{VERSION 5 0 "IBM INTEL LINUX" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Warning" 2 7 1 {CSTYLE "" -1 -1 " " 0 1 0 0 255 1 0 0 0 0 0 0 1 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "restart: with(plots) :\nwith(linalg):" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name cha ngecoords has been redefined\n" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning , the protected names norm and trace have been redefined and unprotect ed\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 240 "#zf felulet: parab oloid \nzf:=x*x+y*y;\nZFPLOT:=plot3d(zf,x=-2..2,y=-2..2,grid=[18,18],s tyle=patchnogrid,\ncolor=green,\naxes=frame,orientation=[20,70],light= [-20,90,1,0,0],lightmodel='light1',shading=ZHUE,scaling=constrained): \ndisplay(ZFPLOT);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#zfG,&*$)%\"xG \"\"#\"\"\"F**$)%\"yGF)F*F*" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 272 "#a plot opcioi a display pa rancsban is megadhatok\nZFPL:=plot3d(zf,x=-2..2,y=-2..2,grid=[18,18],c olor=yellow):\ndisplay(ZFPL,style=patchnogrid,axes=boxed,orientation=[ 20,70],\nscaling=constrained,\nlight=[-20,80,1,0,0],lightmodel='light3 ',shading=XYZ,\nambientlight=[0,0,0.5]);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 231 "#kozvetlenul abrazo lva egy leszukitett tartomanyban \nplot3d(zf,x=-2..2,y=-2..2,grid=[18, 18],color=green,style=patch,\nshading=ZHUE,light=[-140,0,1,1,0],lightm odel='light1',\naxes=framed,view=[-1..2,-2..2,0..4],orientation=[-140, 70]);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "#derivalas\ndzx:=diff(zf,x);\ndzy:=diff(zf,y);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$dzxG,$%\"xG\"\"#" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%$dzyG,$%\"yG\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "#gradient\ngvek:=grad(zf,vector([x,y]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%gvekG-%'vectorG6#7$,$%\"xG\"\"#,$%\"yGF+" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 606 "#szintvonalak es mindegyik en egy szakasz a gradiensvektorral\nfor i from 1 to 5 do \nx0:=1; y0:= i*2/5; z0:=subs([x=x0,y=y0],zf);\nZNIV[i]:=implicitplot3d(zf-z0=0,x=-2 ..2,y=-2..2,z=z0..z0+0.01,color=blue,scaling=constrained,axes=framed): \nzfp:=[x0,y0,z0];\nendp:=zfp+[subs([x=x0,y=y0],gvek[1]),subs([x=x0,y= y0],gvek[2]),subs([x=x0,y=y0],0)];\nGRADL[i]:=polygonplot3d([zfp,endp] ,color=green,thickness=3):\nod:\nZNIVS:=seq(ZNIV[i],i=1..5):\nGRADLS:= seq(GRADL[i],i=1..5):\nYCURVE:=plot3d(zf,x=x0..x0+0.01,y=-2..2,color=y ellow):\ndisplay(\{ZNIVS,GRADLS,YCURVE\},axes=framed,orientation=[20,7 0]);\n#nem tudom, miert nem szines" }}{PARA 13 "" 1 "" {TEXT -1 0 "" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 111 "#szintvonalak\nNLSZ:=plot 3d(zf,x=-2..2,y=-2..2,grid=[18,18],style=patchcontour,\ncontours=4,ori entation=[20,70]):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "#gradient fie ld\nGFIELD:=gradplot3d(zf,x=-2..2,y=-2..2,z=0..8,grid=[6,6,5]):" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "display([NLSZ,GFIELD]);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 13 "" 1 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 229 "#az x=1 feluleti gorbe veko ny szalagkent abrazolva\nXG:=plot3d(zf,x=1..1.05,y=-2..2,grid=[8,18],c olor=blue):\nXG1:=plot3d(zf-0.01,x=1..1.05,y=-2..2,grid=[18,8],color=b lue):\n#kell meg egy gorbe is kicsit letolva, hogy jol latszodjon" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 96 "display([ZFPL,XG,XG1], orien tation=[30,70], axes=framed, style=patchnogrid,lightmodel='light4');" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 230 "#szintvonal a zf=1 megoldasakent, \n#z nincs az egyenletben, \+ ezert a z tartomany tetszoleges \nZG:=implicitplot3d(zf-1=0,x=-2..2,y= -2..2,z=1..1.1,color=red):\ndisplay(\{ZFPLOT,ZG\},scaling=constrained, style=hidden,orientation=[30,70]);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 489 "#erintosik az (x0,y0) pon tban\nx0:=1;y0:=1;\nz0:=subs([x=x0,y=y0],zf);\nnormvek:=[subs([x=x0,y= y0],-dzx),subs([x=x0,y=y0],-dzy),1];\npvek:=[x-x0,y-y0,z-subs([x=x0,y= y0],zf)];\ntangpl:=dotprod(normvek,pvek);\ntpg:=implicitplot3d(tangpl= 0,x=-2..2,y=-2..2,z=0..4,\\\ncolor=blue,style=wireframe):\npont:=[x0,y 0,subs([x=x0,y=y0],zf)];\npmark:=pointplot3d(pont,color=red,symbol=dia mond):\npveg:=pont - normvek;\nfelnorm:=polygonplot3d([pont,pveg],colo r=black,thickness=3):\ndisplay(ZFPLOT,pmark,tpg,felnorm);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#x0G\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%#y0G\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#z0G\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(normvekG7%!\"#F&\"\"\"" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%%pvekG7%,&%\"xG\"\"\"F(!\"\",&%\"yGF(F(F),&%\"zGF( \"\"#F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'tangplG,*\"\"#\"\"\"*&F& F'-%*conjugateG6#%\"xGF'!\"\"*&F&F'-F*6#%\"yGF'F--F*6#%\"zGF'" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%pontG7%\"\"\"F&\"\"#" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%%pvegG7%\"\"$F&\"\"\"" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 107 "#tangent p lanes, animation\nunassign('x0','y0');\nnormvek:=[subs([x=x0,y=y0],-dz x),subs([x=x0,y=y0],-dzy),1];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "pv ek:=[x-x0,y-y0,z-subs([x=x0,y=y0],zf)];\ntangpl:=dotprod(normvek,pvek) ;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 213 "x0:=1; \ntangz:=solve(tangpl= 0,z);\ntpg:=animate3d(tangz,x=-1..2,y=-2..2,y0=-2..2,\n f rames=16,color=pink,style=wireframe):\ndisplay(ZFPLOT,tpg,XG);\n#jobb \+ egerrel az abrara kattintani, majd animacio, play" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(normvekG7%,$%#x0G!\"#,$%#y0GF(\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%pvekG7%,&%\"xG\"\"\"%#x0G!\"\",&%\"yGF(%#y0GF*, (%\"zGF(*$)F)\"\"#F(F**$)F-F2F(F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %'tangplG,(*&%#x0G\"\"\"-%*conjugateG6#,&%\"xGF(F'!\"\"F(!\"#*(\"\"#F( %#y0GF(-F*6#,&%\"yGF(F2F.F(F.-F*6#,(%\"zGF(*$)F'F1F(F.*$)F2F1F(F.F(" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#x0G\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&tangzG,,*$)%#y0G\"\"#\"\"\"F*F*!\"\"*&F)F*%\"xGF*F** (F)F*-%*conjugateG6#F(F*%\"yGF*F**(F)F*F/F*F(F*F+" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 110 "#integrati on\nplot3d(zf,x=-2..2,y=-2..2,style=wireframe,filled=true,axes=framed) ;\nint(int(zf,x=-2..2),y=-2..2);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }} {PARA 11 "" 1 "" {XPPMATH 20 "6##\"$G\"\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 161 "#cylindrical coord. system\n#plot3d(r(theta,z), theta=a..a, z=c..d, coords=cylindrical);\nxc:=r*cos(alf); yc:=r*sin(a lf); zc:=subs([x=r*cos(alf),y=r*sin(alf)],zf);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#xcG*&%\"rG\"\"\"-%$cosG6#%$alfGF'" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%#ycG*&%\"rG\"\"\"-%$sinG6#%$alfGF'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#zcG,&*&)%\"rG\"\"#\"\"\")-%$cosG6#%$alfGF)F*F** &F'F*)-%$sinGF.F)F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 129 "F ELC:=plot3d([xc,yc,zc],r=0..2,alf=0..2*Pi,grid=[18,18],color=green):\n display(FELC,axes=framed,orientation=[20,70],style=hidden);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 228 "#feluleti gorbek\nRK:=plot3d([xc,yc,zc],r=1..1.01,alf=0..2*Pi,grid=[1 8,18],color=red):\nAK:=plot3d([xc,yc,zc],r=0..2,alf=Pi/2..Pi/2+0.01,gr id=[18,18],color=blue):\ndisplay(\{FELC,RK,AK\},axes=framed,orientatio n=[60,80],style=hidden);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 13 "" 1 "" {TEXT -1 0 "" } }{PARA 11 "" 1 "" {XPPMATH 20 "6##\"$G\"\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "int(int(zc*r,r=0..2),alf=0..2*Pi);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#,$%#PiG\"\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "restart: with(plots):" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been redefined\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 540 "#3 valtozos fuggveny es szintfeluletei\n #uf:=(x,y,z)->z-(x^2+y^2);\n# masik peldahoz\nuf:=(x,y,z)->z-x^2+y^2; \nsolve(uf(x,y,z)=0,z);\nFEL1:=implicitplot3d(uf(x,y,z)=0,x=-2..2,y=-2 ..2,z=0..16,color=green,\nnumpoints=81,gridstyle='rectangular'):\nFEL2 :=implicitplot3d(uf(x,y,z)=4,x=-2..2,y=-2..2,z=0..16,color=magenta,num points=81,gridstyle='rectangular'):\nFEL3:=implicitplot3d(uf(x,y,z)=8, x=-2..2,y=-2..2,z=0..16,color=pink,\nnumpoints=81,gridstyle='rectangul ar'):\n\ndisplay(\{FEL1,FEL2,FEL3\},axes=normal,orientation=[110,70], \nscaling=unconstrained);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#ufGf *6%%\"xG%\"yG%\"zG6\"6$%)operatorG%&arrowGF*,(9&\"\"\"*$)9$\"\"#F0!\" \"*$)9%F4F0F0F*F*F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)%\"xG\"\"# \"\"\"F(*$)%\"yGF'F(!\"\"" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "GFIELD3:=gradplot3d(uf(x,y,z),x=-2. .2,y=-2..2,z=0..8,grid=[6,6,3]):\ndisplay(GFIELD3);" }}{PARA 13 "" 1 " " {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 155 "#forgasf eluletek\n#z=sinx fuggveny az x-tengely korul\nxs:=r; ys:=sin(r)*cos(a lf); zs:=sin(r)*sin(alf);\nplot3d([xs,ys,zs],r=0..3*Pi,alf=0..2*Pi,axe s=normal);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#xsG%\"rG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#ysG*&-%$sinG6#%\"rG\"\"\"-%$cosG6#%$alfGF*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#zsG*&-%$sinG6#%\"rG\"\"\"-F'6#%$a lfGF*" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "#ujabb Maple-ben van with(Mathlab); is" }}}}{MARK "23 1 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }