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Lecture 1 (2x2) - .CA9 58A=B=GHF5H=J9 [email protected] DCGH98 CB...

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Unformatted text preview: .CA9 58A=B=GHF5H=J9 GHIR [email protected]@56IG DCGH98 CB [email protected]?6C5F8 @5GG [email protected]=89G [email protected]@ 69 DCGH98 CB [email protected]?6C5F8 HCC *F;5B=N5H=CB C: [email protected] F95? =B H<9 [email protected] 2CIF F=;<HG 5B8 8IH=9G .CA9 8IH=9G -958 F958 -  HH9B85B79 HC [email protected] =G <=;<@M F97CAA9B898 [email protected] B979GG5FM '97HIF9 $BHFC8I7H=CB *) [email protected] '5 +5FF5 +TF9N 0( 5B8 GCA9 F=;<HG G? 5G? .& [email protected] =GGI9G H<=G =G BCH 5B 95GM 7CIFG9 IH [email protected] @=B;I=GH=7 CB9G (M CQ79 <CIFG (CB85M /I9G85M 5B8 198B9G85M 5B8 6M 5DDC=BHA9BH J=5 9 [email protected] @5D5FF5D9F9N 97CB IA8 98I *Q79 /M8=B;G $: H<9F9 =G 5BM [email protected] MCI [email protected]@ 69 BCH=O98 6M 9 [email protected] 5H @95GH <CIFG =B 58J5B79 [email protected] '5 +5FF5 +TF9N 0( 7CB '97HIF9 %5BI5FM S @J5FC '5 +5FF5 +TF9N 0( 7CB '97HIF9 F=9: [email protected]=B9 .CA9 H97<[email protected] BCH9G CB 97CBCA=7 ;FCKH< "FCKH< F5H9G .CA9 H97<[email protected] BCH9G CB 97CBCA=7 ;FCKH< "FCKH< F5H9G +F=79 =B89L9G /<9 [email protected]=CB C: [email protected] K=H< F9GD97H HC H=A9 89F=J5H9 C: H=A9 =G [email protected]@M 9LDF9GG98 5G [email protected] / KFH 9MCB8 97CBCA=7 ;FCKH< 97CBCA=7 [email protected] *F;5B=N5H=CB C: ;CJ9FBA9BH *F;5B=N5H=CBG -9A9A69F H<5H H<9 89F=J5H=J9 K=H< F9GD97H HC H=A9 =G >IGH H<9 [email protected]=CB C: H<9 [email protected] D9F IB=H C: H=A9 ∆ /<9 95G=9GH K5M HC H<=B? 56CIH 5 ;FCKH< F5H9 =G 5G D9F79BH5;9 7<5B;9 ∆ / @=A ∆ [email protected]=CB 5G=7 :F5A9KCF? 5B8 EI9GH=CBG =B CIF 7CIFG9 "FCKH< F5H9 C: & [email protected] '5 +5FF5 +TF9N 0( 7CB '97HIF9 S @J5FC '5 +5FF5 +TF9N 0( 7CB '97HIF9 .CA9 H97<[email protected] BCH9G CB 97CBCA=7 ;FCKH< "FCKH< F5H9G .CA9 H97<[email protected] BCH9G CB 97CBCA=7 ;FCKH< "FCKH< F5H9G [email protected]=75H=CB C: DF9J=CIG :57HG HC 5 [email protected] .CA9 65G=7 DFCD9FH=9G C: [email protected] @C;5F=H<AG $: $: N $: $: $: H<9B @C; @C; @C; H<9B @C; @C; @C; β H<5H ;FCKG [email protected]@M )CH9 H<5H H<9 F5H9 C: ;FCKH< C: M [email protected]@ 69 ;=J9B 6M H<9B @C; β @C; @C; H<9B / @C; H<9B I G=B; /[email protected] 9LD5BG=CB $B CH<9F KCF8G H<9 D9F79BH5;9 7<5B;9 =B DF9J=CIG 9EI5H=CB 5B8 H<9 7<5B;9 =B @C; [email protected]@5H=CBG ; 5F9 [email protected] [email protected] S @J5FC '5 +5FF5 +TF9N 0( 7CB '97HIF9 [email protected] '5 +5FF5 +TF9N 0( 7CB '97HIF9 .CA9 H97<[email protected] BCH9G CB 97CBCA=7 ;FCKH< "FCKH< F5H9G .CA9 H97<[email protected] BCH9G CB 97CBCA=7 ;FCKH< "FCKH< F5H9G "F5D<[email protected] F9DF9G9BH5H=CB C: [email protected] ;FCKH< 5B8 @C; C: [email protected] ;FCKH< $B7CA9G 5FCIB8 K9F9 @CK 9BCI;< 9J9FMK<9F9 =B H<9 [email protected] 9J9B =B H<9 F=7<9GH [email protected] /<9 F5H9 C: 97CBCA=7 ;FCKH< <58 HC 69 J9FM [email protected] HC N9FC :CF 5 J9FM @CB; H=A9 @C; @C; IH 1<M 5F9 K9 [email protected]?=B; 56CIH [email protected] F5H9G C: ;FCKH< $G =H D9FH=B9BH HC IB89FGH5B8 97CBCA=7 ;FCKH< $H 89D9B8G CB H<9 ACA9BH 5B8 [email protected] K<9F9 K9 5F9 S @J5FC '5 +5FF5 +TF9N 0( 7CB '97HIF9 $H K5G BCH [email protected] GCA9H=A9 5:H9F 69;5B 5B8 <5G 7CBH=BI98 M95F [email protected] '5 +5FF5 +TF9N 0( 7CB '97HIF9 H<5H AC89FB 97CBCA=7 ;FCKH< 5H 56CIH D9F .CA9 H97<[email protected] BCH9G CB 97CBCA=7 ;FCKH< "FCKH< F5H9G .CA9 H97<[email protected] BCH9G CB 97CBCA=7 ;FCKH< "FCKH< F5H9G [email protected] /F9B8 @=B9 =B @C; D9F 75D=H5 =B7CA9 69HK99B =B H<9 0. =G 5B8 /F9B8G =B 97CBCA=7 ;FCKH< [email protected] J5F=9G 57FCGG F9;=CBG CF 7CIBHF=9G /<9 89GD9F5H9 G=HI5H=CB C: '95GH [email protected] CIBHF=9G ' S @J5FC '5 +5FF5 +TF9N 0( 7CB '97HIF9 S @J5FC '5 +5FF5 +TF9N 0( 7CB '97HIF9 .CA9 H97<[email protected] BCH9G CB 97CBCA=7 ;FCKH< "FCKH< F5H9G .CA9 H97<[email protected] BCH9G CB 97CBCA=7 ;FCKH< "FCKH< F5H9G [email protected] '5 +5FF5 +TF9N 0( 7CB '97HIF9 [email protected] '5 +5FF5 +TF9N 0( 7CB '97HIF9 .CA9 H97<[email protected] BCH9G CB 97CBCA=7 ;FCKH< "FCKH< F5H9G .CA9 H97<[email protected] BCH9G CB 97CBCA=7 ;FCKH< "FCKH< F5H9G (CF9 7CAA9BHG .CA9 7CAA9BHG K<9B @CC?=B; 5H H<9 DF9J=CIG [email protected] )CH9 H<5H K9 :C7IG =B "+ CF =B7CA9 !CF H<9 ACGH D5FH H<=G 7CIFG9 K9 [email protected]@ [email protected]? 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56CIH 97CBCA=7 ;FCKH< K9 5F9 [email protected]@M 7CB79FB98 56CIH H<9 5ACIBH C: ;CC8G 5B8 G9FJ=79G D9F D9FGCB ∑ [email protected]@9 =B 5 GC7=9HM /<9 [email protected] K=H< H<9 DF9798=B; 9EI5H=CB =G @[email protected]@M CB9 C: 588=B; [email protected] 5B8 CF5B;9G #CK 8C K9 K9=;<H H<9 [email protected] 5B8 CF5B;9G 7CBCA=7 H<9CFM GI;;9GHG H<5H =B 7CAD9H=H=J9 A5F?9HG H<5H H<9 DF=79 C: 5 DFC8I7H [email protected] A5F;[email protected] 7CGH HC H<9 7CBGIA9F 5B8 A5F;[email protected] 69B9OH HC H<9 DFC8I79F .=B79 [email protected]@ 7CBGIA9FG ;5=B 5H @95GH 5G AI7< :FCA 7CBGIA=B; [email protected] 5G H<9 D9FGCB K<C =G H<9 A5F;[email protected] 7CBGIA9F C: [email protected] K<C =G >IGH =B8=R9F9BH 56CIH 6IM=B; 5B [email protected] CF BCH H<9 GIA C: DF=79 EI5BH=HM C: [email protected] =G 5 @CK9F 6CIB8 9GH=A5H9 C: H<9 7CBGIA9F [email protected]:5F9 C: 7CBGIA=B; [email protected] [email protected] '5 +5FF5 +TF9N 0( 7CB '97HIF9 /<9 [email protected]:5F9 BCH=CB =G 7CAD5F5H=J9 H<9 69B9OHG C: 7CBGIA=B; [email protected] 7CAD5F98 HC CH<9F ;CC8G 5B8 G9FJ=79G H5?=B; H<9 DF=79G C: CH<9F ;CC8G 5B8 G9FJ=79G 5G ;=J9B .C K<5H =: H<9 DF=79 C: [email protected] 5B8 CF5B;9G ;C9G ID 6M 5B8 H<9 DFC8I7H=CB 5B8 7CBGIADH=CB C: [email protected] 5B8 CF5B;9G GH5MG H<9 G5A9 19 8C BCH K5BH HC 7CIBH H<9 DF=79 =B7F95G9 5G 97CBCA=7 ;FCKH< G=B79 H<9 [email protected] CIHDIH =B7CA9 C: H<9 97CBCAM <5G BCH 7<5B;98 $: H<9B =B7F95G98 9J9B =: K9 [email protected]@ DFC8I79 H<9 [email protected] C: CIHDIH <5G 1<5H =G [email protected]@M 8CB9 =G HC 7CBGHFI7H 5 DF=79 =B89L [email protected] '5 +5FF5 +TF9N 0( 7CB '97HIF9 .CA9 H97<[email protected] BCH9G CB 97CBCA=7 ;FCKH< +F=79 =B89L9G 9MCB8 97CBCA=7 ;FCKH< 97CBCA=7 [email protected] 5G F9:9F9B79 H<9 19 [email protected]@ [email protected] [email protected]? 56CIH 97CBCA=7 ;FCKH< =B H<=G [email protected] 5G 5B =B7F95G9 =B D9F 75D=H5 =B7CA9 [email protected]@M A95GIF98 6M "+ D9F 75D=H54 7CBCA=7 [email protected] =B 7CBHF5GH =G 56CIH H<9 GHFI7HIF9 69<5J=CF 5B8 B5HIF9 C: H<9 97CBCAM =B 5 GC7=9HM /<=G BCH=CB F9EI=F9G HC H5?9 =BHC 577CIBH H<9 [email protected]=CBG<=DG 69HK99B [email protected]=H=7G 5B8 97CBCA=7G HC IB89FGH5B8 H<9 DFC79GG C: [email protected] 7<5B;9 1<=7< 8=R9F9B79G 69G=89G H<9 CB9G <=;<@=;<H98 K<9B @CC?=B; 5H 97CBCA=7 ;FCKH< F5H9G 75B 69 :CIB8 69HK99B [email protected] 5B8 [email protected]=B; 5F95G *F;5B=N5H=CB C: ;CJ9FBA9BH F95H=CB C: CF;5B=N5H=CBG 0G=B; DF=79G =B M95F H DF=79 =B89L =B =G $B89L 5B8 M95F 65G9 $: DF=79G K9F9 =B M95F 5B8 =B M95F $B89L $: DF=79G <5J9BPH 7<5B;98 5H [email protected]@ H<9 [email protected] N9FC 5B8 H<9 DF=79 =B89L /C 7CBJ9FH + DF=79G =BHC + [email protected] =: M95F [email protected]+ + =G H<9 65G9 / )[email protected] HC G5M H<=B;G 5F9 ACF9 [email protected]=75H98 =B H<9 [email protected] [email protected] *J9F H=A9 H<9 ?=B8 C: H<=B;G H<5H [email protected] 7CBGIA9 7<5B;9G GC H<5H H<9 7CBGIADH=CB [email protected] =G 7<5B;=B; H<FCI;< H=A9 7FCGG 7CIBHF=9G H<9 ?=B8G C: H<=B;G [email protected] 7CBGIA9 =G 8=R9F9BH F=79 =B <=B5 5B8 H<9 0. ,[email protected]=HM 5B8 7<5F57H9F=GH=7G C: 89J=79G 7<5B;9 H<=B? 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