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函数的数值导数和切平面
# ]1 J- ]9 p0 F7 e1 法线! H" W$ R2 X; U; B
8 i4 }. r- Q2 |- k3 P/ c) N6 s" Y【例 1】曲面法线演示。. e- }- j; |6 e$ H0 [
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y=-1:0.1:1;x=2*cos(asin(y));
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- C% d% R, q4 {' d* R' I[X,Y,Z]=cylinder(x,20);( }6 w0 N9 M+ I, W k$ G
- _2 ?4 ~# T0 y+ E1 g- BsuRFnorm(X(:,11:21),Y(:,11:21),Z(:,11:21));) i; a+ E! I3 f* r. h
' W/ D: [: K; Z! ?9 l7 Bview([120,18]) ; ~3 u* O2 H a( c8 V
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! B5 ~/ B p. F0 o" m! Gclear;clf;q=2e-6;k=9e9;a=1.5;b=-1.5;x=-6:0.6:6;y=x;) m5 y$ ^8 o. t
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[X,Y]=meshgrid(x,y);
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% _) K; ?; d' s0 Y4 K) j; q% s, ~: [rp=sqrt((X-a).^2+(Y-b).^2);rm=sqrt((X+a).^2+(Y+b).^2);
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V=q*k*(1./rp-1./rm);
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/ R: {1 i3 h: @$ m[Ex,Ey]=gradient(-V);
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8 ^' a+ b/ Q8 v0 T/ ]AE=sqrt(Ex.^2+Ey.^2);Ex=Ex./AE;Ey=Ey./AE;! q# B2 X5 r* O: v3 L# u
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cv=linspace(min(min(V)),max(max(V)),49);! H/ [/ q% ~6 B1 O$ d
* W% A! g& ?& f2 y5 [& _* R Q3 ]contourf(X,Y,V,cv,'k-'): n9 N. @8 C0 [. G" s, L# k. y
: j) ^2 q7 j- t$ I% d0 L%axis('square')
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title('fontname {隶书}fontsize{22}偶极子的场'),hold on
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quiver(X,Y,Ex,Ey,0.7)
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8 G Z H' Z1 |2 Lplot(a,b,'wo',a,b,'w+')
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plot(-a,-b,'wo',-a,-b,'w-')7 p5 I2 [7 U, |/ \! A7 g5 T+ J
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xlabel('x');ylabel('y'),hold off
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2 多元函数的零点& J4 w2 } _# p" ? E4 k( ?! z
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. b4 x- _! M9 i4 `, P% `1 wx=-2:0.5:2;y=x;[X,Y]=meshgrid(x,y); `3 n% ?6 P' q# q; X1 W" I
0 P0 f. q5 U- `0 \3 x5 Q$ v3 l! R4 K8 jF1=sin(X-Y);F2=cos(X+Y);8 Q. o! g& {# w% T$ o: _
' Z& t9 p, a7 j5 Q: i7 V" z( c4 |8 Xv=[-0.2, 0, 0.2];+ c( a) v2 Z- s. {& ^+ m
% M3 j( L7 y" l/ econtour(X,Y,F1,v)8 f% q# Y! t9 U: g
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hold on,contour(X,Y,F2,v),hold off
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) Z- o' ]. e3 W1 W2 `: x(2)
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[x0,y0]=ginput(2);
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disp([x0,y0])
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-0.7926 -0.7843( l d9 X. i# O
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0.7926 0.7843 0 K5 h# k7 V$ \, e
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(3)
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$ N6 ~* E0 w7 @# R8 dfun='[sin(x(1)-x(2)),cos(x(1)+x(2))]'; %<12>1 D( `+ \+ Q) H$ K0 q- M
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[xy,f,exit]=fsolve(fun,[x0(2),y0(2)]) %<13> 8 v( G: U' Q0 }6 h# u
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Optimization terminated successfully:
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First-order optimality less than OPTIONS.TolFun, and no negative/zero curvature detected0 \$ t8 W# t; M- h7 z3 r
, k4 |$ F4 q( Q& {# f. O6 Q! rxy =. S7 p) B* `* N. m9 \
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0.7854 0.78545 S+ y" i( N, K$ [
& L* ^! s7 ~, s9 |8 Hf =
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1.0e-006 *
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# I; k: l# {0 R m# h* E -0.0984 0.2011& X6 }4 `. C& F6 k
$ \" I/ X1 l0 [- C6 ^exit =
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' V% l3 ~+ n( V+ W4 a1 D 〖说明〗
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function ff=fun(x)
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5 K2 W" \3 P- B8 }! ^5 b/ nff(1)=sin(x(1)-x(2));- }3 P8 Z4 n) V5 A4 q( Q
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ff(2)=cos(x(1)+x(2));5 R- O. J4 k+ u9 l* ?! u
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