高等数学讲义.pdf

《高等数学讲义.pdf》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。

1、RADVANCEDMATHEMATICSFIFTHEDITION7ChapterSixRByZHOUH.Y.18Ùõ¼ê‡È©Æ9ÙA^x1˜m)ÛAÛÄ•£˜!˜m†‹IX‹I:,‹I¶:î¶(x¶),p¶(y¶),ç¶(z¶),mÃ{K‹I¡,%•(–•)˜m:‹I:˜m:†kSê

2、ƒméA'X‹I:,‹I¶,‹I¡‹IA˜mü:mål~1~2!•¡†˜m•‚ÐÚ1.•¡•§F(x;y;z)=0orz=f(x;y)(1)˜„/§‹I÷v•§(1)˜m¤k:8ܤ••¡. •§(1)¤••¡•§.(1)¥¡•§¥%3:M

3、0(x0;y0;z0),¥¡Œ»•R,¥¡þ?¿˜:•M(x;y;z),w,k:jMM0j=R=(xx)2+(yy)2+(zz)2=R2000(2)Ρ•§Î¡:(x)2+(y)2=R2O‚§1‚Ρ:f(x;y)=0ÔΡ§ýΡ(3)^=•¡1‚§^=¶^=Ô¡§I¡0ZhuhaiCampusofBITRADVANCEDMATHEMATICSFIFTHEDITION7ChapterSixRByZHOUH.Y.2.˜m•‚9Ù3‹I¡þÝK˜m•‚˜„•§:(F(x;y;z)=0;(2)G(x;y;z)=0:Š’:˜m•‚˜„•§¥

4、,žz,•§P216:3,5,6(2)(3)(4),H(x;y)=0(3)7(1)(4)(5)¡Î¡(3)•˜m•‚(2)'ux0y¡ÝKΡ.(H(x;y)=0;z=0:•˜m•‚(2)3x0y¡þÝK•‚.~3x2õ¼êÄVgõ¼ê!4•ÚëYć¦:!SNJ‡:n)¼ê3é'˜¼êÄ:þ,ÆSõ¼ê9Ù4•ÚëY.
o‡¯K.½Â,¬¦Ù½Â•;•¼ê˜!ý•£—²¡:84•ÚëYVg.²¡:8‹I²¡þäk,«5ŸP(½÷v˜½^‡):8Ü,¡•²¡:8.=:8:†˜¼êéE=f

5、(x;y)j(x;y)äk5ŸPg',ݺõ¼ê~:±:•¥%,1•Œ»Sܤk:¤˜²¡:8§P•ƒ'¯K.E=f(x;y)jx2+y2<1g•::õ¼ê!4••::P0(x0;y0),>0,¡ÚëYVg.npoU(P0;)=fPjjPP0j<g=(x;y)j(xx0)2+(yy0)2<:J::õ¼ê4••:P0•.n).¡P0••¥%,••Œ».%•:U(P0;)=fPjjPP0j<g«•,>.,m«•,4«•1ZhuhaiCampusofBITRADVANCEDMATHEMATIC

6、SFIFTHEDITION7ChapterSixRByZHOUH.Y.!¼êVgDR2´˜‡²¡:8,Nf:D!R•½Â3D¼ê,Ï~P•:z=f(x;y);(x;y)2D:½z=f(P);P2D:õ¼êÓk½Â•!Š•!gCþ!ÏCþ!ã/Vg.~1n!¼ê4•½Â2:¼êz=f(x;y)3:P0(x0;y0),˜%•kp½Â,A•~ê,XJé?¿">0,ok˜‡ƒA>0,¦0<(xx0)2+(yy0)2<ž,ðkjf(x;y)Aj<",K¡A•¼êz=f(x;y)(x;y)!(x0;

7、y0)ž4•,P•limf(x;y)=A:½f(x;y)!A((x;y)!(x0;y0)):(x;y)!(x0;y0)•PŠlimf(P)=A:½f(P)!A(P!P0):P!P0`²:1.P0™7áuD.2.P!P0•ª´?¿;duP!P0?¿5,¿›Xx;yÓžªux0;y0,ØUkkgS,¼ê4•••4•;3.¦4••{—Ù$Ž{K†˜¼êaq,'…´ØU•½´».4.(½4•Ø•3•{—`²4•†´»k'.~X:(xy;x2+y26=0f(x;y)=x2+y20;x2+y2=03(0;0)÷AÏ´»4••3,

8、4•%Ø•3.p(x+y)sin(xy)(xy+1)1E3OŽ4•(1)limxy;(2)limx;(3)limxy:(x;y)!(0;2)(x;y)!(0;2)(x;y)!(0;0)x3yx2y2E4y²4•Ø•3(1)limx6+y2;(2)limx2y2+(xy)2:(x;y)!(0;0)(x;y)!(0;0)P:(1)y=kx3,x3yx3
kx3klim=lim=:(x;y)!(0;0)x6+y2(x;y)!(0;0)x6+k2x61+k2y=kx34•Ø•3.é(2)?1aq?Ø(y=x;y=x).2Zhuha

9、iCampusofBITRADVANCEDMATHEMATICSFIFTHEDITION7ChapterSixRByZHO