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Dvvhw Phdq +(, VwG +(,

W0eloov 61; 616

Orqj whup W0erqgv 817 <15

Orqj whup frus1 erqgv 913 ;1:

Odujh vwrfnv 451: 5316

Vpdoo vwrfnv 4:1: 6714

Lq dwlrq 615 718

Dyhudjh Dqqxdo Wrwdo Uhwxuqv iurp 4<59 wr 4<<9 +Uhdo,

Dvvhw Phdq +(, VwG +(,

W0eloov 31: 715

Orqj whup W0erqgv 517 4318

Orqj whup frus1 erqgv 51< 4313

Odujh vwrfnv <17 5317

Vpdoo vwrfnv 4714 6618


Uhdo uhwxuqv iurp 4<59 wr 4<<9

Vhfxulw| Lqlwldo Wrwdo Uhwxuq 7o +( s1d1, j +( s1d1,

W0Eloov '4133 4186 31: 715

Orqj Whup W0Erqgv '4133 61;4 517 4318

Frusrudwh Erqgv '4133 8187 51< 4313

Odujh Vwrfnv '4133 4871<8 <17 5317

Vpdoo Vwrfnv '4133 83;14: 4714 6618


51 Uhwxuqv rq ulvn| dvvhwv duh kljko| fruuh0odwhg wr hdfk rwkhu

Furvv Fruuhodwlrqv ri Dqqxdo Qrplqdo Uhwxuqv +4<59 � 4<<9,

Eloov W0erqgv F0erqgv O1 vwrfnv V1 vwrfnv Lq dwlrq

W0eloov 4133 3157 3155 03137 0313< 3174

O1W1 W0erqgv 4133 31<7 314; 3136 03148

O1w1 F0erqgv 4133 3158 3144 03148

Odujh vwrfnv 4133 31;4 03135

Vpdoo vwrfnv 4133 3137

Lq dwlrq 4133

Furvv Fruuhodwlrqv ri Dqqxdo Uhdo Uhwxuqv +4<59 � 4<<9,

Eloov W0erqgv F0erqgv O1 vwrfnv V1 vwrfnv

W0eloov 4133 318; 318< 3144 03139

O1W1 W0erqgv 4133 31<9 3158 313:

O1w1 F0erqgv 4133 3164 3147

Odujh vwrfnv 4133 31;4

Vpdoo vwrfnv 4133


61 Uhwxuqv rq ulvn dvvhwv duh xqfruuhodwhgryhu wlph

Vhuldo Fruuhodwlrqv ri Dqqxdo Dvvhw UhwxuqvVhuldo Fruuhodwlrq

Dvvhw Qrplqdo uhwxuq Uhdo uhwxuq

W0eloov 31<5 3199

Orqj whup W0erqgv 03134 313:

Orqj whup frus1 erqgv 3143 3154

Odujh vwrfnv 03134 03135

Vpdoo vwrfnv 313< 3139

wrslf 43 ulvn dqg uhwxuqweb.mit.edu/15.415d/www/lecture10.pdfg1jurpe24817482idoo4

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