ch4留數(shù)定理課件

1、ch4留數(shù)定理PPT課件ch4留數(shù)定理PPT課件DD nkkDzfzzf1Resi2dch4留數(shù)定理PPT課件Dnz1zkznc1ckcch4留數(shù)定理PPT課件 nkcDkzzfzzf1ddDnz1zkznc1ckc mcmkkmckkzzzazzfddch4留數(shù)定理PPT課件 kkczfazzfkResi2i2d1, 1,1,di21 di21Reskckkckazzzazzfzfkk1 i,2argiln1 , 01d1mzzzzmmzzzzzkkkkckckcmkcmkch4留數(shù)定理PPT課件DD 11Resi2dnkkDzfzzfDkzkc 1Resafch4留數(shù)定理PPT課件Dkzc

2、kc Dnkcczzfzzfzzfkddd1 fazzzazzfmcmkmciRes2 i2 dd1 kczfzzfkResi2d 11Resi2dnkkDzfzzfch4留數(shù)定理PPT課件Dch4留數(shù)定理PPT課件 czzfzfdlimi21Res00 RcRzzffdlimi21Resch4留數(shù)定理PPT課件 2 , 01 ,dd!11Res0111mmfmafmmm 001110dd!11Reszzmmmzfzzzmazf1azch4留數(shù)定理PPT課件)()()(010010zzaazzazzazfmmmmmmmzzazzazzaazfzz)()( )()()(00101010 非零有限

3、值mmzzazfzz00limch4留數(shù)定理PPT課件)( ! )!1()()(dd001011zzmamazfzzzmmm)()(dd)!1(1lim )( Res011100zfzzzmazfmmmzzch4留數(shù)定理PPT課件 zfzzzfzz000limRes一階極點(diǎn)一階極點(diǎn) zzzf zz ,在在z = z0 解析，且解析，且 00zz0是是 的一階零點(diǎn)的一階零點(diǎn) z 000Reszzzfch4留數(shù)定理PPT課件0)(nnmnmazf azRazazfmnnn ,0 , 21am1 , 1azm0111dd!11fmammmch4留數(shù)定理PPT課件) 1(1)(nzzf10z) 1)(

4、1(1) 1(1)(21zzzzzzfnnnnzzzzzfnnz1 ) 1)(1(1) 1(lim ) 1 ( sRe211ch4留數(shù)定理PPT課件zzfsin1)(nz 0nnznznznzzznzznzzfnz) 1(cos1lim )(sin)(lim sinlim)()(lim ch4留數(shù)定理PPT課件354i2)(zzzzfi21 i2i2i24i2)(3323zzzzzzzzzzfch4留數(shù)定理PPT課件8ii811lim )(i2limi)2( sRe3i2i2zzfzfzz8ii81i)2(1lim i21dd! 21lim )(dd! 21lim)0(sRe302203220

5、zzzzfzzfzzzch4留數(shù)定理PPT課件 11e1zzfz1 , 0zz 10Res , 10Res , 0fz 11 ,1!1e01zzznznnz 11Res , 11Res , 1fz 2Res , 1Res , 1Res ,fzch4留數(shù)定理PPT課件 ) 10( 2d1|2zzzz022zz211z zzzf212Oxy1ich4留數(shù)定理PPT課件111111221z1)1 (1 )1)(1 (1 1111222zOxy1iz1z2ch4留數(shù)定理PPT課件 222121221lim )2(1lim sRe22zzzzfzzzz 1i 121i2)( iRes22d2221|2z

6、fzzzzch4留數(shù)定理PPT課件 ?dxxfba xxfbad czzFdabl1xxycch4留數(shù)定理PPT課件cba, czzFd21,ccbaba tzz 1c2ccch4留數(shù)定理PPT課件20d)sin,(cosxxxRI2xyOz平面1x0ch4留數(shù)定理PPT課件zzzzzzRIzidi2,21|11zzxzzxzzxdi1d),(i21sin ),(21cos112xyOz平面1x0ch4留數(shù)定理PPT課件20).1(0 ,dcos11xxI221|21|112 1ii2 2di221/idzzzzzzzzzIch4留數(shù)定理PPT課件202).1(0 ,dcos211xxIzzz

7、zzzzzzzzzzzzIzzzzd)(1(iid ) 1(id)(1/id1|1|221|221|21 ,/1ch4留數(shù)定理PPT課件1i1ilim )(1(i)(lim)( sRe2zzzzfzz22121ii2Ich4留數(shù)定理PPT課件2121d)(limRRRRxxfIRRRxxfxxfPd)(limd)(ch4留數(shù)定理PPT課件dxxfI)(ch4留數(shù)定理PPT課件LRRCRzzfxxfzzfd)(d)(d)(n1)( Resi2 d)(limd)(limkkRRCRRzfzzfxxfR-R+RyCR zkORxch4留數(shù)定理PPT課件0| )(|max | )(|max |d| )

8、(|d)(d)( RCCCzzfRRzzfzzzzfzzzzfzzfRRRnkkzfxxf1)( Resi2d)()()( Resi2d)(上半平面kkzfxxfch4留數(shù)定理PPT課件)()( Resi2d)(下半平面kkzfxxf-R+RyCR zkORxch4留數(shù)定理PPT課件;i21i)i)(i)(lim(i) Resizzzfzi)i)(111)(2zzzzfi0z;i21i2I21dxxIch4留數(shù)定理PPT課件)1,2,3,( ,1d ;1d022nxxIxxInn1211i11ii)2()!1()22() 1( i)(dd)!1(1lim )(i)(dd)!1(1lim(i)

9、Resnnnnznnnznnnnzznzfzznfch4留數(shù)定理PPT課件222122)!1()!22(2i2)!1()!22(i2nnnnInn212)!1()!22(2nnIni2)!1()!22( i2)!1()22() 1( 12212nnnnnnnnch4留數(shù)定理PPT課件0 ,de)(imxxfImxch4留數(shù)定理PPT課件LRRCmzmxmzRzzfxxfzzfde)(de)(de)(iiikRmznkkRRCmzRmxRzfzzfxxfi1iie)( Resi2de)(limde)(lim-R+RyCR zkORxch4留數(shù)定理PPT課件0)(, 0, 0Imzzzfm0de)

10、(limiRCmzRzzf一致地一致地 zfNRN, 0ch4留數(shù)定理PPT課件mmRRRzzfzzfmRmRmRmRCmzCmzRRe1 de2 de2 de de)(de)(2/022/0sin0sinii如果如果 m0, 應(yīng)改為下半平面計(jì)算應(yīng)改為下半平面計(jì)算sinicoseiRRzch4留數(shù)定理PPT課件 202sinOy2/2ysiny1ch4留數(shù)定理PPT課件).0, 0( ,dcos022maxaxmxIamamaaIe2i2ei221xaxxaxImxmxde21deRe2122i22ii2eielim ei)(limeResii22ii22iiaazazazazammzazmz

11、azmzazch4留數(shù)定理PPT課件).0, 0( ,dsin0222maxaxmxxIxaxxxaxxxaxxImxmxmxdei21 dei21dei21222i0222i0222ixaxxmxdei210222ixxch4留數(shù)定理PPT課件amamamamIe4e4i2i21amazmzazmzmzazamazzzazzazzazze4 iedd eiddeResi2ii222i2222iich4留數(shù)定理PPT課件0 ,d)(mxxfIch4留數(shù)定理PPT課件實(shí)軸上上半平面)( Resi )( Resi2d)(jkxfzfxxfRjNjjCNjCRxNjxxxRLzzfzzfxxfxxfxxfzzfd)( d)(d)( d)(d)(d)(11111CRC j-RROjxjxjxch4留數(shù)定理PPT課件nkkNjCLRzfzzfIzzfj1100)( Resi2 d)(limd)(lim)( Resi i )e d(ee )e d( d)(d)(10i000iii1e 01ijkkkkxzCkkjkjCxfaaazxzaxzazzfjjj CRC j-RROjxjxjxch4留數(shù)定理PPT課件實(shí)軸上上半平面)( Resi)( Resi2 d)