Tutorial 1 Exercises

 

 MUUBHKGLK^ GM^LVBMI

6-65 Eimssbabemtb`k `a e`sts, slrvbel slet`r. Gmrclt A`eus bs m gmrcltbkh rlslmred abrg tdmt `rhmkbzls a`-

eus hr`ups a`r e`ksuglr-pr`nuet e`gpmkbls. Lmed a`eus hr`up dms lbhdt bknbvbnumis wd` mrl pmbn $1? plr slssb`k t` pr`vbnl e`gglkts `k klw pr`nuets. ^dlsl a`eus hr`ups gllt bk d`tlis mkn mrl iln fy m trmbkln, bknlplknlkt gmrcltbkh splebmibst dbrln fy Gmrclt A`eus. Lmed splebmibst bs pmbn m abxln rltmbklr t` e`knuet m gbkbgug kugflr `a slssb`ks mkn m plr slssb`k all `a $6,6??. M Gmrclt A`eus stmaa glgflr mttlkns lmed slssb`k t` lksurl tdmt mii tdl i`hbstbemi msplets ruk sg``tdiy. Eimssbay lmed e`st btlg (M―D) ms a`ii`ws:

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m. Nbrlet `r bknbrlet (N `r B) e`sts `a lmed bknbvbnumi a`eus hr`up. f. Qmrbmfil `r abxln (Q `r A) e`sts `a d`w tdl t`tmi e`sts `a Gmrclt A`eus edmkhl ms tdl kugflr `a a`eus hr`ups e`knuetln edmkhls. (Ba bk n`uft, slilet `k tdl fmsbs `a wdltdlr tdl t`tmi e`sts wbii edmkhl sufstmktbmiiy ba tdlrl bs m imrhl edmkhl bk tdl kugflr `a hr`ups e`knuetln.) R`u wbii dmvl tw` mkswlrs (N `r B3 Q `r A) a`r lmed `a tdl a`ii`wbkh btlgs:

E`st Btlg M. _myglkt t` bknbvbnumis bk lmed a`eus hr`up t` pr`vbnl e`gglkts `k klw pr`nuets F. Mkkumi sufserbptb`k `a Gmrclt A`eus t` E`ksuglr Vlp`rts  gmhmzbkl   gmhmzbkl E. _d`kl emiis gmnl fy Gmrclt A`eus stm ﬏ glgflr t` e`k﬍rg bknbvbnumis wbii mttlkn m a`eus hr`up slssb`k (Vle`rns `a bknbvbnumi emiis mrl k`t clpt.) N. Vltmbklr pmbn t` a`eus hr`up ilmnlr t` e`knuet =4 a`eus hr`ups plr ylmr `k klw glnbemi pr`nuets L. Vlerubtbkh e`st t` dbrl gmrcltbkh splebmibsts A. Ilmsl pmyglkt fy Gmrclt A`eus a`r e`rp`rmtl `ſtel H. E`st `a tmpls usln t` rle`rn e`gglkts gmnl fy bknbvbnumis bk m a`eus hr`up slssb`k (^dlsl tmpls mrl slkt t` tdl e`gpmky wd`sl pr`nuets mrl flbkh tlstln.)

N `r B Q `r A

D. Hms`ibkl e`sts `a Gmrclt A`eus stm ﬏ a`r e`gpmky-`wkln vldbeils (Utm﬏ glgflrs sufgbt g`ktdiy fbiis wbtd k` gbilmhl frlmcn`wks.) B. E`sts bkeurrln t` bgpr`vl tdl nlsbhk `a a`eus hr`ups t` gmcl tdlg g`rl l﬏letbvl 6-6> Eimssbabemtb`k `a e`sts, glredmknbsbkh slet`r. Fmkn F`x Lktlrtmbkglkt (FFL) `plrmtls m imrhl

st`rl bk Mtimktm, Hl`rhbm. ^dl st`rl dms f`td m g`vbl (NQN) sletb`k mkn m gusbe (EN) sletb`k. FFL rlp`rts rlvlkuls a`r tdl g`vbl sletb`k slpmrmtliy ar`g tdl gusbe sletb`k. Eimssbay lmed e`st btlg (M―D) ms a`ii`ws:

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m. Nbrlet `r bknbrlet (N `r B) e`sts `a tdl t`tmi kugflr `a NQNs s`in. f. Qmrbmfil `r abxln (Q `r A) e`sts `a d`w tdl t`tmi e`sts `a tdl g`vbl sletb`k edmkhl ms tdl t`tmi kugflr `a NQNs s`in edmkhls. (Ba bk n`uft, slilet `k tdl fmsbs `a wdltdlr tdl t`tmi e`sts wbii edmkhl sufstmktbmiiy ba tdlrl bs m imrhl edmkhl bk tdl t`tmi kugflr `a NQNs s`in.) R`u wbii dmvl tw` mkswlrs (N `r B3 Q `r A) a`r lmed `a tdl a`ii`wbkh btlgs:

E`st Btlg M. Mkkumi rltmbklr pmbn t` m vbnl` nbstrbfut`r F. E`st `a st`rl gmkmhlr‒s smimry E. E`sts `a NQNs puredmsln a`r smil t` eust`glrs N. Uufserbptb`k t` NQN ^rlkns  gmhmzbkl  gmhmzbkl L. Ilmsbkh `a e`gputlr s`atwmrl usln a`r ﬍kmkebmi funhltbkh mt tdl FFL st`rl A. E`st `a p`pe`rk pr`vbnln arll t` mii eust`glrs `a tdl FFL st`rl H. E`st `a eilmkbkh tdl st`rl lvlry kbhdt matlr ei`sbkh D. Arlbhdt-bk e`sts `a NQNs puredmsln fy FFL

N `r B Q `r A

6-6< Eimssbabemtb`k `a e`sts, gmkuameturbkh slet`r. ^dl E``plr Aurkbturl E`gpmky `a _`t`gme,

Gmryimkn, msslgfils tw` typls `a edmbrs (Vleibklrs mkn V`eclrs). Ulpmrmtl msslgfiy ibkls mrl usln a`r lmed typl `a edmbr. Eimssbay lmed e`st btlg (M―B) ms a`ii`ws:

m. `r `r bknbrlet (N `r `r A) B) e`st tdl t`tmi `k kugflr `a Vleibklrs msslgfiln. f. Nbrlet Qmrbmfil abxln (Q e`st a`r nlplknbkh d`w t`tmi e`sts edmkhl ms tdl t`tmi kugflr `a Vleibklrs msslgfiln edmkhls. (Ba bk n`uft, slilet `k tdl td l fmsbs `a wdltdlr tdl t`tmi e`sts wbii edmkhl sufstmktbmiiy ba tdlrl bs m imrhl edmkhl bk tdl t`tmi kugflr `a Vleibklrs msslgfiln.)

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EDM_^LV 6

MK BK^V@N\E^B@K ^@ E@U^ ^LVGU MKN _\V_@ULU

R`u wbii dmvl tw` mkswlrs (N `r B3 Q `r A) a`r lmed `a tdl a`ii`wbkh btlgs:

E`st Btlg M. E`st `a amfrbe usln `k Vleibklrs F. Umimry `a pufibe rlimtb`ks gmkmhlr a`r E``plr Aurkbturl E. Mkkumi e`kvlktb`k a`r aurkbturl gmkuameturlrs3 hlklrmiiy E``plr Aurkbturl mttlkns N. E`st `a iufrbemkt usln `k tdl Vleibklr msslgfiy ibkl L. Arlbhdt e`sts `a Vleibklr armgls sdbppln ar`g Nurdmg t` _`t`gme, GN A. Liletrbebty e`sts a`r Vleibklr msslgfiy ibkl (sbkhil fbii e`vlrs lktbrl pimkt) H. Xmhls pmbn t` tlgp`rmry msslgfiy-ibkl w`rclrs dbrln bk plrb`ns `a dbhd Vleibklr

N `r B Q `r A

pr`nuetb`k (pmbn `k d`uriy fmsbs) D. Mkkumi ﬍rl-bksurmkel p`ibey e`st a`r _`t`gme, GN pimkt B. Xmhls pmbn t` pimkt gmkmhlr wd` `vlrslls tdl msslgfiy ibkls a`r f`td edmbr typls 6-61 Qmrbmfil e`sts, abxln e`sts, t`tmi e`sts. Frbnhlt Msdt`k bs hlttbkh rlmny t` `plk m sgmii rlstmurmkt.

Udl bs `k m tbhdt funhlt mkn gust ed``sl fltwllk tdl a`ii`wbkh i`kh-nbstmkel pd`kl pimks:

_imk M: _my =? elkts plr gbkutl `a i`kh-nbstmkel emiibkh. _imk F: _my m ﬍xln g`ktdiy all `a $=< a`r up t` 6>? i`kh-nbstmkel gbkutls mkn 4 elkts plr gbkutl  tdlrlmatlrr (ba sdl usls  tdlrlmatl usls alwlr tdmk tdmk 6>? gbkutls gbkutls bk mky g`ktd, g`ktd, sdl stbii stbii pmys $=< $=< a`r tdl g`ktd). g`ktd). _imk E: _my m abxln g`ktdiy all `a $66 a`r up t` ?? plr Uuralr3 ^brls, $=?