Chapter 1 Basic Concepts

Transcription

1 Ch Bsc Cocs oduco od: X X ε ε ε ε ε O h h foog ssuos o css ε ε ε ε ε N Co No h X Chcscs of od: cos c ddc (ucod) d s of h soss dd of h ssocd c S qusos sd: Wh f h cs of h soss o cos d dd o h ssocd s? Wh f h s of h soss s os ( X gh o ss) Wh f h d cgoc o coud? Nd d Wddu (97) oducd h gzd od Th shod h coud od o uf dff ssc chqus

2 Ou of gzd ods () od ssuos od: ( ) [ ] Gzd od: g ( ) g[ ( )] g s cd h k fuco ddo h sos hs dsuo h o f kg h fo f ( ) [ ( )] ( ) c( ) u gzd od s h so of h od s h dsuo s o d h k fuco s d fuco h gzd od ducs o h od : ( ) N Th f ( ) ( ) π ( π )

3 π π c : P (Posso) Th!! f! c : B (Bo dsuo fquc) Th f

4 4 c 4: G (G dsuo) Th () () f c ) ( ) ( 5: G (s Guss dsuo) Th

5 5 f π π π c π π () Pos of gzd od o Rsu: h sos hs dsuo h o f kg h fo c f Th [do:]

6 6 fuco khood - f Th Thus so (cou): N Th

7 7 (cou): P (Posso) (cou): B (Bo dsuo fquc) Th 4 (cou): G (G dsuo) Th

8 5 (cou): ( ) G (s Guss dsuo) Th ( ) ( ) ( ) ( ) ( ) (c) k fuco Coc k Fuco: h sos hs dsuo h o f kg h fo [ ( )] c ( ) ( ) f ( ) h k fuco g ( ) g[ ( )] k fuco s cd coc k s h Coo sd k Fucos: Th coc ks fo h foog dsuos No dsuo: g ( ) Posso dsuo: g ( ) ( ) Bo dsuo: g ( ) 8

9 4 G dsuo: g ( ) 5 s Guss dsuo: g Oh sfu k Fucos: Po k: g ( ) Φ ( ) Co - k: Po f of ks: ( ) [ ( )] g g ( ) λ ( ) λ λ od so () Bckgoud ( ) [ f ( )] { f [ h( ) ]} h h( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 9

10 d O O f s h u khood s () h Fuh u ho h Thus od h s quo o gohs c usd o o h u khood s

11 d ) ( ) ( ) ( h u khood s h h d () h os sc No-Rhso hod: Fsh s scog hod: h O Th o o gohs so s ε < N o ε < N N h ε s so scfd s u

12 No: ( ) s cd h sco fuco h ( ) foo s cd h () d ghd s squ (RS) Sco fuco d foo : h sos hs dsuo h o f kg h fo f ( ) [ ( )] ( ) c ( ) h k fuco g g [ ] Thus h -khood fuco fo h h oso s Sc [ f ( )] [ ( )] ( ) ( ) c ( ) ( ) ( ) V

13 h do V Df V Th V V sc Th khood fuco s f d fuco - khood f f Thus h sco fuco s

14 4 Fuh d sc Thfo

15 Fsh s scog hod: Th Fsh s scog hod s [ ] [ ] ( ) h [ ( ) ] d [ ( ) ] ( ) d ( ) sc Th [ ] ( ) h S ( ) ( ) h h coo of ( ) ( ) 5

16 [ ] h ( ) ( ) Fuh ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Th gh sd of Fsh s scog quo s [ ] ( ) ( ) ( ) z 6

17 h h f sd of Fsh s scog quo s h [ ] ( ) z ( ) Thus Fsh s scog quo c ducd o [ ] [ ] ( ) z ( ) z No: z dds o o d ghd s squ (RS): Th o quo c ssd fo ( z X ) T X W 7

18 h X O W O z z z z Th h u khood s h () h o s X T W z T X W X T T ( X W X ) X W z No h c hough s ghd s squ s h gh W co X d h sos co z Thus c gd T T ( X W X ) X Wz T T ( X W X ) X Wz T T ( X W X ) X W z No h h gh W s ghd (chgd) ch o Thfo so f o s d ghd s squ s W c ocd ssgg so u o [ ] T 8

19 9 Th V z g g c od h u Thus W z z z z O c od d z W X W X X T T c gd!! c gd foog h s ocss!!

20 4 sug h goodss of f Sc cs: ssu h fu od s o oso Thus u so s o oso Th h -khood fuco s c Th Suos o us ss (u) od o f h d hch Th h u od

21 Do c d c Th D od) khood(u - khood(og od) - No h D s cd h dc d c usd o su h goodss of f h h u od (cou): N Th

22 D (cou): P (Posso) Th D (cou): B (Bo dsuo fquc) Th

23 D 4 (cou): G (G dsuo) Th D

24 4 5 (cou): G (s Guss dsuo) Th D G cs: Th s od (h u od) coo us o f h d os s g g h s h d ghd s squ s Th h dc fuco D

25 5 h Th dc fuco c usd o ssss h dscc of f h g u g dc s h h dsc h d d h fd u g s g Th s h f h g gh o ss Th fos of h dcs fo dff dsuo g o: No dsuo: Posso dsuo: Bo dsuo ( fquc): G dsuo: s Guss dsuo:

26 5 Rsdus Th kds of sdus hch c usd gzd od Th Pso sdu sco sdu Dc sdu Pso sdu: P ( ) ( ) ( ) ( ) sco sdu: ssu ( ) V ( ) Th Df ( ) d V ( ) ( ) ( ) ( )( ) [ ( )] ( )( ) [ ( )] ( ) ( ) [ ( )] ( ) Th sco sdu s ( ) ( ) [ ( )] ( ) ( ) ( ) ( ) ( ) [ ( )] [ ( )] ( ) ( ) : 6

27 7 P (Posso) Th V Th d d V Th sco sdu s 6 6 Dc sdu: D d sg sg h D d