"

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,

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(1)

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(2)

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(3)

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() f

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1:

2:

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""

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z- " x+y+z=2

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y- " x+y+z=2

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1:

2:

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:

D " x+y+z=2 .

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: " x+z=1 - y+2z=2. y=x2-1 z+y=0 - z=0.

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- 1 "

" " :

:

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Maple

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- 2 " " :

:

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- 3 " " :

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- f D R3, f D " :

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- (: 1):

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:

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D -. D (x,y,z) - (x,y,z). : :

:

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" xy z=4-x2-y2.: G(0,0,4/3).

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> ?coords> ?changecoords> ?plot3d[coords] Maple

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- : -z -z -z

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-

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f (x,y,z) D R3. :

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D - R3 " xy x2+(y-1)2=1 z=x2+y2

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1. D R xy x2 + (y-1)2 = 1 x2 + y2 - 2y + 1 = 1 r2 - 2r sin = 02. -z: M(r,) R z D - z=0 z=x2+y2=r2 .

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3. -r: xy r=0 r=2 sin .

4. -: " R, -x - =0 =.

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:

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D " r=1+cos(), xy "" z=4.

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- : -z

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:

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: > restart;with(plots): > sphereplot([r,theta,Pi/3], r=0..2,theta=0..2*Pi, axes=normal, style=patchnogrid, view=[-2..2,-2..2,0..2]);

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: > restart;with(plots):> sphereplot([r,Pi/3,phi], r=0..2,phi=0..2*Pi, axes=normal, style=patchnogrid, view=[-2..2,-2..2,0..2]);

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f (x,y,z) D R3. :

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" 2,

> s1:=plot3d(4,t=0..2*Pi, p=0..Pi/4,coords=spherical, axes=boxed, scaling=constrained, color=blue):s2:=plot3d(z,t=0..2*Pi, z=0..2*sqrt(2), coords=cylindrical, axes=boxed, scaling=constrained, color=yellow):

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G uvw D xyz "

F x,y,z H u,v,w :

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- :

( )

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- : D G

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http://mathworld.wolfram.com/http://www.math.montana.edu/frankw/ccp/multiworld/multipleIVP/spherical/body.htmhttp://www.math.montana.edu/frankw/ccp/multiworld/multipleIVP/cylindrical/body.htm

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WINPLOT: math.exeter.edu/rparris/winplot.html DPGRAPH: www.dpgraph.com

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