page 11 equation (1.2-10c), break the bar over the right side in the middle

Transcription

1 I. Corrctios Lst Updtd: Ju 00 Complx Vrils with Applictios, 3 rd ditio, A. Dvid Wusch First Pritig. A ook ought for My 007 will proly first pritig With Thks to Christi Hos of Swd pg qutio (.-0c), rk th r ovr th right sid i th middl pg 8 prolm chg multiplictio to divisio pg 9 I th footot Th xprssio! thr is fctoril missig. k! k! ( ) pg 30 I th li ov Eq (.4-9) chg z = r φ to z = r θ pg 33 li i0.995, k= 4. pg 4, li, chg som pth of stright li sgmts to som pth of rcs or li sgmts pg 44 li 3 chg complx plc to complx pl pg 44 li 3, chg z to z pg 46 prolm 8, chg 8 + i to 0.8+ i pg 6, prolm umr 0 should hv z 3iz istd of domitor of th frctio. Thr ws z missig. z 3i i th pg 9 Equtio (.6-3) is wrog: dφ dφ o th lft sid oly, rplc with.kp th ovrr d prthsis o th lft sid. dz Th right sid of th qutio is corrct. pg 06 Prolm should hv Prolm 3 should hv Prolm 5 should hv + i /+ i istd of i / i istd of + i i istd of ; /+ i / i pg I Exmpl, 3 rd li, chg y = 0 to y = θ. pg 4 i prolm 9, dd 0 ftr (turl log).

2 θ pg 9 Prolm 3, th xprssio Log cosθ θ rplcd with Log cos if if is wrog d must I prolm 4, o th right sid d to hv Not tht th θ ws missig i th ook Log( cos r ) θ +r if pg 7, prolm c) Aswr i ck (pg 66) should sy Not tht -+i is ot i cut pl. pg 3 prolm, chg i to i i pg 37 For prolm 4, sctio 3.7, thr is sig rror i th scod swr i th solutios mul: d i.76 i i pg 63 li 7 Chg f( z) = to f( z) = + +, th xprssio giv s for f ( z) i th txt is wrog. pg 69 I Exmpl 4, first li, th lowr limit of th itgrl is wrog. It should + i 0 d ot i + i0. Thus w wt 0+ i / z + i0 dz p. 70 prolm, rror i solutios mul, th umricl s. is corrct, ut d uppr limit of for th y itgrls. p. 89 i EXAMPLE 3 prt c) Vrify Thorm 8...,should chgd to Vrify Thorm 7 pg 99 Prolm 4, should rd roud z = pg 99 prolm 6, rror i solutio mul, d 3 i domitor i swr pg prolm should hv txt.] π i θ dθ = π [ot tht th dθ is missig i th 0 pg 3, prolm 7(d) th right hd sid should [ot tht thr ws missig i th xpot]. ( )! ( ) π!

3 pg 37 O th top li of th pg I should rfr to Eq. (5.-8) ot Eq. (5.-7). pg 38 EXAMPLE 6 Us Thorm to show tht th sris of Exmpl 3 divrgs for z.[istd of z > ] pg 38 DEFINITION (Asolut d Coditiol Covrgc) Th word Coditiol should dltd from th dfiitio. pg 44, Solutio. From Eq. (5.-7).. should chg (5.-7) to (5.-8). pg 44 EXAMPLE covrgt i y circulr rgio rmov th. pg 44 Four rows from ottom of pg, chg From Eq. (5.-7) to From Eq. (5.-8) pg 47 prolm 5, thr is mild rror i th solutios mul whr th sum of th sris of M trms is icorrctly sttd. pg 6, prolm 8, should ppr o th lft sid of th qutio, i.., chg / z + th mius sig o th lft i th txt to plus sig. pg 75 li 6 should rd with th id of () i.. chg th () i th txt to (). pg 9 I Figur (), w hv plottd, ot tht th () is missig i th txt. pg 9, For compriso, w hv plottd i Fig () Not tht th () is missig i th txt. pg 305, chg wordig i prolm 4 to rd is lytic i th disc z r whr r <, d is udfid for z. pg 34 I Equtio(5.8-) chg th lowr cs f ( w) to th cp F( w ) pg 34 I prolm 6 w wt cosh(/ zdz ), i.., rmov th pg 35 prolm 0 swr i solutios ook is prtly icorrct. hv simpl pol t z = othr pols r scod ordr pg 357 prolm umr 4, prt (). Th solutios mul is corrct i ssrtig tht thr is o pol t z = 0. Howvr th proof of this giv i th mul is wrog. Th mul should show tht lim f( z) = 0 which provs tht th giv fuctio dos ot hv z 0

4 limit of ifiity s zro is pprochd. Not tht th mul fils to sy tht th rsidu t z = is zro. pg 397 li 7 i th itgrl ε ε iπ chg th z to x i th domitor to rd iπ z + 4 x + 4 R R pgs Not tht limε 0 should chgd to limε 0 + throughout sctio 6.0. pg 44 5 lis from ottom of pg, To choos othr xmpl, it chg it to if pg 444 : li 7 should rd f( z) = ( z ζ) φ( z) (6.-4) w hv ddd qutio umr hr tht is (6.-4) li 0 should rd Not tht. Diffrtitig Eq. (6.-4) w rriv t w hv chgd th qutio umr from Eq.(6.) to Eq.(6.-4) li should rd Dividig Eq.(6.-4) y Eq.(6.-4), w oti pg 445 First li of th scod prgrph should rd Equtios (6.-6) d (6.-3) provid two diffrt wys... Not tht w hv chgd th first qutio umr which usd to (6.-). pg 445 rmov th scod ullt mrk d mov it to pg 447 t th d of th first prgrph, ftr th words i this cs. pg 447 lis d 3, (compr with Eq. (6.)) should chgd to (compr with Eq. (6.-4)) pg 449 prolm 3,scod figur i th solutios mul for this prolm is upsid dow,.g., d should i uppr hlf pl pg 487 prolm 6. Th hit should pply to prolm 6, ot 5 or 7. Mov th hit so tht it is xt to prolm (6) or dirctly udrth it pg 49 li 4, Eq.(6.-0) is wrog d should chgd to Eq.(6.-9) pg 505 th followig should usd i plc of lis 8- A rsult quivlt to Eq. (7.4-4) is

5 f ( x) δ ( x) = f ( x) δ( x) which c vrifid y doig th itgrtio o th right. Similrly ( ) ( ) ( ) = ( ) ( ) ( ) ( ) f x δ x f x δ x pg 59 fil prgrph should rd : s pir of qutios u= uxy (, ) d v= vxy (, ). Not tht th u is missig i u( x, y). pg 66 sctio 3.5 c) Not - + i is ot i cut pl. [th word pl is missig] pg 66 sctio 3.8Th swr to prolm 3 ) is icorrct d should chgd to.078- i.4694, i.4694 (for Mtl) Th swr to prolm 3 c) is icorrct d should giv s c) i.063, for oth. pg 665 (swr sctio)for sctio 5.8, th swr to prolm 3 should 3. f(0 T) = 0, f( T) = 0, f( T) = for ; pg 669 th idx try for Bssl fuctio, modifid, should chgd to pg 404 pg 674 th idx try for limit poit should chgd to pg 43 from 4 pg 669 Th idx try for ccumultio poit should pgs 43, 47 ot th pgs listd hr pg 67 t th top lft of pg, th idx try for oth simply coctd d multiply coctd should pg 4, ot th pg umr sttd hr. pg 675 idx try for rtio tst should iclud pg 40. pg 675 i idx d to dd Rtio tst 3, 40 pg 675 i idx d to dd Rsidu t ifiity to idx.