II. grafika

sia aris Tanamedrove daprogramebis enebis ZiriTadi obieqti. Mathematica

sistemis gamosaxulebebis nebismieri mimdevroba Cawerili figurul frCx-

ilebSi warmoadgens sias. wvdoma siis elementebTan xorcieldeba ormagi

kvadratuli frCxilebis gamoyenebiT. Mathematica sistemaSi sul arsebobs

frCxilebis oTxi tipi:

(a+b)c,{a,b,c},f[x],m[[i]] an mPiT.

grafikebis ageba

grafikis asagebad gamoiyeneba Plot funqcia, romelic Seicavs or

aucilebel arguments: funqcia f[x], romlis grafiki unda avagoT (an funq-

ciebis sia), da funqciis gansazRvris are {xmin, xmax}, romelic Seicavs

formalur cvlads x:

Plot[f[x], {x, xmin, xmax}]

Plot@Tan@xD, 8x, -Pi, Pi<D

-3 -2 -1 1 2 3

-6-4-2

246

SevinaxoT miRebuli grafiki rogorc suraTi *.gif (*.bmp,*.jpg,*.pdf)

gafarToebiT.

Export@"c:�grafiki.gif", %D;Import@%D

avagoT y=x^2 funqciis grafiki da SevinaxoT miRebuli grafiki rogorc

suraTi *.jpg gafarToebiT

Export@"c:�ff.jpg", Plot@x^2, 8x, -1, 1<DD;Import@"c:�ff.jpg"D

Plot da Table funqciebi aqvT erTnairi struqtura im TvalsazrisiT, rom

isini Seicaven formalur cvlads (Table funqciisaTvis es cvladi aris

iteratori, Plot funqciisaTvis es cvladi warmoadgens abscisas, romelic

icvleba xmin-dan, xmax-mde). ganvixiloT Semdegi magaliTi.

x = 2;

Plot@x^2, 8x, -3, 3<D

-3 -2 -1 1 2 3

2

4

6

8

aqedan Cans, rom Plot funqciaSi x cvladi aris formaluri,da masze ar

moqmedebs gareT gansazRvruli mniSvneloba x=2.

Expand@Hx + 2L^2D

16

sxva funqciebisagan gansxvavebiT Plot funqcia asrulebis winaswari argu-

mentebis gamoTvlis blokirebas da formaluri cvladi x gamoTvlis pro-

cesSi yovelTvis rCeba ganusazRvreli. winaamRdeg SemTxvevaSi Cven miviReb-

diT Secdomas, radgan formaluri cvladis magivrad iqneboda ricxvi 2:

x=2; Plot[x^2,{x,-3,3}])®Plot[4,{2,-3,3}]. im SemTxvevaSi roca ar

aris saWiro winaswar argumentebis gamoTvlis blokireba, unda visarge-

bloT Evaluate funqciiT, romelSic uyve iqneba Casmuli cvladis

gansazRvruli mniSvneloba. ganvixiloT magaliTi.

Plot@Evaluate@x^2D, 8x, -3, 3<D

-3 -2 -1 1 2 3

2

4

6

8

exla wavSaloT x cvladis mniSvneloba.

x =.

Plot@8Sin�x, 1 � Sin@xD<, 8x, -2, 2<D

-2 -1 1 2

-4

-2

2

4

aq Cven avageT ori funqciis grafiki erT sibrtkeze.

Plot funqciis opciebis gamoyeneba

funqciis grafikis asagebaT xSiradDsaWiroa damatebiTi parametrebis

miTiTeba. damatebiTi parametrebi, romlebic gansazRraven grafikis saxes,

warmodgenili arian opciis saxiT (Options). opcia aris funqciis argu-

menti, romelic Cawerilia lokaluri Casmis formaSi. magaliTad, rom

avagoT Sin[x] funqciis grafiki CarCoSi Plot[x] funqciiaSi davweroT

opcia Frame ® True.

2 leqcia_6.nb

Plot@Sin@xD, 8x, 0, 2 Pi<, Frame ® TrueD

0 1 2 3 4 5 6-1.0

-0.5

0.0

0.5

1.0

aq Frame opciis saxelia, xolo True misi mniSvneloba. opcias SeiZleba

hqondes ramdenime mniSvneloba. gaCumebis principiT erTi maTgani (opciis

mniSvneloba) uyve aris dayenebuli. kerZod, am magaliTSi Frame opciis

mniSvneloba gaCumebis principiT aris False, amitom Cven SevcvaleT am

opciis mniSvneloba da miviReT Sin[x] funqciis grafiki CarCoSi.

Plot@8Sin@xD, Sin@2 xD<, 8x, 0, 2 Pi<, Axes ® 8False, True< D

-1.0

-0.5

0.0

0.5

1.0

Plot@8Sin@xD, Sin@2 xD<, 8x, 0, 2 Π<, Axes ® 8True, False<D

0 1 2 3 4 5 6

Plot@8Sin@xD, Sin@2 xD<, 8x, 0, 2 Π<, Axes ® None, PlotLabel ® funqciis grafiki,

LabelStyle ® Directive@Italic, FontFamily ® "AcadNusx"DD

funqciis grafiki

Plot@8Sin@xD, Sin@2 xD<, 8x, 0, 2 Pi<, PlotStyle ® Thick, Ticks ® None, AxesLabel ® 8X, Y<D

X

Y

SeadareT es magaliTebi. qvemoT aris Plot funqciis opciebis sia.

leqcia_6.nb 3

Options@PlotD

:AlignmentPoint ® Center, AspectRatio ®1

GoldenRatio, Axes ® True,

AxesLabel ® None, AxesOrigin ® Automatic, AxesStyle ® 8<, Background ® None,

BaselinePosition ® Automatic, BaseStyle ® 8<, ClippingStyle ® None,

ColorFunction ® Automatic, ColorFunctionScaling ® True, ColorOutput ® Automatic,

ContentSelectable ® Automatic, CoordinatesToolOptions ® Automatic,

DisplayFunction ¦ $DisplayFunction, Epilog ® 8<, Evaluated ® Automatic,

EvaluationMonitor ® None, Exclusions ® Automatic, ExclusionsStyle ® None, Filling ® None,

FillingStyle ® Automatic, FormatType ¦ TraditionalForm, Frame ® False, FrameLabel ® None,

FrameStyle ® 8<, FrameTicks ® Automatic, FrameTicksStyle ® 8<, GridLines ® None,

GridLinesStyle ® 8<, ImageMargins ® 0., ImagePadding ® All, ImageSize ® Automatic,

ImageSizeRaw ® Automatic, LabelStyle ® 8<, MaxRecursion ® Automatic, Mesh ® None,

MeshFunctions ® 8ð1 &<, MeshShading ® None, MeshStyle ® Automatic, Method ® Automatic,

PerformanceGoal ¦ $PerformanceGoal, PlotLabel ® None, PlotPoints ® Automatic,

PlotRange ® 8Full, Automatic<, PlotRangeClipping ® True, PlotRangePadding ® Automatic,

PlotRegion ® Automatic, PlotStyle ® Automatic, PreserveImageOptions ® Automatic,

Prolog ® 8<, RegionFunction ® HTrue &L, RotateLabel ® True,

Ticks ® Automatic, TicksStyle ® 8<, WorkingPrecision ® MachinePrecision>

ganixileT da SeadareT Semdegi ori magaliTi:

Plot@Sin@xD, 8x, 0, 10<, Frame ® True,

FrameTicks ® Automatic, FrameTicksStyle ® Directive@Orange, 12DD

Plot@Cos@xD, 8x, 0, 10<, Frame ® True, FrameTicks ® All,

FrameTicksStyle ® 88Black, Blue<, 8Red, Green<<D

Tu saWiroa gragikis ageba ramdenime funqciisaTvis erTi da igive opciebis

gamoyenebiT, maSin jobia es opciebi calke CavweroT, magaliTad Semdegi

saxiT:

opt =

8Axes ® 8True, False<, Frame ® False, PlotStyle ® Thick, PlotRange ® 88-2, 2<, 8-2, 2<<<;

amis Semdeg visargebloT Evaluate funqciiT:

4 leqcia_6.nb

Plot@8x^3, Cos@xD<, 8x, -2, 2 <, Evaluate@optDD

-2 -1 0 1 2

Plot@Sin@1 + x � 2 xD, 8x, -Pi, Pi<, Evaluate@optDD

-2 -1 0 1 2

ganvsazRvroT f[x],g[x] funqciebi Semdegi saxiT:

f@x_D := Plot@Sin@xD, 8x, 0, 2 Π<, Axes ® 8True, False<Dg@x_D := Plot@Sin@xD � 2, 8x, 0, 2 Π<, Axes ® 8True, False<D

Show funqciis meSveobiT xorcieldeba funqciis grafikis gamotana.

Show@f@xD, g@xDD

0 1 2 3 4 5 6

ganvixiloT Semdegi magaliTebi.

Table@Plot@Cos@x + aD, 8x, -10, 10<D, 8a, 0, 2<D

:-10 -5 5 10

-1.0

-0.5

0.5

1.0

,-10 -5 5 10

-1.0

-0.5

0.5

1.0

,-10 -5 5 10

-1.0

-0.5

0.5

1.0

>

Show@%, Axes ® NoneD

Plot@Sin@x^2D � x, 8x, 0, 10<D

Show@%, PlotRange ® 888, 10<, 8-.3, .3<<, AxesOrigin ® 88.0, 0<D

leqcia_6.nb 5

{8.0, 0}

Plot3D funqcia

zemod moyvanil yvela magaliTSi iyo ganxiluli mxolod erTi cvladis

funqciebi da Sesabamisad Cven vRebulobdiT funqciis grafiki sibrtkeze.

Plot3D funqciis gamoyenebiT SegviZlia avagoT funqciis grafiki sivrceSi:

Plot3D[f[x,y],{x, xmin, xmax},{y, ymin, ymax}]. ganvixiloT magaliTi.

Plot3D@Sin@x + y^2D, 8x, -3, 3<, 8y, -2, 2<D Plot3D@8Sin@xD, Cos@xD<, 8x, 0, 2 Pi<, 8y, 0, 2 Pi

PlotStyle ® 8Red, Blue<D

-2

02

-2-1

01

2

-1.0-0.5

0.0

0.5

1.0

Plot3D@8x^2 + y^2, -x^2 - y^2<,8x, -2, 2<, 8y, -2, 2<,Axes ® 8False, False, False<, Mesh -> NoneD

Plot3D@Sqrt@1 - x^2 - y^2D,8x, -1, 1<, 8y, -1, 1<,Mesh ® 3, ColorFunction ® HueD

-1.0-0.5

0.00.5

1.0

-1.0-0.5

0.00.5

1.00.0

0.5

1.0

Options[Plot3D] gamoyenebiT ganixileT am funqciis opciebi.

ListPlot funqcia

xSirad saWiro aris funqciis grafikis ageba, roca funqcia mocemullia

cxrilis saxiT: {{x1,y1},{x2,y2},...}, sadac yi warmoadgens funqciis

mniSvnelobas Sesabamis xi wertilSi. am SemTxvevaSi gamoiyeneba ListPlot

funqcia. ganvixiloT ramdenime magaliTi.

6 leqcia_6.nb

ListPlot@881, 2<, 82, 3<, 83, 4<, 84, 5<<, PlotStyle ® PointSize@0.02DD

1.5 2.0 2.5 3.0 3.5 4.0

2.53.03.54.04.55.0

ListPlot@881, 2<, 82, 3<, 83, 4<, 84, 5<<, PlotStyle ® PointSize@0.02D, Joined ® TrueD

1.5 2.0 2.5 3.0 3.5 4.0

2.53.03.54.04.55.0

8ListPlot@Table@8Sin@xD, Cos@xD<, 8x, 0, 10, 0.1<D, AspectRatio -> AutomaticD, ListPlot@Table@8Sin@xD, Cos@xD<, 8x, 0, 10, 0.1<D, AspectRatio -> Automatic, AxesOrigin ® 80, 2<D<

:-1.0 -0.5 0.5 1.0

-1.0

-0.5

0.5

1.0

,

-1.0 -0.5 0.5 1.0

-1.0

-0.5

0.0

0.5

1.0

1.5

>

ListPlot@Table@8Sin@nD, Sin@2 nD<, 8n, 50<DD

-1.0 -0.5 0.5 1.0

-1.0

-0.5

0.5

1.0

a = Table@8x Sin@xD, x Cos@xD<, 8x, 0, 4.5 Pi, 0.05 Pi<D;ListPlot@a, AspectRatio -> Automatic, Joined ® True, PlotStyle -> RedD

-10 -5 5 10

-5

5

10

ListPlot funqciis argumenti SeiZleba iyos Cveulebrivi sia {y1,y2,...},

sadac yi warmoadgens funqciis mniSvnelobas Sesabamis i wertilSi

(i=1,2,3,...). am SemTxvevaSi Cven vRebulobT wertilebi

{{1,y1},{2,y2},{3,y3},...}.

leqcia_6.nb 7

ListPlot@Table@Sin@iD, 8i, 1, 9, 0.3<D, Filling ® AxisD

5 10 15 20 25

-1.0

-0.5

0.5

1.0

s1 = Table@Mod@i � 2, 10D � 10, 8i, 100<D;ListPlot@s1, Filling ® TopD

20 40 60 80 100

0.2

0.4

0.6

0.8

ListPlot@RandomInteger@5, 810<D, PlotStyle ® 8Red, PointSize@0.05D<D

2 4 6 8 10

1

2

3

4

5

ganixileT PistPlot funqciis opciebi: Options[ListPlot].

ParametricPlot, ParametricPlot3D funqciebi

funqcia ParametricPlot

arsebobs kidev erTi mniSvnelovani xerxi grafikuli obieqtebis age-

bisaTvis. amisaTvis gamoiyeneba funqcia ParametricPlot[{f[t],g[t-

]},{t,a,b}] romelic qmnis wirs aRwerili wertiliT {f[t],g[t]}, roca

tÎ[a,b].

ParametricPlot@8Cos@uD, Sin@uD<, 8u, 0, 2 Pi<D

-1.0-0.5 0.5 1.0

-1.0

-0.5

0.5

1.0

ParametricPlot@8Sin@uD u , Cos@uD u<, 8u, 0, 100<,Axes ® False, PlotStyle -> Directive@Red, ThickDD

8 leqcia_6.nb

ParametricPlot@8 Sin@uD + 7 u , Cos@uD u<, 8u, 0, 100<,Axes ® False, PlotStyle -> Directive@Blue, Thick, DashedDD

ParametricPlot@882 Cos@tD, 2 Sin@tD<,

82 Cos@tD, Sin@tD<, 8Cos@tD, 2 Sin@tD<, 8Cos@tD, Sin@tD<<, 8t, 0, 2 Pi<D

-2 -1 1 2

-2

-1

1

2

bolo magaliTSi moyvanilia oTxi parametriulad mocemuli funqciis

grafiki erT naxazze. Semdeg magaliTSi Cven vRebulobT elipss.

ParametricPlot@82 Cos@uD, Sin@uD<, 8u, 0, 2 Pi<D

-2 -1 1 2-1.0-0.5

0.51.0

ganvixiloT Semdegi ori magaliTi.

Show@8Plot@x, 8x, -1, 1<D, ParametricPlot@8Cos@uD, Sin@uD<,8u, Pi � 4, 5 Pi � 4<, PlotStyle ® RedD<, AspectRatio ® AutomaticD

-1.0 -0.5 0.5 1.0

-1.0

-0.5

0.5

1.0

Show@8Plot@x � 2, 8x, -2, 2<D, ParametricPlot@82 Cos@uD, Sin@uD<,8u, Pi � 4, 5 Pi � 4<, PlotStyle ® RedD<, AspectRatio ® AutomaticD

-2 -1 1 2

-1.0-0.5

0.51.0

funqcia ParametricPlot3D

ParametricPlot3D[{f[u],g[u],h[u]},{u,umin,umax}] funqciis meSveobiT

vRebulobT grafikul obieqts sivrceSi. ganixileT ParametricPlot, Para-

metricPlot3D funqciebis opciebi: Options[ParametricPlot3D], Options[-

ParametricPlot].

leqcia_6.nb 9

ParametricPlot3D@8Sin@uD, Cos@uD, u � 10<, 8u, 0, 20<, PlotStyle -> Directive@Green, ThickDD

-1.0-0.5

0.00.5

1.0

-1.0-0.5

0.00.5

1.0

0.00.51.0

1.5

2.0

am magaliTSi Cven miviReT mwvane wiri sivrceSi. ganvixiloT Semdegi magal-

iTi.

ParametricPlot3D@8Cos@tD H3 + r Cos@t � 2DL, Sin@tD H3 + r Cos@t � 2DL, r Sin@t � 2D<,8r, -1, 1<, 8t, 0, 2 Pi<, Mesh ® NoneD

-20

24

-2

0

2-1.0-0.50.00.51.0

am magaliTSi aris ori parametri: r da t.

ParametricPlot3D@884 + H3 + Cos@vDL Sin@uD, 4 + H3 + Cos@vDL Cos@uD, 4 + Sin@vD<,

88 + H3 + Cos@vDL Cos@uD, 3 + Sin@vD, 4 + H3 + Cos@vDL Sin@uD<<,8u, 0, 2 Pi<, 8v, 0, 2 Pi<, PlotStyle ® 8Red, Green<D

0

5

10

02

46

8

0

2

4

6

8

grafikebis animacia. Animate da Manipulate funqciebi

SevqmnaT Sin[x] funqciis animacia. jer ganvixiloT am funqciis grafiki,

roca icvleba x argumenti.

Plot@Sin@xD, 8x, -10, 10<D

-10 -5 5 10

-1.0

-0.5

0.5

1.0

10 leqcia_6.nb

Plot@Sin@x + 1D, 8x, -10, 10<D

-10 -5 5 10

-1.0

-0.5

0.5

1.0

Plot@Sin@x + 2D, 8x, -10, 10<D

-10 -5 5 10

-1.0

-0.5

0.5

1.0

Animate funqciis meSveobiT SevqmnaT animacia:

Animate@Plot@Sin@x + aD, 8x, -10, 10<D, 8a, 0, 5<D

a

-10 -5 5 10

-1.0

-0.5

0.5

1.0

aq a icvleba 0-dan 5-mde bijiT 1. ganvixiloT animaciis Seqmnis meore

xerxi.

ManipulateBPlot@Sin@x + aD, 8x, -10, 10<D, 8a, 0, 5<,

BaseStyle ® Red, FrameLabel ® "sinx funqciis animacia"F

a

-10 -5 5 10

-1.0

-0.5

0.5

1.0

sinx funqciis animacia

aqac a icvleba 0-dan 5-mde bijiT 1.

leqcia_6.nb 11

AnimateAPlotAt Ix2 - 1M, 8x, -2, 2<,Axes ® 8True, False<, PlotRange ® 88-1, 1<, 8-4, 2<<E, 8t, 0, 4<E

t

-1.0 -0.5 0.0 0.5 1.0

aRvniSnoT, rom Manipulate funqciia gamoiyeneba ara mxolod grafikis

animaciisaTvis, aramed sxva saxis amocanebSi. ganvixiloT magaliTebi.

Manipulate@N@Pi, nD, 8n, 1, 20<D

n 3.1415926535898

a =.; Manipulate@Expand@Ha + bL^nD, 8n, 1, 10, 2<D

na3 + 3 a2 b + 3 a b2 + b3

bolo magaliTSi n icvleba 1-dan 10-mde bijiT 2.

ganvixiloT da SevadaroT Semdegi ori magaliTi.

Manipulate@Plot@Sin@a xD + Sin@b xD, 8x, 0, 10<D, 8a, 1, 5<, 8b, 1, 5<D

a

b

2 4 6 8 10

-2

-1

1

2

12 leqcia_6.nb

Animate@Plot@Sin@a xD + Sin@b xD, 8x, 0, 10<D, 8a, 1, 5<, 8b, 1, 5<D

a

b

2 4 6 8 10

-2

-1

1

2

aq a da b cvladebi icvlebian erTdroulad 1-dan 5-mde bijiT 1.

Manipulate@ParametricPlot@8Sin@uD u , Cos@uD u<, 8u, 0, k<,

Axes ® False, PlotStyle -> Directive@Red, ThickDD, 8k, 1, 100<D

k

SevqmnaT Semdegi obieqti.

opTable@o_, n_D :=

TableForm@Table@o@n1, n2D, 8n1, 1, n<, 8n2, 1, n<D, TableHeadings ® 8Range@nD, Range@nD<DManipulate@opTable@o, nD, 8n, 1, 10<, 8o, 8Plus, Times, Subtract, Divide<<D

n

o Plus Times Subtract Divide

1 2 3

1 2 3 4

2 3 4 5

3 4 5 6

ganvixiloT Tu rogor muSaobs funqcia opTable:

opTable@o_, n_D :=

TableForm@Table@o@n1, n2D, 8n1, 1, n<, 8n2, 1, n<D, TableHeadings ® 8Range@nD, Range@nD<D

Table@Plus@n1, n2D, 8n1, 1, 3<, 8n2, 1, 3<D �� TableForm

2 3 4

3 4 5

4 5 6

leqcia_6.nb 13

8opTable@Plus, 3D, opTable@Times, 3D, opTable@Times, 4D, opTable@Divide, 3D<

:1 2 3

1 2 3 4

2 3 4 5

3 4 5 6

,

1 2 3

1 1 2 3

2 2 4 6

3 3 6 9

,

1 2 3 4

1 1 2 3 4

2 2 4 6 8

3 3 6 9 12

4 4 8 12 16

,

1 2 3

1 11

2

1

3

2 2 12

3

3 33

21

>

Manipulate@opTable@o, nD, 8n, 1, 10<, 8o, 8Plus, Times, Subtract, Divide<<D

n

o Plus Times Subtract Divide

1 2

1 11

2

2 2 1

damatebiTi funqciebi

ganvixiloT MenuView, ActionMenu, Tooltip, PopupView funqciebis

sintaqsi da SevadaroT gamoTvlis Sedegi:

MenuView@8"I" ® 1, "II" ® 2, "III" ® 3, "IV" ® 4, "V" ® 5<, 4DMenuView@Table@Plot@Sin@n xD, 8x, 0, 10<D, 8n, 5<DD

ActionMenu@"Print Factorials", 8"4!" ¦ Print@4!D, "7!" ¦ Print@7!D, "10!" ¦ Print@10!D<D

Tooltip@x + y, "label"DPlot@Tooltip@8Sin@xD, Cos@xD<D, 8x, 0, 10<DPlot@Tooltip@Sin@xD, "sine"D, 8x, 0, 10<D

PopupView@8a, b, x + y, z<DPopupView@Table@Plot@Sin@n xD, 8x, 0, 10<D, 8n, 3<DD

ganvixiloT Rilakis Seqmnis ori martivi magaliTi:

a = Grid@88PasteButton@ΑD, PasteButton@ΒD<, 8PasteButton@ΓD, PasteButton@∆D<<,Frame ® True, Spacings ® 81, 1<, Background ® GreenD

ButtonA"faqtoriali", Print@10!DE

arsebobs ferebis ori standartuli sistema da Mathematica-Si

Sesabamisad aris ori funqcia: CMYKColor da RGBColor. ganvixiloT

Semdegi ori magaliTi:

Plot@x^2, 8x, -1, 1<,PlotStyle ® 8RGBColor@0.4, 0.1, 0.3D,

Thickness@0.02D<D

Plot@x^2, 8x, -1, 1<,PlotStyle ® 8CMYKColor@0.4, 0.1, 0.3D,

Thickness@0.02D<D

-1.0 -0.5 0.5 1.0

0.20.40.60.81.0

-1.0 -0.5 0.5 1.0

0.20.40.60.81.0

14 leqcia_6.nb

Û davaleba

1. aageT F(x)= x^2+Sin[53x] funqciis grafiki {-2,2} Sualedze.

2. ggamoTvaleT Semdegi gamosaxuleba:

Plot@Evaluate@S = Input@"Please input a function of x to plot on the unit interval"DD,8x, -4, 4<, PlotLabel ® Style@Framed@SD, Background ® Lighter@GreenDD,LabelStyle ® Directive@Bold, RedDD

3. ganixileT Semdegi sami obieqti:

Manipulate@Plot@x^2, 8x, -1, 1<,PlotStyle ® 8RGBColor@0.4, 0.1, 0.3, kD, Thickness@0.02D<D, 8k, 0.1, 1, 0.01<D

Manipulate@Plot@x^2, 8x, -1, 1<,PlotStyle -> 8RGBColor@red, green, blueD, Thickness@0.02D<D,

8red , 0.01, 1, 0.01<, 8green, 0.01, 1, 0.01<, 8blue, 0.01, 1, 0.01<DManipulate@Plot@Sin@xD, 8x, 0, 10<,

PlotLabel ® Style@"sinHxL", LargeD, LabelStyle ® 8c, s<D,88c, Red, "color"<, Red<, 88s, Plain, "style"<, 8Plain, Italic, Bold<<D

4. aageT fAx_, y_E := ã-100 HHx-.5L^2 + y^2L funqciis grafiki. ganixileT am amocanis

moyvanili ori amoxsna da Sesabamisi funqciebi (opciebi): Plot3D, Parametric-Plot3D.

f@x_, y_D := ã-100 HHx-.5L^2 + y^2L H* I amoxsna *LPlot3D@f@x, yD, 8x, -1, 1<, 8y, -1, 1<, PlotPoints ® 850, 50<,PlotRange ® 8-1, 1<, Boxed ® False, Axes ® FalseD

h@x_, y_D := Exp@-100 HHx - .5L^2 + y^2LD H* II amoxsna *LParametricPlot3D@8r Cos@ΘD, r Sin@ΘD, h@r Cos@ΘD, r Sin@ΘDD<, 8r, 0, 1<, 8Θ, -Π, Π<,Boxed ® False, Axes ® False, PlotPoints ® 850, 50<, PlotRange ® 8-1, 1<D

5. gamoTvaleT da gamoiyeneT sxvadasxva opcia:

ParametricPlot@88Sin@5 tD Cos@tD, Sin@5 tD Sin@tD<, 8Cos@tD, Sin@tD<<,8t, 0, 2 Pi<, AspectRatio ® 1D

ParametricPlot3D@8Cos@ΦD Sin@ΘD, Sin@ΦD Sin@ΘD, Cos@ΘD<,8Φ, 0, 2 Pi<, 8Θ, 0, Pi<, Boxed ® False, Axes ® FalseD

ParametricPlot3D@8Cos@uD, Sin@uD, 2 v<, 8u, 0, 2 Pi<, 8v, 0, 1<DParametricPlot3D@8v Cos@uD, v Sin@uD, 2 v<, 8u, 0, 2 Pi<, 8v, 0, 1<DParametricPlot3D@

8H2 + Cos@vDL Cos@uD, H2 + Cos@vDL Sin@uD, Sin@vD<, 8u, 0, 2 Pi<, 8v, 0, 2 Pi<DParametricPlot3D@8Cos@uD, Sin@uD + Cos@vD, Sin@vD<, 8u, 0, 2 Π<, 8v, -Π, Π<DParametricPlot3D@8u Sin@tD, u Cos@tD, t<,

8t, 0, 8<, 8u, -1, 1<, Mesh ® None, Axes ® False, Boxed ® TrueDParametricPlot3D@8Sin@uD, Cos@vD, Sin@uD Sin@vD<, 8u, 0, 2 Pi<, 8v, 0, 2 Pi<, Axes ® FalseD

6. gamoTvaleT Semdegi ori gamosaxuleba:

ListLinePlot@Table@8Cos@k 2 Pi � 7D, Sin@k 2 Pi � 7D<, 8k, 0, 21, 3<D,Frame ® False, Axes ® False, Filling ® AxisD

ListPlot@Table@8Cos@k 2 Pi � 5D, Sin@k 2 Pi � 5D<, 8k, 0, 21, 3<D,Joined ® True, Axes ® False, Filling ® AxisD

7. ras dabeWdavs Semdegi programa?

Manipulate@Style@RotateLeft@Range�9, iD �� TableForm, Red, 14D,8i, 0, Length�Range�9 - 1, 1<D

leqcia_6.nb 15