11高等数学完整版详细PPT演示课件

1、ab),(zyxkkkks),(nk 10limmks1kmkm),(kkkkkkksf),(),(zyxfszyxfd),(是定),(zyxf),(zyxfszyxmd),(nk 10limks1kmkm),(kkkkknkksf),(lim10lsyxfd),( ldsyxf),(?d 表示什么问lsszyxfd ),() 1 (szyxfkd),()2(szyxfd),()3(21, sd)4(),(zyxgszyxfd),(szyxgd),(szyxfkd),(l21d),(d),(szyxfszyxftttttfsdyxfld)()()(, )(),(22),(yxf设)()(tty

2、),(:txl,d),(存在lsyxfkknkksf),(lim10lsyxfd),(, ,1kkktt),(kktttskkttkd)()(122,)()(22kkktnk 10limlsyxfd),(kkkt)()(22 )(, )(kkf连续注意)()(22tt), 1 ,0(nktk,1kkkttnk 10limkkkt)()(22 )(, )(kkfxdydsdxyolsyxfd),(tttttfd)()()(),(22, 0, 0) 1 (kkts!22)(d)(ddyxstttd)()(22x),()(bxaxylsyxfd),(),()(: rrlsyxfld),()sin)(

3、,cos)(rrf)()(, )(),(:ttztytxszyxfd),(ttttd)()()(222xx d)(12d)()(22rrbaxxf) )(,()(),(, )(tttf,dlsx2xy )10(:2xxyllsxd10 xxxd)2(12xxxd4110210232)41 (121x)155(1211lxy2xy o) 1 , 1 (b2r xyolsyild2d)cos()sin(sin2222rrrdsin23 r0342sin22 r)cossin(3 r)(sincos:ryrxl,dsxil)0()()(222222ayxayx)40(2cos:1 arlsxild4

4、14022d)()(cos4rrr402dcos4a222a,2cos:22arlyox,d)(222szyxszyxd)(22220222)()sin()cos(t ktatattkakad202222202322223tktaka)43(3222222kakatktatad)cos()sin(222)20(,sin,costtkztaytax,d2sx2222azyx0zyxsx d2szyxsxd)(31d2222sa d312aa2312332asy d2sz d2kkknkksf),(lim10szyxfd),(kknkksf),(lim10lsyxfd),(szyxgzyxfd),

5、(),() 1 (21d),(d),(d),()2(szyxfszyxfszyxf),(21组成由ls d)3(lszyxfd),(),(为常数szyxgld),(, )( , )(, )(:ttytxllsyxfd),(, )()(:bxaxyllsyxfd),(baxxf) )(,(),()(: rrllsyxfd),()sin)(,cos)(rrftttd)()(22xx d)(12d)()(22rr)(),(ttf134:22yxlsyxxyld)432(220d2sxylsyxld)34(1222sld12a12o22yx3sxyld2sxyld2上sxyld2下x2xyd1222)

6、(2xxyd1222xyo, ar 04seicyxd222)24(aeaa4xy 0yar xeiaxd0d40aeaxeaxd22022021ablxycosabfw abf abf),(, ),(),(yxqyxpyxf221kmkmabxylkkmm1),(kkyx),(kkkkkkyqxp),(),(kk,kwkkmm1kkkkmmfw1),(k),(kkfnkkww1kkmm1kkmm1kykx23nkw1kkkkkkyqxp),(),(nkw10limkkkkkky)q(x)p,(1kmkmabxyl),(kkfkykx24lyyxqxyxpd),(d),(kkkxp),(kkk

7、yq),(nk 10lim, ),(yxp),(, ),(),(yxqyxpyxf),(yxf),(yxq25lxyxpd),(,),(lim10nkkkkxplyyxqd),(,),(lim10nkkkkyq)d,(ddyxs llyyxqxyxpsfd),(d),(d),(, ),(, ),(),(zyxrzyxqzyxpzyxfzzyxryzyxqxzyxpsfd),(d),(d),(d)d,d,(ddzyxs 26), 1(kililyyxqxyxpd),(d),(kiliyyxqxyxp1d),(d),(lyyxqxyxpd),(d),(lyyxqxyxpd),(d),(27),(,

8、 ),(yxqyxp设)()(tytx,:tlyyxqxyxpd),(d),( )(),(ttp)(t)(ttd)(),(ttq0)()(22tt且28,:),(baxxyxxxqxxpbad )(,)(,)(xlyyxqxyxpd),(d),(zzyxryzyxqxzyxpd),(d),(d),()(t)(t)(t)(, )(),(tttq)(, )(),(tttrtd )(, )(),(tttp,:)()()(ttztytx29,dlxyxxy 2obaol:01:,:xxyao10:,:xxyobobaolxyxxyxxyxdddxxxd)(0154d21023xxyyyyxyxld)(

9、d2112xyxy 11:,:2yyxl54d2114yyxxxd10) 1, 1 ()1, 1(ba到)1 , 1(b)1, 1( aoyx30,:, 0aaxyybaoaa x,d2xyl0:,sin,costtaytaxxyld2ttadsin2203332axyld2ta202sinttad)sin(132334aaaxd0031yxo,dd22yxxyxl; 10:,:2xxyl;10:,:2yyxl.:aboal22xxxx d4103yyy222yy d5104yxxyxoadd22102d)002(xxx1)0, 1(a)1 , 1(b2yx 2xy 10(xxxd)2210(

10、yyd)4yxxyxabdd2210d)102(yy1132),2,0,(krb)0, 0,(ra.)2(abzzyxxydddttkr2022d)(kttzyrx20:,0,abzzyxxydddktt20dbazyx;,sin,cos) 1(tkztrytrx)(222rk 222k),(zxyfsfwdsfwd33)()(, )( ttyytxxlyyxqxyxpd),(d),(lsyxqyxpdcos),(cos),(34zryqxpdddsrqpdcoscoscos35yyxqxyxpld),(d),(0222xyx).0 , 2()0 , 0(bo到从oyxbyyxqxyxpld)

11、,(d),(syxqyxpld),(),(22xx )1(x36kkkknkyqxp),(),(limkk10lyyxqxyxpd),(d),(), 1(kililyyxqxyxpd),(d),(ilkiyyxqxyxpd),(d),(1lyyxqxyxpd),(d),(lyyxqxyxpd),(d),(37,)()(:tytxl: tlyyxqxyxpd),(d),(tttqttpd )(),( )(),()(t)(tbaxxyl:, )(:xxxqxxpbad )(,)(,)(xlyyxqxyxpd),(d),(38zzyxryzyxqxzyxpd),(d),(d),(:,)()()(tt

12、ztytx)(, )(),(tttp)(t)(t)(tlyqxpddsqpldcoscoszryqxpdddsrqpdcoscoscos)(, )(),(tttq)(, )(),(tttrtd 39)0 , 0 , 1 (a)0 , 1 , 0(b) 1 , 0 , 0(coxyzzyyxidddi001d)1 (yy10dx2)211 ( 12101d2 x1 yx1 zyyxabddzyybcddoaxd40zxoyabzk222zyxkzjyi xzklzyxzzzyyxxk222ddd:l22 tx22 ty1 tz) 10:(t101d3ttk2ln3k)1 ,2,2(a, )2,4

13、,4(bsfwldf)(0r) 1 , 2 , 2(abr412222azyxaxyx22,)0, 0(的交线az.ddd222zxyzxyc22222)()(aayx222yxaztxaacos22tyasin22sintaz 20:t42ta38sin3tttadcos)cos1 (2283tu20uuuaacoscossin2223833uuuadsin)cos1 (22830232auuudcos2cos134attacossin222343ozyx,d)(d)(d)(zyxyzxxyzi,2122zyxyx,sin,costytx)02:(sincos2tttz20itttcos)s

14、incos22(tttttd )sin)(cossin(costt d)cos41 (220)sin)(cos2(tt 244kkknkksf),(lim10szyxfd),(kknkksf),(lim10lsyxfd),(szyxgzyxfd),(),() 1 (21d),(d),(d),()2(szyxfszyxfszyxf),(21组成由ls d)3(lszyxfd),(),(为常数szyxgld),(45, )( , )(, )(:ttytxllsyxfd),(, )()(:bxaxyllsyxfd),(baxxf) )(,(),()(: rrllsyxfd),()sin)(,cos)

15、(rrftttd)()(22xx d)(12d)()(22rr)(),(ttf46kkkknkyqxp),(),(limkk10lyyxqxyxpd),(d),(), 1(kililyyxqxyxpd),(d),(ilkiyyxqxyxpd),(d),(1lyyxqxyxpd),(d),(lyyxqxyxpd),(d),(47,)()(:tytxl: tlyyxqxyxpd),(d),(tttqttpd )(),( )(),()(t)(tbaxxyl:, )(:xxxqxxpbad )(,)(,)(xlyyxqxyxpd),(d),(48lyqxpddsqpldcoscoszryqxpddds

16、rqpdcoscoscos4950ld, ),(yxp),(yxqldyqxpyxypxqdddd51bxaxyxd)()(:21dycyxyd)()(:21yxxqddddcyyyqd),(2)()(21dyyxxqcbeyyxqd),(caeyyxqd),(cbeyyxqd),(eacyyxqd),(dcyyyqd),(1dcyddcyxoecbabad52yxxqdddlyyxqd),(yxypdddlxyxpd),(ldyqxpyxypxqdddd53yxol1dnd2dnkdyxypxqk1ddyxypxqdddnkdkyqxp1ddlyqxpdd)(的正向边界表示kkdd54lxy

17、yxadd21ldyqxpyxypxqdddd20,sincos:byaxllxyyxadd212022d)sincos(21ababab550dd22yxxyxl,22xqyxpypxqyxxyxldd22022xxdyxdd0056,dd2dyyxe2, 0yexqpypxqdyyxedd2dyyexd2yexoayd2yeyyd102)1(211exy oyx) 1 , 1 (a) 1 , 0(bd2ye57,dd22lyxxyyx,022时则当 yx22222)(yxxyxq,)0 , 0(时当d0dd22lyxxyyx,22yxyp22yxxqypyxol58dsincos20222

18、22rrr2,)0 , 0(时当d,:222ryxl1d1dlyxxyyx22ddlyxxyyx22ddllyxxyyx22dd0dd01yxdllyxxyyxyxxyyx2222ddddl1dloyx59),(),(yxqyxp.0ddlyqxpyqxpdd ),(yxuyqxpyxudd),(d.xqyplyqxpdd6021, ll21ddddllyqxpyqxp1ddlyqxp2ddlyqxp21ddllyqxp0ab1l2l2ddlyqxp1ddlyqxpbayqxpddabyqxpdd61),(00yxa),(),(00dd),(yxyxyqxpyxu),(),(yxuyxxuux

19、),(yxpxuxuxx0lim),(lim0yxxpx),(),(ddyxxyxyqxp),(),(dyxxyxxpxyxxp),(yu),(yxqyqxpuddd),(yxxc),(yxb),(00yxa62yqxpuddd),(),(yxqyuyxpxuxyuyxu22所以xqypxyuxqyxuyp22,63dd 上因此在dxqypyxxqxqyqxplddd)(ddddl064yx,xqypdyx),(00,),(dyxyyxqxyxpyxuyxyxd),(d),(),(),(),(00 xxxyxp0d),(0yyyyxqyxu0d),(),(00y0 xyyyyxq0d),(xx

20、xyxp0d),(65ya xol,d)(d)3(22yxyxyxl24xxy,aodyxyxyxaold)(d)3(22dyxdd4oayxyxyxd)(d)3(22402dxx3648 66yyxxyxdd22,22yxqyxpxqyxyp2yyxxyxuddd22),()0 , 0(22dd),(yxyyxxyxyxu)0 , 0(),(yx)0 ,(xxxx0d0yyxyd02yyxyd022221yx6722ddyxxyyx2222,yxxqyxyp)0()(22222xyqyxxyxp),()0 , 1 (22dd),(yxyxxyyxyxuxx1d0)0(arctanxxyoxy

21、yyxyx022d)0 ,(x)0 , 1(),(yx68oxy)0 ,(x)0 , 1(),(yx),()0 , 1 (22dd),(yxyxxyyxyxu), 1 (y69lyqxpddypxqyqxpudddyxypxqdddlyqxpdd0ddlyqxp70,4:, 1:222412yxlyxllyxxyyx22d4d) 1(lyxxyyx22d4dlxyyxd4d41do2y1x2lldd5415lyxxyyx22dd)2(lyxxyyx22ddlxyyxdd41dd2412时022 yxypxq) 1(ypxq)2(71, )56,4(),(grad42234yyxxyxyxu).

22、,(yxu求),(dyxuxxyxd)4(34yyyxd)56(422),(yxuyox),(yx)0 ,(xxxxd04yyyxyd)56(0422c551x322yxcy 5xxyxd)4(34yyyxd)56(422),()0 , 0(yxc72cccdyxoaacyxaxyxaxxaycd)ln(2d22222222ayx), 0(a), 0(a321aaayayd)ln2(d222xaya222xayyxddc7374oxyz),(zyxkkkks),(nk 10limm),(kkk75szyxmd),(kkkksf),(nk 10limszyxfd),(ssd76,21szyxfd

23、),(1d),(szyxf2d),(szyxfszyxgkzyxfkd),(),(21则为常数设,21kkszyxgkszyxfkd),(d),(21),(zyxf若77oxyzyxdyxyxzz),(),(:szyxfd),(yxdyxf),(szyxfd),(),(yxzyxyxzyxzyxdd),(),(122yxd),(kkkyxk)(78zydzyzyxx),(),(zxdzxzxyy),(),(或79yxd,dzs222zyx)0(ahhzyxdyxyxaz),( ,:2222222:hayxdyx221yxzz 222yxaazsd20da0)ln(2122222haraahaa

24、ln2yxdyxayxa222dd22022dhararr2aoxzyha802222azyx) (dzs) (dzs0hln4aahhoxzy81,dszyxozyx1114321,4dszyx,1:4yxz1010:),(xxydyxyxxyyxy10d)1 (12031zyx, 0, 0, 0zyx10d3xx1zyx4321szyxd82xozy2222:azyx),(zyxf.d),(szyxfi22yxz的222yxaz.,2222122azayx 1设,),(22122ayxyxdyx,22yx ，022yxz当22yxz当1yxd1d)(22syxi831d)(22syxiyx

25、dyx)(22rrraraadd202222021)258(614a222yxaayxddxozy1yxd84szyxfd),(iiiisf),(ni 10lim,),( , ),(:yxdyxyxzzszyxfd),(yxdyxf,(),(yxz)221yxzz yxdd85,),( ,0:yxdyxzyxdyxyxfszyxfdd),(d),(086oyxz22:22 yxdyxyxzzsyxdd1d22yxyxdd)(4122yxdsyxyxsdd)(41d22rrrd41d202203132xyd)(2:22yxz87yxyxyxszyxddd1)(21d2222rrrd1d21202

26、320354tttd) 1(302221rt令o21yxdzyx88),0(:2222zazyx在第为1;d4d)(1sxsxa;d4d)(1sxsyb;d4d)(1sxszc.d4d)(1szyxszyxdc89)(322yxz,22zyx,2:22 yxdyxsmdrrrd41d322020)41d(418162202rryxyxyxddd)(4132213909192coscoscos,)(yxssyxs)(,0)(yxyxs)(,)(yx,)(yx,0时当0cos时当0cos时当0coszxyzss)( ,)(93s),(),(),(zyxrzyxqzyxpv )cos,cos,(co

27、snvcosvs nvsnv94ni 10lim0limni 1iiiipcos),(iiiircos),(0limni 1zyiiiisp)(,(xziiiisq)(,(yxiiiisr)(,(iiiiqcos),(is),(),(),(zyxrzyxqzyxpv iniviiisnv)cos,cos,(cosiiiin设950limni 1zyiiiisp)(,(xziiiisq)(,(yxrxzqzypddddddyxiiiisr)(,(xdydzdpqr),(),(),(zyxrzyxqzyxpa 96zypddxzqddyxrddyxrxzqzypdddddd9798yxdyxyxz

28、z),( , ),(:),(zyxryxzyxrdd),() ,(yxdyxr),(yxzyxdd0limni 1yxiiiisr)(,(yxis )(yxi)(),(iiiz0limni 1) ,(iir),(iizyxi)(yxx,yzyxryxddd)(,(yxzyxrdd),(99,),( , ),(:zydzyzyxxzyzyxpdd),(), (zy,pzyd),(zyxzydd,),( , ),(:xzdxzxzyyxzzyxqdd),() z, ,(xzdxq),(xzyxzddyxzyxrdd),() ,(yxdyxr),(yxzyxdd100yxxzxzzyzyyxdd)(

29、dd)(dd)(yxxzdd)(3),(:2221aaayxz),(:2222aaayxz1dd)(3yxxzyxdyxxadd)2(3yxxz2dd)(yxxayxddd)2(yxdyxadd333axzy1012211:yxz0ddyxxyz,ddyxxyz2xozyx112yxd0,01:),(22yxyxdyxyx2221:yxz122zy102yxdyxyxyxdd 1222221cossin2rryxdrrrd1210315220d2sinozyx112yxdyxzyxdd2ddyxzyx1ddyxzyxyxdyxxydd )1(22yx yxdyxxydd 221yx ddrr1

30、03ni 1zyiiiisp)(,(xziiiisq)(,(yxrxzqzypddddddyxiiiisr)(,(0lim0limni 1iiiipcos),(iiiiqcos),(iiiircos),(issrqpdcoscoscos104yxrxzqzypddddddsrqpdcoscoscossand),(rqpa )cos,cos,(cosn)dd,dd,d(dddyxxzzysns sa dnaansnad105yxz111,1:22yxz.dcos2sziszidcos2yxzdd2rrrd)1(d210202yxdyxyxdd)1(22n106221cosyxxzyxzdd)(2

31、)(2xzsdcosyxddcoscosoyxz2)( x )(2xzyxzdd,dddd)(2yxzzyxz)(2221yxz)(2xz2211cosyx 107)( xxyxd222)(41yx oyxz2)(2221yx yxyxxyxddd)(22212rrrrd)cos(221220220d8yxdd得代入将,)(2221yxz108szyxfd),(iiiniisf),(lim10yxrxzqzypddddddzyiiiinisp),(lim10yxiiiisr),(xziiiisq),(109yxrxzqzypddddddyxrxzqzypddddddyxrxzqzypddddd

32、dsrqpdcoscoscos110111yxdyxyxzz),( , ),(:yxzzyxzyxfszyxfyxdyxdd1),(,(d),(22yxyxzyxryxzyxryxddd),(,(dd),(112,),( ,0:yxdyxzyxzyxrdd),(yxdyxyxrdd),(0yxzyxrdd),(yxdyxyxrdd),(0113,),(czyxf1zyxzyxzyxfidd),(xzyzyxfdd),(2yxzzyxfdd),(szyxid)(31sd31yxxd3d01103121114115zyxzryqxpdddyxrxzqzypdddddd zyxzrdddyxrdd

33、116231zyxyxd) ,(yxryxyxrdd) ,(, ),(:11yxzz yxdyxyxzyxzyxz),(, ),(),(),(:21,321zzryxzyxzd),(),(21yxd),(2yxz),(1yxzyxrdd yxd2 zyxzrdddyxdd1 3yxrdd),(:22yxzz yxyxrdd) ,(yxdyxd),(2yxzyxyxrdd) ,(),(1yxz117zyxzrdddyxrdd zyxyqdddyxrxzqzypdddddd zyxzryqxpdddxzqdd zyxxpdddzypdd 118zyxzyyxyxdd)(dd)(122 yxzyxz

34、yddd)(zrrzrddd)sin(zzrrrd)sin(dd30102029x3oz1y,)(xzyp, 0qyxr119szyxid)coscoscos(222222zyxhozyx,:1hz ,:),(222hyxdyxyx1(i1szyxd)coscoscos)(2220,21上在1,记h1zyxzyxddd)(2yxhyxddd2120zyxzyxiddd)(2yxhyxddd2421hhozyxh1121.dddddd)(2223yxzxxzyzxzyxzxi21,222zyxz1:1z1:),(22yxdyxyxi11zyxdddyxxdd)(2xyd) 1(20d10drr2

35、21drz202dcos103drr41zoxy211122kzyxrjzyxqizyxpzyxv),(),(),(),(yxrxzqzypddddddsrqpdcoscoscossnvd123yxrxzqzypddddddnzyxzryqxpdddn124m),(m记作vmlimzyxzryqxpvmddd1lim),(limzryqxpmmzryqxp),(125kzyxrjzyxqizyxpzyxa),(),(),(),(snadadivzryqxp1260diva0diva0diva0diva),(),(为常数其中zyxzyxvvvvvvv 0divv127yxrxzqzypddddd

36、dzyxzryqxpddd128),(rqpa snadzryqxpadiv129,:2222取外侧设rzyx,222zyxryxrzxzryzyrxdddddd333333vrd324 r31ryxzxzyzyxdddddd33331rvzyxd)(3222130131132yozxyxypxqxzxrzpzyzqyrddddddzryqxpddd rqp,yxdyxyxfz),(, ),(:nyxdc133xpdcxyxzyxpd),(,(yxyxzyxpyyxddd),(,(yxyzzpypyxdddsfzpypydcos,cos2211yxff ,cos221yxyfffcoscosy

37、fyozxnyxdc134szpypxpdcoscoscosdsypzpdcoscosyxypxzzpddddyqdzyzqyxxqddddxrdxzxrzyyrdddd135136rqpzyxyxxzzyddddddzryqxpddd srqpzyxdcoscoscoszryqxpddd 137yxzyxxzzyzyxddddddzxy111ozyyxxzdddzyyxxzdddyxxzzyddddddyxdyxdd323yxd138.ddd2zxzyxyxyioz2yx,0cossidszyd)(210,21cos21coscoscoscoszyxzxyxy2yyx222139yxxzzy

38、ypxqxrzpzqyrdd)(dd)(dd)(zryqxpdddsypxqxrzpzqyrdcoscoscossrqpd)coscoscos()cos,cos,(cosn)cos,cos,(cos140),(rqpa arot)(),(),(ypxqxrzpzqyrrqpkjizyxsazryqxpddddsasnaddrotsasandd)(rot141ozxylm),(zyxr r), 0, 0(rvvrotzyxkji00)0,(xy0 xykjizyx)2, 0, 0(2142sasandd)(rot143zryqxpdddrqpyxxzzyzyxddddddsrqpzyxdcoscoscos144zuyuxu, ),(zyxuu , ),(rqpa uradgzryqxprqpkjizyxarotadiv145,222zyxr设.)radg(rot;)radg(divrrrradgrzryrx,)(rxx2rrrxx,322rxr )(ryy322ry