)) ~ 0 =-gt AIL) (lt1- tl z - ~ z~) 1 of- 22 - 2z =L

bullbull

QttoAo94middotAS fi1 =t 4 bull bull

(11Z ~)

Tof o~tftA ~ ricro oelajAD~ CJnAtJovV Ai- Y~JJ~7IIt__ l 1 p~cS(- (~

[ J 1 0 - ~ ( 1 middotc ~ tl J o middot - ~ ~~

V bull bull middot llaquov )(1 OfJ~+t cP

f fCw on 1c l6ogt tw ---t71 ~t6 7- O J110~rYv ~f9~~~ ~~Ko) rt

Y I 0 tpound) n middot bull

LI ~

J~7 [97 ---) j YJ

t 1 J ~ t1D Q I

1q ~dJ

pound1 [ ACz) -Qo 1 -10 A(z1 = 1 middot 1-~z

A(z~ ~ -4qo ~ ~~ -i(y =

A(z) (1-1OZ) 2 at ~ bull

B+ shy

bullbull

1- 1 10

1 ~ -- - 1- _ 1

-~ t

-1 1-~z

aot 1

LIe 0 A (z)= -shy1-10z 3 n

qn = (~o1l) 1011 shy

1

J (z) = bullbull 1-1 oz

lufJ t (J v Av L

A L et ItfQC~ Itti 7 f ~~7rJl1 r Ii 6kyv

~= A ~ =3 ~(2Y-l )al1t1 =-20 l

Xf~61 fflfv11f~V of ZVJV(Aql-A Tfp3P~7~A) o ~)o bull 0 e-- r tgt~OI4 5~otf~q

UiJ 71-] W U ~ n ~ 71 lIo i Y4fr 14 ~

~ C(I () Z (~)

-

r~o

r

omiddot 0 ~ oj 0

~

lt- Of-dlaquo -

~omiddot~Ct~ middot middot 1s n ifP~~ o (to nf0~ 70 11if)

C ~tl) ~ c (~-41) = t~-4~ (1 +) i () I

• DMath Notes Part1
• DMath Notes Part2pdf

middot l~ 1~ ~middot t) W1rT~v 1 ~~t 4 en 7 ~ao1 ( ~~ ~2 ) ~ ArzJ f f (3 Cz))r lt

00

~ 7 f 2 0 01 Z m 11 )

K Al2

_p A(z) - _ 1_o fl =i 1 Z

( ~)

O f ~ () +2--Pt ~ Z- 1 1gt 3 lt middot 2 3 A(~) = 3 - -2 ) 2 +- 9 1 - 1- - -J

1 -~2 f - z amp-2)t 1-5 1z

- q 0 - 0 0 1=-CJ 2 i a~ r bull

~ - 1u 1gt =amp0

2 zmiddot

J

~ -1 7 11 B- )btv t ~Ol

1v

2+1 1fQ~~~ 3 A(z)=z_z+2 I Qn

21 bull_ z 1 A A(2) = z~ut - (tr1)(z-2) -oz- i

z-t1 rA - tgt 1~)(2-Z) ~ L7r +shy -z Joz-1 amp

31 - - A-Ishy ~ G - 1) oz- 2 Z-J

~

bull I

- -zbull

~ g(~-L)

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fn ~av~ ~ fa ~oA0 v9 Cl fA v~ ()UJf~~J bull bull

Clil -I ~(rtlJ olCe~9 f ~ = 11 ~ n-1 o~o -) f2 ftf1 -fl ~ 0 Q 11

bull-

n -fJt ~ f~-lt() On ~ (4t L) tfi bull 1

(f 40 -) f ~J U)S c(( seJtICJ ~fmiddotIpoundgt

--

QZ -2 ~ - =(Alz) -oo-a-t=J-2i[Mz) -J --He) = D Fgt

Z-2[ A(z) ~ i -22) -2

z-1(

II (z) -1) -gt ~ (io) 0 1=)

A(~)-1- ~z (A(2) 1) _~z2 (f+z)) ~ 0 =-gt AIL) (lt1- tl z - ~ z~) 1 of- 22 - 2z =L

bullbull

QttoAo94middotAS fi1 =t 4 bull bull

(11Z ~)

Tof o~tftA ~ ricro oelajAD~ CJnAtJovV Ai- Y~JJ~7IIt__ l 1 p~cS(- (~

[ J 1 0 - ~ ( 1 middotc ~ tl J o middot - ~ ~~

V bull bull middot llaquov )(1 OfJ~+t cP

f fCw on 1c l6ogt tw ---t71 ~t6 7- O J110~rYv ~f9~~~ ~~Ko) rt

Y I 0 tpound) n middot bull

LI ~

J~7 [97 ---) j YJ

t 1 J ~ t1D Q I

1q ~dJ

pound1 [ ACz) -Qo 1 -10 A(z1 = 1 middot 1-~z

A(z~ ~ -4qo ~ ~~ -i(y =

A(z) (1-1OZ) 2 at ~ bull

B+ shy

bullbull

1- 1 10

1 ~ -- - 1- _ 1

-~ t

-1 1-~z

aot 1

LIe 0 A (z)= -shy1-10z 3 n

qn = (~o1l) 1011 shy

1

J (z) = bullbull 1-1 oz

lufJ t (J v Av L

A L et ItfQC~ Itti 7 f ~~7rJl1 r Ii 6kyv

~= A ~ =3 ~(2Y-l )al1t1 =-20 l

Xf~61 fflfv11f~V of ZVJV(Aql-A Tfp3P~7~A) o ~)o bull 0 e-- r tgt~OI4 5~otf~q

UiJ 71-] W U ~ n ~ 71 lIo i Y4fr 14 ~

~ C(I () Z (~)

-

r~o

r

omiddot 0 ~ oj 0

~

lt- Of-dlaquo -

~omiddot~Ct~ middot middot 1s n ifP~~ o (to nf0~ 70 11if)

C ~tl) ~ c (~-41) = t~-4~ (1 +) i () I

• DMath Notes Part1
• DMath Notes Part2pdf

_p A(z) - _ 1_o fl =i 1 Z

( ~)

O f ~ () +2--Pt ~ Z- 1 1gt 3 lt middot 2 3 A(~) = 3 - -2 ) 2 +- 9 1 - 1- - -J

1 -~2 f - z amp-2)t 1-5 1z

- q 0 - 0 0 1=-CJ 2 i a~ r bull

~ - 1u 1gt =amp0

2 zmiddot

J

~ -1 7 11 B- )btv t ~Ol

1v

2+1 1fQ~~~ 3 A(z)=z_z+2 I Qn

21 bull_ z 1 A A(2) = z~ut - (tr1)(z-2) -oz- i

z-t1 rA - tgt 1~)(2-Z) ~ L7r +shy -z Joz-1 amp

31 - - A-Ishy ~ G - 1) oz- 2 Z-J

~

bull I

- -zbull

~ g(~-L)

~qPf4I~t Av~e li~S rJltt~Us fl 670pound9fPO~gt JJYlf~~l (~ Qrtf i(t-i (tHf -1 + + (0 an ~ n- ~ Ii I f 0 7 7 i- 1

fn ~av~ ~ fa ~oA0 v9 Cl fA v~ ()UJf~~J bull bull

Clil -I ~(rtlJ olCe~9 f ~ = 11 ~ n-1 o~o -) f2 ftf1 -fl ~ 0 Q 11

bull-

n -fJt ~ f~-lt() On ~ (4t L) tfi bull 1

(f 40 -) f ~J U)S c(( seJtICJ ~fmiddotIpoundgt

--

QZ -2 ~ - =(Alz) -oo-a-t=J-2i[Mz) -J --He) = D Fgt

Z-2[ A(z) ~ i -22) -2

z-1(

II (z) -1) -gt ~ (io) 0 1=)

A(~)-1- ~z (A(2) 1) _~z2 (f+z)) ~ 0 =-gt AIL) (lt1- tl z - ~ z~) 1 of- 22 - 2z =L

bullbull

QttoAo94middotAS fi1 =t 4 bull bull

(11Z ~)

Tof o~tftA ~ ricro oelajAD~ CJnAtJovV Ai- Y~JJ~7IIt__ l 1 p~cS(- (~

[ J 1 0 - ~ ( 1 middotc ~ tl J o middot - ~ ~~

V bull bull middot llaquov )(1 OfJ~+t cP

f fCw on 1c l6ogt tw ---t71 ~t6 7- O J110~rYv ~f9~~~ ~~Ko) rt

Y I 0 tpound) n middot bull

LI ~

J~7 [97 ---) j YJ

t 1 J ~ t1D Q I

1q ~dJ

pound1 [ ACz) -Qo 1 -10 A(z1 = 1 middot 1-~z

A(z~ ~ -4qo ~ ~~ -i(y =

A(z) (1-1OZ) 2 at ~ bull

B+ shy

bullbull

1- 1 10

1 ~ -- - 1- _ 1

-~ t

-1 1-~z

aot 1

LIe 0 A (z)= -shy1-10z 3 n

qn = (~o1l) 1011 shy

1

J (z) = bullbull 1-1 oz

lufJ t (J v Av L

A L et ItfQC~ Itti 7 f ~~7rJl1 r Ii 6kyv

~= A ~ =3 ~(2Y-l )al1t1 =-20 l

Xf~61 fflfv11f~V of ZVJV(Aql-A Tfp3P~7~A) o ~)o bull 0 e-- r tgt~OI4 5~otf~q

UiJ 71-] W U ~ n ~ 71 lIo i Y4fr 14 ~

~ C(I () Z (~)

-

r~o

r

omiddot 0 ~ oj 0

~

lt- Of-dlaquo -

~omiddot~Ct~ middot middot 1s n ifP~~ o (to nf0~ 70 11if)

C ~tl) ~ c (~-41) = t~-4~ (1 +) i () I

• DMath Notes Part1
• DMath Notes Part2pdf

2 zmiddot

J

~ -1 7 11 B- )btv t ~Ol

1v

2+1 1fQ~~~ 3 A(z)=z_z+2 I Qn

21 bull_ z 1 A A(2) = z~ut - (tr1)(z-2) -oz- i

z-t1 rA - tgt 1~)(2-Z) ~ L7r +shy -z Joz-1 amp

31 - - A-Ishy ~ G - 1) oz- 2 Z-J

~

bull I

- -zbull

~ g(~-L)

~qPf4I~t Av~e li~S rJltt~Us fl 670pound9fPO~gt JJYlf~~l (~ Qrtf i(t-i (tHf -1 + + (0 an ~ n- ~ Ii I f 0 7 7 i- 1

fn ~av~ ~ fa ~oA0 v9 Cl fA v~ ()UJf~~J bull bull

Clil -I ~(rtlJ olCe~9 f ~ = 11 ~ n-1 o~o -) f2 ftf1 -fl ~ 0 Q 11

bull-

n -fJt ~ f~-lt() On ~ (4t L) tfi bull 1

(f 40 -) f ~J U)S c(( seJtICJ ~fmiddotIpoundgt

--

QZ -2 ~ - =(Alz) -oo-a-t=J-2i[Mz) -J --He) = D Fgt

Z-2[ A(z) ~ i -22) -2

z-1(

II (z) -1) -gt ~ (io) 0 1=)

A(~)-1- ~z (A(2) 1) _~z2 (f+z)) ~ 0 =-gt AIL) (lt1- tl z - ~ z~) 1 of- 22 - 2z =L

bullbull

QttoAo94middotAS fi1 =t 4 bull bull

(11Z ~)

Tof o~tftA ~ ricro oelajAD~ CJnAtJovV Ai- Y~JJ~7IIt__ l 1 p~cS(- (~

[ J 1 0 - ~ ( 1 middotc ~ tl J o middot - ~ ~~

V bull bull middot llaquov )(1 OfJ~+t cP

f fCw on 1c l6ogt tw ---t71 ~t6 7- O J110~rYv ~f9~~~ ~~Ko) rt

Y I 0 tpound) n middot bull

LI ~

J~7 [97 ---) j YJ

t 1 J ~ t1D Q I

1q ~dJ

pound1 [ ACz) -Qo 1 -10 A(z1 = 1 middot 1-~z

A(z~ ~ -4qo ~ ~~ -i(y =

A(z) (1-1OZ) 2 at ~ bull

B+ shy

bullbull

1- 1 10

1 ~ -- - 1- _ 1

-~ t

-1 1-~z

aot 1

LIe 0 A (z)= -shy1-10z 3 n

qn = (~o1l) 1011 shy

1

J (z) = bullbull 1-1 oz

lufJ t (J v Av L

A L et ItfQC~ Itti 7 f ~~7rJl1 r Ii 6kyv

~= A ~ =3 ~(2Y-l )al1t1 =-20 l

Xf~61 fflfv11f~V of ZVJV(Aql-A Tfp3P~7~A) o ~)o bull 0 e-- r tgt~OI4 5~otf~q

UiJ 71-] W U ~ n ~ 71 lIo i Y4fr 14 ~

~ C(I () Z (~)

-

r~o

r

omiddot 0 ~ oj 0

~

lt- Of-dlaquo -

~omiddot~Ct~ middot middot 1s n ifP~~ o (to nf0~ 70 11if)

C ~tl) ~ c (~-41) = t~-4~ (1 +) i () I

• DMath Notes Part1
• DMath Notes Part2pdf

2+1 1fQ~~~ 3 A(z)=z_z+2 I Qn

21 bull_ z 1 A A(2) = z~ut - (tr1)(z-2) -oz- i

z-t1 rA - tgt 1~)(2-Z) ~ L7r +shy -z Joz-1 amp

31 - - A-Ishy ~ G - 1) oz- 2 Z-J

~

bull I

- -zbull

~ g(~-L)

~qPf4I~t Av~e li~S rJltt~Us fl 670pound9fPO~gt JJYlf~~l (~ Qrtf i(t-i (tHf -1 + + (0 an ~ n- ~ Ii I f 0 7 7 i- 1

fn ~av~ ~ fa ~oA0 v9 Cl fA v~ ()UJf~~J bull bull

Clil -I ~(rtlJ olCe~9 f ~ = 11 ~ n-1 o~o -) f2 ftf1 -fl ~ 0 Q 11

bull-

n -fJt ~ f~-lt() On ~ (4t L) tfi bull 1

(f 40 -) f ~J U)S c(( seJtICJ ~fmiddotIpoundgt

--

QZ -2 ~ - =(Alz) -oo-a-t=J-2i[Mz) -J --He) = D Fgt

Z-2[ A(z) ~ i -22) -2

z-1(

II (z) -1) -gt ~ (io) 0 1=)

A(~)-1- ~z (A(2) 1) _~z2 (f+z)) ~ 0 =-gt AIL) (lt1- tl z - ~ z~) 1 of- 22 - 2z =L

bullbull

QttoAo94middotAS fi1 =t 4 bull bull

(11Z ~)

Tof o~tftA ~ ricro oelajAD~ CJnAtJovV Ai- Y~JJ~7IIt__ l 1 p~cS(- (~

[ J 1 0 - ~ ( 1 middotc ~ tl J o middot - ~ ~~

V bull bull middot llaquov )(1 OfJ~+t cP

f fCw on 1c l6ogt tw ---t71 ~t6 7- O J110~rYv ~f9~~~ ~~Ko) rt

Y I 0 tpound) n middot bull

LI ~

J~7 [97 ---) j YJ

t 1 J ~ t1D Q I

1q ~dJ

pound1 [ ACz) -Qo 1 -10 A(z1 = 1 middot 1-~z

A(z~ ~ -4qo ~ ~~ -i(y =

A(z) (1-1OZ) 2 at ~ bull

B+ shy

bullbull

1- 1 10

1 ~ -- - 1- _ 1

-~ t

-1 1-~z

aot 1

LIe 0 A (z)= -shy1-10z 3 n

qn = (~o1l) 1011 shy

1

J (z) = bullbull 1-1 oz

lufJ t (J v Av L

A L et ItfQC~ Itti 7 f ~~7rJl1 r Ii 6kyv

~= A ~ =3 ~(2Y-l )al1t1 =-20 l

Xf~61 fflfv11f~V of ZVJV(Aql-A Tfp3P~7~A) o ~)o bull 0 e-- r tgt~OI4 5~otf~q

UiJ 71-] W U ~ n ~ 71 lIo i Y4fr 14 ~

~ C(I () Z (~)

-

r~o

r

omiddot 0 ~ oj 0

~

lt- Of-dlaquo -

~omiddot~Ct~ middot middot 1s n ifP~~ o (to nf0~ 70 11if)

C ~tl) ~ c (~-41) = t~-4~ (1 +) i () I

• DMath Notes Part1
• DMath Notes Part2pdf

bull I

- -zbull

~ g(~-L)

~qPf4I~t Av~e li~S rJltt~Us fl 670pound9fPO~gt JJYlf~~l (~ Qrtf i(t-i (tHf -1 + + (0 an ~ n- ~ Ii I f 0 7 7 i- 1

fn ~av~ ~ fa ~oA0 v9 Cl fA v~ ()UJf~~J bull bull

Clil -I ~(rtlJ olCe~9 f ~ = 11 ~ n-1 o~o -) f2 ftf1 -fl ~ 0 Q 11

bull-

n -fJt ~ f~-lt() On ~ (4t L) tfi bull 1

(f 40 -) f ~J U)S c(( seJtICJ ~fmiddotIpoundgt

--

QZ -2 ~ - =(Alz) -oo-a-t=J-2i[Mz) -J --He) = D Fgt

Z-2[ A(z) ~ i -22) -2

z-1(

II (z) -1) -gt ~ (io) 0 1=)

A(~)-1- ~z (A(2) 1) _~z2 (f+z)) ~ 0 =-gt AIL) (lt1- tl z - ~ z~) 1 of- 22 - 2z =L

bullbull

QttoAo94middotAS fi1 =t 4 bull bull

(11Z ~)

Tof o~tftA ~ ricro oelajAD~ CJnAtJovV Ai- Y~JJ~7IIt__ l 1 p~cS(- (~

[ J 1 0 - ~ ( 1 middotc ~ tl J o middot - ~ ~~

V bull bull middot llaquov )(1 OfJ~+t cP

f fCw on 1c l6ogt tw ---t71 ~t6 7- O J110~rYv ~f9~~~ ~~Ko) rt

Y I 0 tpound) n middot bull

LI ~

J~7 [97 ---) j YJ

t 1 J ~ t1D Q I

1q ~dJ

pound1 [ ACz) -Qo 1 -10 A(z1 = 1 middot 1-~z

A(z~ ~ -4qo ~ ~~ -i(y =

A(z) (1-1OZ) 2 at ~ bull

B+ shy

bullbull

1- 1 10

1 ~ -- - 1- _ 1

-~ t

-1 1-~z

aot 1

LIe 0 A (z)= -shy1-10z 3 n

qn = (~o1l) 1011 shy

1

J (z) = bullbull 1-1 oz

lufJ t (J v Av L

A L et ItfQC~ Itti 7 f ~~7rJl1 r Ii 6kyv

~= A ~ =3 ~(2Y-l )al1t1 =-20 l

Xf~61 fflfv11f~V of ZVJV(Aql-A Tfp3P~7~A) o ~)o bull 0 e-- r tgt~OI4 5~otf~q

UiJ 71-] W U ~ n ~ 71 lIo i Y4fr 14 ~

~ C(I () Z (~)

-

r~o

r

omiddot 0 ~ oj 0

~

lt- Of-dlaquo -

~omiddot~Ct~ middot middot 1s n ifP~~ o (to nf0~ 70 11if)

C ~tl) ~ c (~-41) = t~-4~ (1 +) i () I

• DMath Notes Part1
• DMath Notes Part2pdf

--

QZ -2 ~ - =(Alz) -oo-a-t=J-2i[Mz) -J --He) = D Fgt

Z-2[ A(z) ~ i -22) -2

z-1(

II (z) -1) -gt ~ (io) 0 1=)

A(~)-1- ~z (A(2) 1) _~z2 (f+z)) ~ 0 =-gt AIL) (lt1- tl z - ~ z~) 1 of- 22 - 2z =L

bullbull

QttoAo94middotAS fi1 =t 4 bull bull

(11Z ~)

Tof o~tftA ~ ricro oelajAD~ CJnAtJovV Ai- Y~JJ~7IIt__ l 1 p~cS(- (~

[ J 1 0 - ~ ( 1 middotc ~ tl J o middot - ~ ~~

V bull bull middot llaquov )(1 OfJ~+t cP

f fCw on 1c l6ogt tw ---t71 ~t6 7- O J110~rYv ~f9~~~ ~~Ko) rt

Y I 0 tpound) n middot bull

LI ~

J~7 [97 ---) j YJ

t 1 J ~ t1D Q I

1q ~dJ

pound1 [ ACz) -Qo 1 -10 A(z1 = 1 middot 1-~z

A(z~ ~ -4qo ~ ~~ -i(y =

A(z) (1-1OZ) 2 at ~ bull

B+ shy

bullbull

1- 1 10

1 ~ -- - 1- _ 1

-~ t

-1 1-~z

aot 1

LIe 0 A (z)= -shy1-10z 3 n

qn = (~o1l) 1011 shy

1

J (z) = bullbull 1-1 oz

lufJ t (J v Av L

A L et ItfQC~ Itti 7 f ~~7rJl1 r Ii 6kyv

~= A ~ =3 ~(2Y-l )al1t1 =-20 l

Xf~61 fflfv11f~V of ZVJV(Aql-A Tfp3P~7~A) o ~)o bull 0 e-- r tgt~OI4 5~otf~q

UiJ 71-] W U ~ n ~ 71 lIo i Y4fr 14 ~

~ C(I () Z (~)

-

r~o

r

omiddot 0 ~ oj 0

~

lt- Of-dlaquo -

~omiddot~Ct~ middot middot 1s n ifP~~ o (to nf0~ 70 11if)

C ~tl) ~ c (~-41) = t~-4~ (1 +) i () I

• DMath Notes Part1
• DMath Notes Part2pdf

QttoAo94middotAS fi1 =t 4 bull bull

(11Z ~)

Tof o~tftA ~ ricro oelajAD~ CJnAtJovV Ai- Y~JJ~7IIt__ l 1 p~cS(- (~

[ J 1 0 - ~ ( 1 middotc ~ tl J o middot - ~ ~~

V bull bull middot llaquov )(1 OfJ~+t cP

f fCw on 1c l6ogt tw ---t71 ~t6 7- O J110~rYv ~f9~~~ ~~Ko) rt

Y I 0 tpound) n middot bull

LI ~

J~7 [97 ---) j YJ

t 1 J ~ t1D Q I

1q ~dJ

pound1 [ ACz) -Qo 1 -10 A(z1 = 1 middot 1-~z

A(z~ ~ -4qo ~ ~~ -i(y =

A(z) (1-1OZ) 2 at ~ bull

B+ shy

bullbull

1- 1 10

1 ~ -- - 1- _ 1

-~ t

-1 1-~z

aot 1

LIe 0 A (z)= -shy1-10z 3 n

qn = (~o1l) 1011 shy

1

J (z) = bullbull 1-1 oz

lufJ t (J v Av L

A L et ItfQC~ Itti 7 f ~~7rJl1 r Ii 6kyv

~= A ~ =3 ~(2Y-l )al1t1 =-20 l

Xf~61 fflfv11f~V of ZVJV(Aql-A Tfp3P~7~A) o ~)o bull 0 e-- r tgt~OI4 5~otf~q

UiJ 71-] W U ~ n ~ 71 lIo i Y4fr 14 ~

~ C(I () Z (~)

-

r~o

r

omiddot 0 ~ oj 0

~

lt- Of-dlaquo -

~omiddot~Ct~ middot middot 1s n ifP~~ o (to nf0~ 70 11if)

C ~tl) ~ c (~-41) = t~-4~ (1 +) i () I

• DMath Notes Part1
• DMath Notes Part2pdf

bullbull

1- 1 10

1 ~ -- - 1- _ 1

-~ t

-1 1-~z

aot 1

LIe 0 A (z)= -shy1-10z 3 n

qn = (~o1l) 1011 shy

1

J (z) = bullbull 1-1 oz

lufJ t (J v Av L

A L et ItfQC~ Itti 7 f ~~7rJl1 r Ii 6kyv

~= A ~ =3 ~(2Y-l )al1t1 =-20 l

Xf~61 fflfv11f~V of ZVJV(Aql-A Tfp3P~7~A) o ~)o bull 0 e-- r tgt~OI4 5~otf~q

UiJ 71-] W U ~ n ~ 71 lIo i Y4fr 14 ~

~ C(I () Z (~)

-

r~o

r

omiddot 0 ~ oj 0

~

lt- Of-dlaquo -

~omiddot~Ct~ middot middot 1s n ifP~~ o (to nf0~ 70 11if)

C ~tl) ~ c (~-41) = t~-4~ (1 +) i () I

• DMath Notes Part1
• DMath Notes Part2pdf

r~o

r

omiddot 0 ~ oj 0

~

lt- Of-dlaquo -

~omiddot~Ct~ middot middot 1s n ifP~~ o (to nf0~ 70 11if)

C ~tl) ~ c (~-41) = t~-4~ (1 +) i () I

• DMath Notes Part1
• DMath Notes Part2pdf