20復 嬋柺



僷儔儊乕僞昞帵偝傟偨嬋柺

S:(x(s,t),y(s,t),z(s,t)), s伕[a,b], t伕[c,d]


傪昞帵偟偰傒傑偟傚偆丅椺偊偽丄媴柺S:(sin scos t ,sin s sin t ,cos s), s伕[0,兾],t伕[0,2兾]傪昞帵偡傞偵偼丄師偺傛偆偵擖椡偟傑偡丅

>plot3d([sin(s)*cos(t),sin(s)*sin(t),cos(s)],s=0..Pi,t=0..2Pi)


幚廗20.1丂師偺嬋柺傪昞帵偟側偝偄丅偨偩偟丄嬋柺偼幚嵺偺僗働乕儖偱昞帵乮夋憸傪僋儕僢僋偡傞偲昞帵偝傟傞侾丗侾儃僞儞傪慖戰乯偟偰偔偩偝偄丅
(1)丂(2cos s,2sin s, t), s伕[0,2兾], t伕[-1,1]
(2)丂儊價僂僗偺椫
丂丂((2+tcos s/2)cos s,(2+tcos s/2)sin s,tsin s/2), s伕[0,2兾], t伕[-1,1]
(3)丂僩乕儔僗
丂丂((2+cost)cos s, (2+cost)sin s,sint), s伕[0,2兾], t伕[0,2兾]

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y=f(x) (a亝x亝b)偺僌儔僼傪x幉偺夞傝偵夞揮偟偰偱偒傞夞揮懱偵偍偄偰丄夞揮柺偼

(s,f(s)cost,f(s)sint), s伕[a,b],t伕[0,2兾]

偲僷儔儊乕僞昞帵偱偒傑偡丅傑偨



偑惉傝棫偪傑偡丅偙偙偱丄maple偱偼 |x| 偼 abs(x) 偲昞偟傑偡丅



幚廗20.2丂y=sinx (0亝x亝3兾)偺僌儔僼傪x幉偺夞傝偵夞揮偟偰偱偒傞夞揮懱偵偮偄偰丄師偺栤偄偵摎偊側偝偄丅
(1)夞揮柺傪昞帵偟側偝偄丅偨偩偟丄嬋柺偼幚嵺偺僗働乕儖偱昞帵乮夋憸傪僋儕僢僋偡傞偲昞帵偝傟傞侾丗侾儃僞儞傪慖戰乯偟偰偔偩偝偄丅
(2)懱愊傪媮傔側偝偄丅
(3)昞柺愊傪媮傔側偝偄丅

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2偮埲忋偺嬋柺傪摨帪偵昞帵偟偰傒傑偟傚偆丅

>with(plots):
>A:=plot3d([sin(s)*cos(t),sin(s)*sin(t),cos(s)],s=0..Pi,t=0..0.5*Pi)
(媴柺x2+y2+z2=1忋偱乽x>0偐偮y>侽偺晹暘乿傪昞帵乯


>B:=plot3d([sin(s)*cos(t),sin(s)*sin(t),cos(s)],s=0..Pi,t=Pi..1.5*Pi)
乮媴柺丂x2+y2+z2=1忋偱乽x<0偐偮y<0偺晹暘乿傪昞帵乯

>display({A,B})


幚廗20.3丂師傪昞帵偟側偝偄丅
(侾)媴柺x2+y2+z2=1忋偱>0偐偮z>0偺晹暘苼uy<0偐偮z<0偺晹暘乿
(俀)媴柺x2+y2+z2=1忋偱乽x>0偐偮y>0偐偮z>0偺晹暘乿偲乽x>0偐偮y<0偐偮z<0偺晹暘乿偲乽x<0偐偮y>0偐偮z<0偺晹暘乿偲乽x<0偐偮y<0偐偮z>0偺晹暘乿

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幚廗20.4丂寽悅慄y=(ex+e-x)/2, x伕[-1,1]傪x幉偺夞傝偵夞揮偟偰偱偒傞寽悅柺傪昞帵偟側偝偄丅偨偩偟丄嬋柺偼幚嵺偺僗働乕儖偱昞帵乮夋憸傪僋儕僢僋偡傞偲昞帵偝傟傞侾丗侾儃僞儞傪慖戰乯偟偰偔偩偝偄丅 傑偨丄偦偺昞柺愊傪媮傔側偝偄丅

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幚廗20.5丂幚廗侾(俁)偺僩乕儔僗偼墌(x-2)2+z2=1(俀偮偺娭悢x=2亇併(1-z2)偺僌儔僼乯傪z幉偺夞傝偵夞揮偟偰偱偒傞夞揮懱偱偡丅 偡側傢偪丄y=2亇併(1-x2)偺僌儔僼傪x幉偺夞傝偵夞揮偟偰偱偒傞夞揮懱偲崌摨偱偁傞丅師偺栤偄偵摎偊側偝偄丅
(侾)懱愊傪媮傔側偝偄丅
(俀)昞柺愊傪媮傔側偝偄丅

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